H2 Physics 2012 - PBworks

H2 Physics 2012

Year 1 Revision (Part 2)

Source:

2010 Prelim Structured Questions &

JJC Promotional Exams (with solutions)

Please visit http://jjphysics.pbworks.com for

more questions or detailed solutions.

1. Measurement

2. Kinematics

3. Dynamics

4. Forces

5. Work, Energy and Power

6. Thermal Physics

http://jjphysics.pbworks.com/

H2 Physics/ 2012/ Year 1/ Revision/ Measurement Source: 2010 Prelim Questions

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2010 RI H2 P2 Q1

1 A cylindrical thermos flask is used to store hot water. The internal diameter and depth of the

thermos flask are measured to be (8.50 ± 0.01) cm and (17.0 ± 0.1) cm respectively.

(a) State the instrument used to measure its diameter and a systematic error that can occur with

the use of this instrument.

[2]

(b) Calculate the capacity of the thermos flask and its associated uncertainty.

Volume = cm3

[3]

2010 VJC H2 P3 Q1

2 (a) Distinguish between a random error and a systematic error in the measurement of

a physical quantity.

[2]

(b) A student set up the apparatus shown in Fig 1 in order to determine the spring

constant k of a spring by finding the extension of the spring when additional mass

is loaded.

metre rule

scale reading

mass

Fig 1


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The following readings with their errors were recorded in a particular experiment:

mass added initial scale reading final scale reading

(20 1) g (32.00 0.05) cm (36.30 0.05) cm

Using the readings above, calculate the spring constant k with its associated

uncertainty and present your answer in SI units of N m-1

.

[4]

(c) A second student repeated the experiment in (b) with the same spring. In this new

experiment, the additional masses were loaded and the corresponding extension

readings were tabulated. A graph showing the variation of the extension and

loaded masses was then plotted. Discuss three advantages of this procedure for

the determination of the spring constant as compared to that used in (b).

[3]

2010 ACJC H2 P2 Q1

3 (a) Give reasonable estimates of the following quantities. In each case, give your answer in an SI unit.

(i) The volume of the 2010 official World Cup soccer ball.

volume = m3 [1]

(ii) The kinetic energy of an olympic sprinter near the ending point of a 100-metre dash.

Kinetic energy = J [1]

(iii) The density of the head of a human being.

density = kg m-3

[1]


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(b) An experiment is conducted to determine the density of cooking oil, which floats on water. Three sets

of results are obtained from the experiment. The unit for density is kg m .

A B C

810 1500 740

800 1490 870

805 1495 790

(i) Which set of results is precise but inaccurate? Explain your reasoning.

[2]

(ii) Assuming the measurement of volume has been done correctly, suggest one possible source of

experimental error that causes the aforementioned set of results inaccurate.

[1]

2010 H2 P2 Q1

4 (a) Complete Fig. 1.1 to show each quantity and its base units. [2]

quantity base units

speed

density

……………………

electric field strength

m s-1

kg m-3

kg m s-1

……………………

Fig. 1.1

(b) In the classroom, a student wishes to determine the mass of a plastic semi-circular protractor.

Fig. 1.2

x


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(i) Give a reasoned estimate of the mass of the semi-circular protractor and express your answer in an

SI unit.

mass = ………………………… unit ……………. [2]

(ii) State an instrument which is most appropriate for the measurement of the thickness of the protractor x,

as indicated in Fig. 1.2.

……………………………………………………………………………..…..…….….. [1]

(iii) For the measurement of x, suggest a way to reduce random errors.

…..…………………………………………………………………………..……………….

……………………………………………………………………………..…..…….….. [1]

2010 MI H2 P2 Q1

5. (a) Distinguish between a scalar quantity and a vector quantity, providing an example for each.

…………………………………………………………………………………………………

…………………………………………………………………………………………………

……………………………………………………………………………………………....[2]


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(b) A ship is initially cruising in the direction bearing of 045 at a speed of 10 m s-1

changes

direction to head in a new direction bearing of 145 at a speed of 5 m s-1

, as seen in Fig. 1.1.

The manoeuvre was completed in 30 s.

Fig. 1.1

Using a vector diagram or otherwise, calculate the acceleration of the ship during the change

in direction.

acceleration of the ship =…………………..m s-2

at bearing of ………… [3]

2010 NJC H2 P2 Q1

6 (a) Distinguish between systematic and random errors.

[2]

(b) There are two possible methods of measuring the volume of a cylindrical container. The

first method is by measuring the inner diameter and the height of the container and calculating

the volume. The readings are as follows:

Inner diameter = 2.57 0.01 cm

Height = 7.8 cm 0.1 cm


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The second method is by filling the container with water, and then pouring the water out into a

measuring cylinder. The measuring cylinder can read to the nearest cm3. With the aid of

suitable calculations, explain which method would give more precise value of the volume.

[3]

2010 CJC H2 P2 Q1

7 When a solid is heated, the thermal energy required is given by the expression

gain in thermal energy = mass X c X temperature rise, where c is a constant.

(a) Name the quantities in the expression that are SI base quantities.

……………………………………………………..........................................................................

[1]

(b) Express, in terms of SI base units, the units of

(i) thermal energy,

unit of thermal energy = …………………………

[2]

(ii) the constant c.

unit of c = …………………………

[2]


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2010 MJC H2 P2 Q6

8 Most Singapore buildings are built using a framework of concrete beams, slabs and columns. The

concrete columns need to carry both the ultimate vertical load, N and the ultimate bending moment, M

induced from the attached beam/s as shown in the 3-D pictorial diagram of Fig. 6.1. In practice, the

concrete columns are reinforced with steel bars.

To design for the steel bars in such columns, design charts are available from the British Standard

Structural Use of Concrete, BS8110.

Fig. 6.1

Beam

M

Column

N


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In order to choose the correct design chart, the values of the following must match the design details:

fcu = Ultimate crushing pressure limit of concrete

fy = Ultimate characteristic strength of steel bar

d

h where d is the distance from the edge of the column to the centre of the steel bar that is furthest from

that edge and h is the larger dimension of the column

The cross section of a column is shown in Fig. 6.2:

Dimensions of the column are:

h = 450 mm (larger dimension of the column)

b = 200 mm

d = distance from the edge of the column to the centre of the steel bar that is furthest from that

edge.

(a) The chosen design details for the column above are:

fcu = 50 N mm-2

fy = 460 N mm-2

cover = 40 mm (from edge of column to edge of steel bar)

Assuming that 4 numbers of 32 mm diameter steel bars are to be used. Determine the value of d

h

and hence explain why Chart No. 49 is appropriate to be used.

d

h………………

[1]

Explanation:

..............................................................................................................................................

.....................................................................................................................................

[1]

Fig. 6.2

32 mm diameter steel bar

cover= 40 mm

b = 200 mm

d h = 450 mm

Fig. 6.3

h = 450 mm

b = 200mm

Height of column


9 | P a g e

(b) The coordinates of the chart derived from the values of N

bh and

2

M

bh can be used to establish the

corresponding value of SC100A

bh such that ASC (the total required cross-sectional area of

steel bars) can be calculated. It is necessary to provide enough steel bars, with a total area more

than ASC.

An example of reading off the SC100A

bh value is:

Value of N

bh = 32.5 N mm

-2

Value of 2

M

bh = 3.20 N mm

-2

From Chart No. 49, the corresponding coordinate is marked with a cross and labelled ‘A’. This

coordinate corresponds to a value of SC1004 5

A

bh . More specifically, the value of SC100A

bh is

4.5. Using this value, ASC can then be calculated.

Based on the same design details in (a), the loads carried by the column in Fig 6.2 are:

M = Ultimate bending moment = 91.2 kN m

N = Ultimate vertical load = 2460 kN

(i) Determine the values of N

bh and

2

M

bh for the column in Fig 6.2.

N

bh ……………… N mm

-2

2

M

bh……………… N mm

-2

[2]


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(ii) Using Chart No. 49, determine whether 4 steel bars of diameter 32 mm with a total area of

3220 mm2 is sufficient. [4]

(c) A young engineer designed the same column except that he used a different concrete with an

ultimate crushing pressure limit, fcu of 25 N mm-2

. Compare your calculated value of N

bh in (b)(i)

with this value of fcu = 25 N mm-2

. Comment what would happen to the concrete.

.............................................................................................................................................

.............................................................................................................................................

....................................................................................................................................

[2]

(d) The height of the column designed is 3.8 m. Suggest one possible problem with another 12.0 m

height column of similar size subjected to a similar vertical load and bending moments.

.............................................................................................................................................

....................................................................................................................................

[1]

(e) The design of another column has the values of SC1002.0

A

bh and

22.0

M

bh .

Using Charts No. 39 and 49, determine the percentage decrease in ultimate vertical load, N if fcu

= 50 N mm-2

changes to fcu = 40 N mm-2

.

Percentage decrease of N = .....................................%

[4]


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2010 SRJC H2 P2 Q1

9) (a) In a certain equation,

where C has unit Newtons, D has the unit metres, E has the unit Pascal, B1 and B2 have the unit metres, F has the

unit metres, and H has the unit Joules.

(i) Determine the unit of A.

(ii) The value of C -9 m, what percentage uncertainty does this introduce into the value of A?

(b) Peter decides to go skydiving. From an altitude of 3500 m, he jumps off the aircraft. He delays opening his

parachute until he reaches 800 m. He attains terminal velocity before he reaches 800 m. Assume that he falls

vertically.

(i) Describe qualitatively, and with an explanation, Peter’s motion after he jumped off till he reaches terminal

velocity.

………………………………………………………………………………….…………

……………………………………………………………………………...…………..…

..................................................………………………………………..………….. [1]

(ii) When Peter opens his parachute, his velocity is 55 m s-1 downwards. His landing speed is 4 m s-1

.

Sketch a velocity- time graph from the time Peter has just started falling at t = 0 s until he is about to land.

The time till which Peter lands is not needed.

Note that when the parachute is first opened, the force by the parachute on Peter is larger than his weight. [2]

(iii) Explain the shape of the graph from the time the parachute opens till the landing.

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

…………………………………………………………………………………………[2]

END

H2 Physics/ 2012/ Year 1/ Revision/ Kinematics Sources: 2010 Prelim Questions

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2010 NYJC H2 P3 Q1

1 (a) Define acceleration.

[1]

(b) A boy throws his slipper from a height of 1.0 m at 75o above the horizontal in an attempt to hit a durian

hanging on a tree which is 4.75 m above the ground. The slipper reached its maximum height of 0.25 m

directly below the durian. Neglect air resistance.

(i) Calculate the velocity of the slipper when the slipper leaves the boy’s hand.

velocity = m s-1

[2]

(ii) Calculate the horizontal distance travelled when his slipper hits the ground.

distance = m [2]

(iii) Sketch a labelled velocity - time graph for the vertical component of the slipper from the time it

leaves the boy to the time when it hits the floor.

[2]

(iv) If the velocity calculated in part (b)(i) is the maximum velocity he can provide when throwing his

slipper, suggest with a reason what he should do in order to ensure his slipper hits the durian.

[1]

2010 PJC H2 P2 Q1

2 (a) Define velocity and acceleration.

.......................................................................................................................................

.......................................................................................................................................

................................................................................................................................. [2]


2 | P a g e

(b) Fig. 1.1 shows the variation with time t of the velocity v for an object.

Fig. 1.1

(i) State the time at which the object is at maximum displacement from the starting point.

time = ........................................ s [1]

(ii) Calculate the displacement of the object at t = 12.0 s.

displacement = ........................................ m [1]

(iii) On Fig. 1.2, sketch a graph to show the variation with time t of the displacement s for the object.

(You are not expected to label values of the displacement.) [2]

Fig. 1.2

t / s

v / ms–1

20

2.0 4.0 6.0 8.0 10.0 12.0

−20

−10

10

0

t / s

s / m

2.0 4.0 6.0 8.0 10.0 12.0 0


3 | P a g e

2010 RVHS H2 P2 Q1

3 (a) A lecturer holds a flat S$2 note just above a student’s open fingers as shown in Fig. 1.1.

Fig. 1 1

He challenges the students that whoever can catch the S$2 note when he releases it can keep it.

Explain quantitatively whether any student would be able to catch the note when the lecturer

releases it.

[3]

(b) A lecturer sees a student who owes him homework a distance d away. The lecturer

immediately moves towards the student with a constant velocity vL. The student sees the

lecturer moving towards him to seconds later and starts moving away in the same direction at a

constant velocity vS.

Write down an expression for the time taken t for the lecturer to catch up with the student

from the instant he sees the student. Show your derivation clearly.

[4]

sp

ec

ime

n


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2010 TJC H2 P2 Q1

4 The velocity-time graph in Fig. 1.1 shows the first 1.6 s of the motion of a ball which is thrown vertically

downward at an initial speed of 6.0 m s1

.

(a) How far does the ball travel before hitting the ground?

distance travelled = m [2]

(b) What is the maximum height attained by the ball after it hits the ground?

maximum height = m [1]

(c) Calculate the magnitude of the acceleration of the ball when it is in the air.

acceleration = m s

2 [1]

(d) At what time does the ball next reach the ground?

time = s [1]

6

12

10

0.8 1.6 t / s

Fig. 1.1

0

v / m s1


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(e) Taking upward direction to be positive, sketch on Fig. 1.2, a clearly labelled displacement-time graph

for the motion of the ball from time t = 0 up to the second time it hits the ground.

[2]

2010 HCI H2 P2 Q1

5. The figure below shows a juggler performing a trick called “the shower” in which three balls are kept

moving around between the two hands and through the air in the trajectory shown in Figure 1.

Figure 1

t / s

s / m

Fig. 1.2

Right (Throw)

Left (Catch)

Trajectory of balls.

Ball 1

Ball 2

Ball 3

1.75 m


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(a) Ball 1 leaves the right hand at an angle of 80.0o to the horizontal and reaches a maximum height of

1.75 m above the level of the juggler’s hands. Show that ball 1’s initial speed of projection must be

5.95 m s-1

.

[2]

(b) Calculate how far the juggler must position his hands apart so that the ball lands on his left hand.

distance =_______________ m [2]

(c)

For a fixed speed of projection, suggest two advantages for the juggler to throw the balls at such a

large angle to the horizontal

Advantage 1:

_______________________________________________________________________

_______________________________________________________________________

_____________________________________________________________________[1]

Advantage 2:

_______________________________________________________________________

_______________________________________________________________________

_____________________________________________________________________[1]


7 | P a g e

(d) When Ball 1 is just at its maximum height, the juggler throws Ball 2 up with the same speed and in

the same direction as he did Ball 1. How much time does the juggler have to transfer Ball 3 from

his left to right hand so that his left hand is available to catch Ball 1?

time = ______________ s [1]

(e) Suggest a minimum value for the horizontal distance between the two hands and explain your

answer clearly.

________________________________________________________________________

________________________________________________________________________

______________________________________________________________________[2]

2010 IJC H2 P2 Q2

6 ‘Clay pigeon shooting’ is a sport whereby the shooter aims and hits the clay disc projected by a launcher. A

certain clay disc is launched from the horizontal ground with a velocity of 20 m s-1

at an angle of 30o to the

horizontal.

(a) Assuming that air resistance can be neglected, calculate

(i) the maximum height of the disc,

maximum height = ………………………… m [2]

(ii) the horizontal distance between the point from which the disc is launched and where it lands on the

ground.

horizontal distance = ………………………… m [2]


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(b) The path N for the above disc is as given in Fig. 2.1 where air resistance is neglected.

Fig. 2.1

(i) Draw the path of the clay disc on Fig. 2.1, assuming that air resistance cannot be neglected. Label this

path A. [1]

(ii) Suggest an explanation for any differences between the two paths N and A.

.………………………………………………………………………………………………

.………………………………………………………………………………………………

.………………………………………………………………………………………………

.…………………………………..……………………………………………………… [2]

2010 JJC H2 P2 Q1

7 The speed limit of one segment of the Pan Island Expressway is 90 km h-1

. A police

radar speed detector detects a motorcycle moving at a constant speed of 35 m s-1

. 20 seconds

later, a police car, hiding at a distance 100 m after the speed detector, accelerates from rest at 4.0

m s-2

for 13.0 s to reach its top speed.

(a) Show that the motorcycle has exceeded the speed limit stated. [1]

(b) Calculate the top speed of the police car. [1]

(c) When the police car just reached its top speed, calculate the distance between the

motorcycle and the police car. Show your working clearly. [4]

30o

20 m s-1

N


9 | P a g e

(d) How long does the police car take to catch up with the motorcycle, after reaching its top

speed? [2]

2010 MI H2 P2 Q2

8. (a) A body accelerates at 10 m s-2

over a period of time.

Explain what is meant by the phrase in italics.

…………………………………………………………………………………………………

……………………………………………………………………………………………....[1]

(b) A Singapore Army soldier is undergoing marksmanship training by firing at the target, as

seen in Fig. 2.1 below. He uses the SAR 21 Rifle, which has a muzzle velocity (velocity at

which the bullet exits the rifle) of 900 m s-1

.

Fig. 2.1

He ensures his rifle is perfectly horizontal while aiming for the head of the target. He then

fires a bullet at the target, which is 300 m away from his current position.

(i) Calculate the time taken for the bullet to reach the target after it is fired.

time taken =……….…..s [1]


10 | P a g e

(ii) What is the assumption made in this calculation?

…………………………………………………………………………………………

………………………………………………………………………………………[1]

(iii) Assuming that it is a perfect shot (i.e. the rifle was perfectly horizontal and was aimed

properly at the head of the target), calculate the vertical distance between his aiming

point and where the bullet actually hits the target.

vertical distance =………………m [2]

(iv) After passing through the target, the bullet is entrenched 4.0 m deep into a sandbag

that is directly behind the target board.

Calculate the average deceleration of the bullet as it moves within the sandbag

average deceleration =…………….m s-2

[2]

(v) If the assumption was not made in (b) (ii), state whether the bullet would hit the target

at a lower or higher point than what was calculated in (b) (iii).

…………………………………………………………………………………………

………………………………………………………………………………………[1]

2010 CJC H2 P2 Q2

9 An aeroplane is flying horizontally at a steady speed of 67 m s-1

and an object is dropped off from the aeroplane.

(a) Assume that the air resistance is negligible.

(i) Show that the vertical component of the velocity of the object is approximately 40 m s-1

when it has

fallen 80 m. [2]


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(ii) Determine the magnitude and direction of the resultant velocity of the object at this point.

Magnitude of velocity =........................................................ m s-1

Direction of velocity =.................................................................

[3]

(b) In practice, air resistance acts on the object during the fall. The air resistance may be assumed to be

proportional to the square of the speed.

State and explain how the magnitude of the horizontal and vertical components of the velocity of the

object vary with time.

Horizontal component of velocity:

............……………………………………………………………………………………………...

............……………………………………………………………………………………………...

............……………………………………………………………………………………………...

[1]

Vertical component of velocity:

...........……………………………………………………………………………………………....

...........……………………………………………………………………………………………....

............……………………………………………………………………………………………...

............……………………………………………………………………………………………...

[2]


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(c) Sketch and label the path of the object in Fig. 2

(i) without air resistance,

(ii) with air resistance.

Fig. 2

[2]

2010 MJC H2 P3 Q1

10 (a) A charged body falls vertically in a vacuum near the Earth’s surface. The variation with

time t of its vertical speed v is shown in Fig. 1.1 below.

Fig. 1.1

An electric field induces a horizontal force on the body that causes the body to accelerate

horizontally at 2.25 m s-2

. Calculate the displacement of this body after 0.50 s falling from

rest.

v/ m s-

1

t/ s 0

Start of fall

Horizontal distance from the point of drop off

vertical distance

from the point of

drop off


13 | P a g e

displacement = ........................m

angle = ........................... [4]

(b) Another object moving in a straight line has a graph of the variation with time of its

velocity shown in Fig. 1.2.

Fig. 1.2

(i) Sketch on Fig. 1.2, a graph of the variation of the acceleration with time for

the same object within the same time frame.

[2]

(ii) Explain your sketch in (i) between time t1 and t2.

…………………………………………………………………………………………........

………………………………………………………………………………………….......

…………………………………………………………………………………….....

[2]

END

0 t2 t1

v/ ms-1

t/ s

H2 Physics/ Year 1/ Revision 2012/ Dynamics Source: 2010 Prelim Questions

1 | P a g e

2010 NYJC H2 P3 Q6

1 (a) Define linear momentum.

[1]

Fig. 1.1 shows an airboat of mass 420 kg which is propelled forward by a propeller generating a

column of air backward.

(b) (i) By using Newton’s laws, show that the forward thrust acting on the airboat is given by F =

r2v

2 where is the density of air, r is the effective radius of propeller and v is the speed

of the air moving backward.

[3]

(ii) Calculate the initial acceleration of the airboat when r = 0.70 m, v = 20 m s-1

and = 1.2

kg m-3

.

acceleration = m s-2

[2]

airboat

propeller

Fig. 1.1


2 | P a g e

(c) (i) Calculate the rate of transfer of kinetic energy to the air by the propeller.

Rate of transfer = W [2]

(ii) Given that the propeller is powered by a motor with a useful power 16 kW and moving

along a river with a constant speed of u. Use the answer for (c)(i) to determine u.

u = m s-1

[3]

(d) (i) Fig. 6.2 show a side view of the boat partially submerged in water. Draw the other forces

acting on the airboat paying particular attention to the point of application of these forces.

[2]

water level

Total weight of

airboat

Drag force

Fig. 1.2


3 | P a g e

(ii) Fig. 1.3 shows the outline of an airboat and a speed boat. Based on the diagram below, the

front part of the airboat is wider or less streamline than a speedboat. By considering the

stability of the airboat, explain why this is so.

[2]

(iii) By considering the airboat and the air generated as a system, explain why the total

momentum of this system is not conserved when the airboat is moving at a constant speed.

[2]

(e) (i) Suggest why airboats are more suitable for use in shallow rivers compared to other types

of boats.

[1]

(ii) Discuss two problems caused by using a much bigger propeller in order to increase the

forward thrust.

[2]

airboat speed boat

Fig. 1.3


4 | P a g e

2010 RVHS H2 P2 Q2

2 Jane, whose mass is 50.0 kg, needs to swing across a river (having width D) filled with man-

eating crocodiles to save Tarzan from danger. She must swing on a vine into a wind exerting

a constant horizontal force F. The vine has a length L and initially makes an angle with the

vertical (Fig. 2.1). Take D = 50.0 m, F = 110 N,

L = 40.0 m, and = 50.0°.

Fig 2.1

(a) Show that the angle is 28.9.

[1]

D

F

Wind Jane

Tarzan

L


5 | P a g e

(b) Calculate the minimum speed Jane needs to begin her swing in order for her to just

reach Tarzan.

minimum speed of Jane = ………………………… m s–1

[3]

(c) Once the rescue is complete, Tarzan and Jane must swing back across the river. With

what minimum speed must they begin their swing if Tarzan has a mass of 80.0 kg?

minimum speed = ………………………… m s–1

[2]


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2010 SAJC H2 P2 Q1

3 The three sketch graphs in Fig. 3.1, plotted against time, show changes which occur in a small

fraction of a second and which result in almost vertical lines on the graphs. These three sketch

graphs are possible for ordinary objects.

Fig. 3.1

From the graphs of Fig. 3.1, choose any two graphs and describe and explain an everyday situation

which illustrates how that graph can arise.

1. Graph letter ……………….

…………………………………………………………………………………............

…………………………………………………………………………………............

…………………………………………………………………………………............

…………………………………………………………………………………............

…………………………………………………………………………………............

……..………………………………………………………………………………..[3]

time

velocity

time

acceleration

time

resultant force

B A

C


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2. Graph letter ……………….

…………………………………………………………………………………............

…………………………………………………………………………………............

…………………………………………………………………………………............

…………………………………………………………………………………............

…………………………………………………………………………………............

……..………………………………………………………………………………..[3]

2010 SAJC H2 P3 Q5

4 (a) (i) State Newton’s first law of motion and show how it leads to the

concept of force.

…………………………………………………………………………..

…………………………………………………………………………..

…………………………………………………………………………..

…………………………………………………………………………..

……………………………………………………………………….[2]

(ii) Newton’s second law states that “the rate of change of momentum of a body is

proportional to the resultant force acting on it”.

Show how this law, together with a suitable definition of the unit of force, leads to the

relationship F = ma for a body of constant mass. [3]


8 | P a g e

(b) A stone is dropped from a point a few metres above the Earth’s surface. Considering the

system of stone and Earth, discuss briefly how the principle of conservation of momentum

applies before the impact of the stone with the Earth.

…………………………………………………………………………………...

…………………………………………………………………………………..

…………………………………………………………………………………..

…………………………………………………………………………………..

………..………………………………………………………………………[3]

(c) A stationary radium nucleus ( 224

88Ra) of mass 224 u spontaneously emits an α-particle ( 4

2 He)

of mass 4 u. The α-particle is emitted with an energy of 9.2 x 10-13

J and the reaction gives

rise to a nucleus of radon (Rn).

(i) Write down a nuclear equation to represent the α-decay of a radium nucleus. [1]

(ii) Show that the speed at which the α-particle is ejected from the

radium nucleus is 1.7 x 107

m s-1

.

[2]

(iii) Calculate the speed of the radon nucleus on emission of the

α-particle. Explain how the principle of conservation of linear momentum is applied

in your calculation.


9 | P a g e

…………………………………………………………………………………

…………………………………………………………………………………

…………………………………………………………………………………

………………………………………………………………………………[3]

(d) (i) Define the centre of gravity of an object.

………………………………………………………………………………….

…………………………………………………………………………….. [1]

(ii) State the principle of moments.

………………………………………………………………………………….

…………………………………………………………………………….. [1]

(iii) Fig. 4.1 shows a massive column held stationary in position by a group of people

pulling at a rope.

Fig. 4.1

The 4.0 m high column has a mass of 180 kg and its centre of gravity X is at a

distance of 2.3 m from the base. The rope makes an angle of 350 to the column and

the column itself makes an angle of 450 to the horizontal.

1. Show that the moment exerted by the weight of the column about the base is 2.9

x 103 N m.


10 | P a g e

[2]

2. Calculate the tension T in the rope.

T = ………… N [2]

2010 TJC H2 P3 Q1

5 In a nuclear reactor, a fast moving neutron with initial speed u1 makes a head-on elastic collision with a

stationary nucleus of carbon-12. The speed of the neutron and the carbon nucleus after the collision are

v1 and v2 respectively as shown in Fig. 1.1.

(a) What is meant by head-on and elastic?

[2]

(b) In an elastic collision, the relative speed of separation is equal to the relative speed of approach.

Write an equation in terms of the velocities given to illustrate this fact.

[1]

(c) By considering your answer to (b), find the ratio of the final speed of the neutron v1 to its initial

speed u1.

u1 v1

v2 Before collision After collision

Fig 5.1

neutron carbon nucleus neutron carbon nucleus


11 | P a g e

ratio = [3]

(d) Hence determine the fraction of the kinetic energy of the neutron that is transferred to the carbon

nucleus.

fraction = [3]

(e) If the head-on elastic collision is with a stationary neutron instead of carbon-12, how would the

answers in part (c) and (d) be different? In your explanation, state the new ratio of the speeds and

the new fraction of the kinetic energy transferred.

[3]

2010 VJC H2 P3 Q3

6 (a) State the Law of Conservation of Momentum.

[1]

(b) Explain what is meant by an elastic collision.

[1]


12 | P a g e

(c) A 200g rubber ball is tied to a 1.0 m long string and released from rest at angle θ.

It swings down and at the very bottom has a elastic collision with a 1.0 kg block.

The block is resting on a frictionless surface and is connected to a 20 cm long

spring of spring constant 2.0 kN m-1

. After collision, the spring compressed a

maximum distance of 2.0 cm.

(i) Determine the strain energy stored in the spring.

[2]

(ii) Determine the speed of the block after collision with the ball.

[2]

(iii) Given that the collision is elastic, determine the speed of the ball before

collision with the block.

[2]

(iv) Hence, determine from what angle was the rubber ball released.

[2]

spring 1.0 kg

200 g

1.0 m θ

20 cm


13 | P a g e

2010 YJC H2 P3 Q1

7 A car that is moving along a horizontal road may be considered to have three forces acting on it as shown in

Fig. 1.1 below.

(a) Explain why X and Z are resultant forces. [2]

………………………………………………………………………………………………………

………………………………………………………………………………………………………

………………………………………………………………………………………………………

(b) The car and its contents have a total mass of 1200 kg. Force Y is horizontal and has magnitude 2000

N. If the car is accelerating at 8 m s2

, calculate

1. the magnitude of force Z

2. the angle that Z makes with the road

[6]

magnitude of Z = ………..…….. N

Resultant force X of Earth on car

Resultant force Y of air on car

Resultant force Z of road on car

Fig. 7.1


14 | P a g e

angle = …………..

2010 TPJC H2 P2 Q1

8 (a) Galileo’s famous demonstration at the Tower of Pisa showed that falling objects

accelerate equally, regardless of their masses. This is strictly true if air resistance is

negligible.

Using Newton’s Second Law, show that a 10 kg canon ball and a 1 kg stone, when

dropped together from the top of the tower, can strike the ground at the same time. [2]

(b) A body is released in a fluid. With the aid of a free body diagram, explain how the

body falling through a fluid can reach terminal velocity. [4]

(c) A parachutist has a mass of 80 kg. When he falls with his parachute open, the air

resistance R he encounters is given by the equation R = k v2, where v is the

parachutist’s velocity and k has the value of 35 N s2 m

-2.

Determine the magnitude and direction of the acceleration of the parachutist when

his velocity is 5.0 m s-1

. [3]


15 | P a g e

2010 TPJC H2 P2 Q2

9 Sphere P of mass 2.0 kg and sphere Q of mass 1.0 kg are moving towards each other

with speeds 2.0 m s–1

and 1.0 m s–1

respectively, as shown in Fig. 2.1.

The spheres have a head-on, inelastic collision. The force that P exerts on Q during the

collision varies with time as shown in Fig. 2.2.

(a) State the principle of conservation of momentum. [1]

(b) Determine the momentum change of mass Q after the collision. [1]


16 | P a g e

(c) Sketch, with clear labeling of values, a graph of the force that Q exerts on P using

the axes provided. [2]

(d) Calculate the velocities of P and Q after collision. [2]

(e) Calculate percentage loss in total kinetic energy of P and Q after the collision. [2]


17 | P a g e

2010 HCI H2 P3 Q1

10 Tom was driving his car on the expressway one evening when he spotted a van travelling towards

him at a high speed from a short distance away. The driver in the van was apparently drunk and

not aware that he was driving on the wrong lane. Unfortunately, Tom was unable to stop his car

on time and the two vehicles collided eventually.

The variation of the velocity of both vehicles from the time Tom saw the oncoming van to the

time after the accident occurred is shown in the graph below.

time /s

velocity /km h-1

20

40

60

80

0

–20

–40

–60

1 2 3 4 5 6

A B

C

D

E

Tom's car

Van


18 | P a g e

(a) Using information from the graph, briefly describe and explain what happened to Tom's car

during the following periods of time:

AB: __________________________________________________________

__________________________________________________________

BC: __________________________________________________________

__________________________________________________________

CD: __________________________________________________________

__________________________________________________________

DE: __________________________________________________________

__________________________________________________________

[4]

(b) The mass of Tom's car is 1200 kg. Determine the average force experienced by Tom's car

during the collision.

Average force = ____________ N [2]

(c) Hence or otherwise, calculate the mass of the van.

Mass of van = ____________ kg [2]

(d) Is the collision between the two vehicles elastic or inelastic? Explain your answer.

________________________________________________________________

________________________________________________________________

________________________________________________________________

[2]


19 | P a g e

2010 IJC H2 P3 Q5

11 (a) (i) State Newton’s first law of motion and show it leads to the concept of force.

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

.………………………………..……..…………………………………………………. [2]

(ii) Using diagrams, with labelled arrows showing the velocity v and acceleration a, describe

situations in which an object

1. has an acceleration in the opposite direction to its velocity,

2. has an acceleration at right angles to its velocity.

In each case, include in your diagram, a labelled arrow to illustrate the direction of the resultant force F

acting on the object.

1.

…....……………………………………………………………………………………….

……....………………………………………………………………………………… [2]

2.

…....……………………………………………………………………………………….

……....………………………………………………………………………………… [2]


20 | P a g e

(b) A ship of mass 1.2 107 kg is moving backwards with a velocity of 0.50 m s

-1 towards a dockside. In order

to stop the ship, the engines are ordered full ahead.

(i) Calculate the initial kinetic energy of the ship.

kinetic energy = ………………………… J [1]

(ii) Assuming that viscous effects are negligible, calculate the magnitude of the constant retarding force

which must be exerted on the ship if it is to stop in a distance of 15 m.

retarding force = ………………………… N [3]

(iii) Calculate the time taken by the ship to stop under these conditions.

time = ………………………… s [2]

(iv) Explain qualitatively how your answer in (iii) would be affected by viscous forces.

…......……..…………………………………………………………………………………

…......……..…………………………………………………………………………………

…......……..…………………………………………………………………………………

.....……..………………………………………………………………………………..... [3]


21 | P a g e

(v) Calculate the change in momentum of the ship as it comes to a complete halt at the dock.

change in momentum = ………………………… N s [2]

(vi) Using your answer in (v) and with the aid of a diagram, explain how the law of conservation of

momentum is applied in this example.

……..……..…………………………………………………………………………………

……..……..…………………………………………………………………………………

……..……..…………………………………………………………………………………

……..……..…………………………………………………………………………………

……..……..…………………………………………………………………………………[3]

2010 JJC H2 P3 Q6

12 (a) State Newton’s second law of motion. [2]

(b) In Fig. 6.1 below, a 40 kg slab A rests on a frictionless floor. A 10 kg block B rests on top of

slab A. The frictional force between the two slabs is 40 N if B slides over A. If B is acted on

by a horizontal force of 100 N,

Fig. 6.1

B

A

100 N


22 | P a g e

(i) sketch and label the free-body diagram of block B. [2]

(ii) sketch and label the free-body diagram of slab A. [2]

(iii) describe quantitatively the subsequent motion of slab A. [2]

(iv) identify the two pairs of action-reaction forces between slab A and block B only.(With

reference to the free-body diagrams of slab A and block B) [2]

(c) State the principle of conservation of momentum [2]


23 | P a g e

(d) A rifleman, who together with his automatic rifle has a mass of 100 kg stands on roller

skates and fires ten shots horizontally. Each bullet has a mass of 4.0 x 10-2

kg and a muzzle

velocity of 800 m s-1

.

(i) If the rifleman moves back without friction, calculate the final mass of the rifleman

and the rifle after the ten shots. [1]

(ii) Estimate his velocity at the end of the ten shots. Give your answer to three significant

figures. [1]

(iii) If the shots were fired in 10 s, calculate the average force exerted on the rifleman. [2]

(iv) In reality, the actual force exerted on the rifleman is much greater than the calculated

force. Comment on the difference. [2]


24 | P a g e

(v) The butt of the rifle is sometimes fitted with a thick rubber pad as shown in Fig. 6.2

Fig. 6.2

Describe and explain how the pad will affect the recoil of the rifle, as experienced by

the rifleman. [2]

Rifle butt

Thick rubber pad


25 | P a g e

2010 MI H2 P3 Q1

13. An intelligent elevator as seen in Fig. 1.1, can take passengers to the top of a skyscraper.

The elevator has a built-in weight sensor below its floor that can be used to measure the

combined weight of the elevator’s occupants.

Fig. 1.1

An emergency braking mechanism can be activated within a few seconds if the steel cable

holding onto the elevator snaps.

A man decides to take the elevator to reach the upper floors. He has a mass of 80 kg, and

the elevator has a mass of 1.0 103 kg.

(a) Calculate the initial reading of the weight sensor when the elevator is stationary.

initial reading of weight sensor =……………..N [1]


26 | P a g e

(b) The lift accelerates upwards with an acceleration of 2.5 m s-2

.

(i) Draw a free-body diagram of the man, indicating and labelling the forces

acting on him.

There is no need to show the magnitude of the forces involved.

[1]

(ii) Hence or otherwise, calculate the reading of the weight sensor when the

elevator is accelerating upwards at 2.5 m s-2

.

Reading of weight sensor =…………….N [2]

(iii) If the maximum G-force that can be experienced safely by a human is 1.5G

(i.e. 1.5 times of the human’s weight), calculate the maximum upward

acceleration of the elevator that is still considered safe.

Maximum safe upward acceleration =……………. m s-2

[1]


27 | P a g e

(c) A computer simulation is designed to test the response of the emergency braking

mechanism and the weight sensor should the elevator’s cable snap when there are

passengers onboard. The simulation takes place in the following sequence:

Time / s Incident

0 Elevator is stationary at a height of 250 m.

t1 Steel cable snaps and elevator starts to

freefall.

t2 Emergency braking system kicks in and

elevator undergoes deceleration.

t3 Elevator comes to a complete stop.

Sketch a graph using the axes provided in Fig. 1.2 below to show the variation of the

weight sensor’s reading with time during the simulation. The original reading, W, is

indicated.

[2]

Fig. 1.2


28 | P a g e

(d) The owner of the skyscraper decided to replace the motor powering the elevator as it

was not efficient enough. He decided to use a motor that is 75% efficient, replacing

the original model which is 60% efficient.

(i) If the elevator is designed to hold up to 8000 N of passenger weight, and is

required to rise up to a height of 250 m in 60 s, calculate the power required to

achieve the task.

power required =…………… W [2]

(ii) Hence, calculate the input power that is required to operate the new motor.

input power =…………….W [1]


29 | P a g e

2010 AJC H2 P3 Q1

14 (a) State Newton’s first law of motion and show it leads to the concept of force.

(b) A transport plane is to take off from a level landing field with two gliders in tow, one behind the

other as shown in Fig.1.1. Each glider has a mass of 1200 kg, and the friction force or drag on each

may be assumed to be constant and equal to 2000 N. The tension in the cable between the transport

plane and the first glider is not to exceed 10 000 N.

(i) Determine the maximum acceleration acquired by the gliders.

(ii) If a velocity of 40 m s-1

is required for take off, calculate the minimum length of

runway required.

(iii)Explain how the minimum length of runway will vary if only one glider is towed.

End

H2 Physics/ 2012/ Year 1/ Revision/ Forces Source: 2010 Prelim Questions

1 | P a g e

2010 NYJC H2 P2 Q1

1 (a) State, in words, the 2 conditions that need to be satisfied in order to achieve static equilibrium.

Condition 1:

[1]

Condition 2:

[1]

(b) A uniform trapdoor of mass 12 kg and length 1.00 m is smoothly hinged to the wall as shown in

Fig. 1.1 (not drawn to scale). It is supported in equilibrium by a stay wire connecting the wall to

a point on the trapdoor at a distance of 0.25 m from its free end. The stay wire makes an angle of

60° with the wall and the trapdoor makes an angle of 30° with the horizontal.

Show that the tension in the stay wire is 78 N.

[2]

0.25 m

60°

30°

Fig. 1.1


2 | P a g e

(c) A 20.0 kg sphere of uniform density rests between two smooth planes as shown in Fig. 1.2.

Determine the magnitude of the force acting on the sphere exerted by each plane.

force due to plane A = N

force due to plane B = N [3]

2010 PJC H2 P2 Q2

2 A solid iron sphere of density 8000 kg m–3

and volume 41050.4 m3 is completely submerged in a

liquid of density 800 kg m–3

. The iron sphere is resting on a spring, as shown in Fig. 2.1. The spring is

compressed by 10.2 cm.

Fig. 2.1

20 kg

70° 30°

Plane A

Plane B

Fig. 1.2

iron sphere

liquid

compressed spring


3 | P a g e

(a) Show that the upthrust on the iron sphere is 3.53 N.

[1]

(b) Hence, calculate the spring constant of the spring.

spring constant = ........................................ Nm–1

[2]

(c) A string of breaking strength 32.0 N is used to lift the iron sphere vertically upwards, as shown in

Fig. 2.2. The iron sphere is then lifted partially out of the liquid as shown in Fig. 2.3.

Fig. 2.2 Fig. 2.3

string


4 | P a g e

(i) Explain why the string breaks.

..................................................................................................................................

..................................................................................................................................

........................................................................................................................... [1]

(ii) Calculate the volume of the fluid displaced at the instant when the string breaks.

volume = ........................................ m3 [2]

2010 PJC H2 P3 Q1

3 (a) State Newton’s second law of motion.

.......................................................................................................................................

................................................................................................................................. [1]

(b) Fig. 1.1 shows block A of mass 4.0 kg and block B of mass 1.0 kg connected by a light cord that

passes over a frictionless pulley. Block A lies on a rough plane inclined at 45° to the horizontal. The

frictional force between block A and the plane is 15 N.

Fig. 1.1

A

4.0 kg

1.0 kg B

45° C

6.0 kg rough plane

smooth ground


5 | P a g e

(i) Determine the magnitude of the acceleration of the two blocks and the tension in the cord.

acceleration = ........................................ ms–2

tension = ........................................ N [4]

(ii) When block A is 1.0 m vertically above the ground, the cord breaks. The velocity of block A at

that instant is 0.5 ms–1

. Calculate the speed of block A just before it reaches the ground.

speed = ........................................ m s–1

[2]

(c) After reaching the smooth ground, block A travels some further distance before colliding with a

stationary block C of mass 6.0 kg. The velocity of block A before collision is 1.6 m s–1

, as shown in

Fig. 1.2.

Fig. 1.2

(i) State the principle of conservation of momentum.

..................................................................................................................................

........................................................................................................................... [1]

1.6 ms–1

C

6.0 kg

A


6 | P a g e

(ii) Upon collision, block C moves to the right with a speed of 0.70 m s–1

. Calculate the speed of

block A immediately after the collision.

speed = ........................................ m s–1

[2]

(iii)Hence, discuss quantitatively, whether the collision between blocks A and C is elastic.

..................................................................................................................................

........................................................................................................................... [2]

2010 RI H2 P2 Q2

4 (a) A mass hanging from a spring balance in air gives a reading of 50 N. When the mass is

completely immersed in water, the reading on the balance is 40 N. It is now completely

immersed in another liquid, giving a reading of 34 N. Calculate the density of this liquid.

Assume that the density of water is 1000 kg m-3

.

Density = kg m-3

[2]


7 | P a g e

(b) In Fig. 2 below, a uniform beam of length 10.0 m and weight 500 N is hinged to a wall at

point O. Its far end is supported by a cable that makes an angle of 53.0° with the

horizontal. A 70.0 kg worker stands on the beam.

[2]

(i) Draw a labelled diagram showing the forces acting on the beam.

(ii) The worker walks towards the far end of the beam from O. Calculate the furthest

distance s he can walk if the maximum possible tension in the cable is 1000 N.

s = m

[2]

O

beam

cable

53.0°

s

Fig. 2


8 | P a g e

(iii)

Calculate the magnitude of the force exerted by the hinge on the beam when the

tension in the cable is 1000 N.

Reaction force = N

[3]

2010 RI H2 P3 Q5

5 A ball of mass m = 3.00 kg is released from rest at a height h = 0.500 m on a frictionless incline

as shown in Fig 5.1. The incline, which makes an angle = 30.0o to the horizontal, is fastened to

an immovable table of height H = 2.00 m.

Fig. 5.1

(a) Determine the contact force between the incline and the ball, after the ball is released.

Contact force = N

[2]

m

h

H

R


9 | P a g e

(b) Determine the acceleration of the ball as it slides down the incline.

Acceleration = m s-2

[2]

(c) Hence, or otherwise, show that the speed of the ball as it leaves the incline is 3.13 m s-1

. [2]

(d) Calculate the horizontal range R of the ball.

Horizontal range = m [4]


10 | P a g e

(e) The estimated normal contact force acting on the ball upon hitting the floor is shown in

Fig. 5.2. Assume that the floor is frictionless.

Fig. 5.2

(i) Determine the impulse delivered to the ball in the vertical direction.

Vertical component of impulse = N s

[2]

(ii) Hence, determine the vertical speed of the ball at the instant it rebounds from the

floor.

Vertical speed of rebound = m s-1

[4]

Normal contact force / N

Time / s 0 0.200

360


11 | P a g e

(iii)

State and explain whether this is an elastic or inelastic collision. Describe the energy

changes during the collision.

[4]

2010 RVHS H2 P3 Q2

6 (a) Define moment of a force.

……………………………………………………………………………………………

……………………………………………………………………………………… [1]

(b) A person supports a load of 20 N in his hand as shown in Fig 2.1. The system of the

hand and load is represented by Fig 2.2. The rod represents the forearm and T

represents the tension exerted in the biceps. The forearm weighs 65 N.

(i) Show that the tension T in the biceps is 410 N. [2]


12 | P a g e

(ii) Determine the magnitude and direction of the force acting at the elbow.

force acting at the elbow = ………………………… N

direction the force: ………………………… [4]

(c) A karate expert can split a stack of bricks by bringing her arm and hand swiftly against

the bricks with considerable speed. Using Newton’s laws of motion, explain why she

has to execute the karate strike very quickly.

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

…………………………………………………………………………….............. [4]


13 | P a g e

2010 ACJC H2 P3 Q4

7 A metal spring of natural length 20.0 cm fixed to the ceiling such that the bottom end is at a height of 30.0 cm

from the ground as shown in Fig 4.

(a) When the box of mass 5.00 kg hangs in equilibrium, the bottom end of the spring is at a distance of 25.0

cm from the ground. Determine the spring constant of the spring.

Spring constant = …………….. N m [3]

(b) The box was then brought to a higher point, such that the bottom of the spring was 40.0 cm above the

ground. The box was subsequently released from rest.

(i) Calculate the speed of the box when the bottom of the spring is 30.0 cm above the ground.

Speed = ……………… m s-1

[3]

30.0 cm

20.0 cm

Fig 4


14 | P a g e

(ii) Determine the nearest distance of the bottom of the spring from the ground.

Distance = ……………… m [3]

(c) Explain why in practice, we expect the answer obtain in (b)(ii) to be larger.

[1]

2010 MI H2 P2 Q4

8. (a) A 1 kg solid block of iron, when placed on water, will sink. The same block of iron is

shaped into a model of a boat, and this model would float on water.

Explain why the boat model would float, and not sink.

…………………………………………………………………………………………

…………………………………………………………………………………………

…………………………………………………………………………………………

………………………………………………………………………………………[2]


15 | P a g e

(b) A string supports a solid iron object of mass 200 g. The solid iron object is hence

suspended in mid-air

(i) Calculate the tension in the string when the solid iron object is suspended by

the string in mid-air

tension in the string =…………. N [1]

(ii) Given that the density of iron is 8000 kg m-3

, calculate the volume of the solid

iron object

Volume of solid iron object =………….. m3 [1]

(iii) Calculate the new tension in the string when the solid iron object is completely

immersed in a liquid of density 800 kg m-3

.

New tension in string =…………… N [2]


16 | P a g e

(c)

A solid cube with sides of length, x is placed on the surface of a fluid. The cube is

then slowly pushed downwards into the fluid, as seen in Fig.. The distance from the

base of the cube to the surface of liquid is given by h. The cube is pushed downwards

until h >> x.

Fig. 4.1

Fig. 4.2

Sketch in, Fig. 4.2 above, the graph showing the variation of the upthrust acting on

cube due to the fluid against the distance from the base of the cube to the fluid

surface, h. Your graph should show the variation of upthrust for values of h that are

greater than x.

[2]


17 | P a g e

2010 NJC H2 P2 Q2

9 Fig. 2.1 shows an improved water collection system.

Fig. 2.1

The uniform tipping gutter of mass 50.0 g is supported by the edge of the water

tank and by a rope that passes over a pulley. The other end of the rope is

attached to a bucket. By trial and error, the set-up is adjusted so that, when the

bucket is empty, the tipping gutter slopes down towards the bucket and all

parts remain at rest. The empty bucket is 30 cm tall and is about 10 cm

underneath the left end of the gutter.

A simplified diagram when the bucket is empty is as shown below.

(a) (i) Indicate the all the forces acting on the gutter in a free body diagram when

the bucket of base area = 0.10 m2 is empty. Identify and label the forces.

[1]

5 cm

30 cm

10 cm

bucket

tipping gutter

clean water

dirty water from roof pulley

Water tank


18 | P a g e

(ii) Assuming the gutter measures 1.5 m long, determine the mass of the

empty bucket.

Mass =…………………kg

[2]

(b) (i) When the rain starts to fall, dirty water from the roof flows into the

suspended bucket. Explain how this system enables clean water to be

collected in the water tank.

Assume that the roof and gutter are cleaned up when the gutter is at a

horizontal position.

[1]

(ii) In practice, the pulley is not frictionless which offers an advantage.

Suggest what this can be.

[1]

(c) In a downpour, the rainwater is flowing from the roof into the gutter at a

rate of 50 cm3 s

-1 and has a speed of 0.50 ms

-1 when it leaves the gutter.

Density of rainwater = 1000 kgm-3

.


19 | P a g e

(i)

Determine the vertical resultant force on the water when it first falls

into the bucket.

Force = …………………….N

[3]

(ii) In 2c (i), you may have made assumption about the final speed of the

water upon contact with the bucket. State and explain what would

happen to your answer in 2c (i) if the assumption fails.

[2]

2010 CJC H2 P2 Q3

10 (a) A train of mass 2.2 x 105 kg is traveling at a speed of 20 km h

-1 and it requires a power of 900 kW.

(i) Calculate the driving force exerted on the train.

driving force = …………..……………... N

[2]


20 | P a g e

(ii) What additional power must be supplied if the train is to maintain at a speed of 20 km h-1

on a

slope which rises 1 m for every 60 m of track?

additional power = ………………………….. W

[2]

(iii) A simple pendulum hangs from the roof of one of the compartments. Calculate the inclination of

the string to the vertical as seen by a passenger as it slows down and reaching station at a rate of

0.667 m s-2

. Explain your reasoning with a suitable diagram.

angle of inclination = ………………..°

[3]


21 | P a g e

(b)

A student wishes to find the volume of stone. He suspends the stone in air from a cord which is attached

to a force sensor as shown in Fig. 2.a. He then submerges the stone fully in a beaker of water (see Fig.

2.b).

(i) State and explain the change in the force sensor reading.

…………………………………………………………………………….......................................

................................................................................................................................................

[1]

(ii) Explain how volume of the stone can be determined from the readings of the force sensor and the

density of water.

…………………………………………………………………………….......................................

................................................................................................................................................

…………………………………………………………………………….......................................

................................................................................................................................................

[3]

Force sensor

Stone

Fig. 2.a

Force Sensor

Fig. 2.b

Beaker of water

Cord


22 | P a g e

2010 AJC H2 P2 Q1

11 (a) State the principle of floatation.

(b) A uniform cylindrical wooden rod of length L and weight 60 N, attached at one end to a light string, is

slowly lowered into water. It is found that, when the system is in equilibrium, the string is vertical and

exactly half of the rod is underwater, as shown in Fig. 1.1. The upthrust is acting through a point S which is

0.25L from the end of the rod immersed in the water.

i. Calculate the upthrust experienced by the rod

ii. Calculate the density of the wood from which the rod is made if the density of water is 1.0 x 103 kg

m-3

.

iii. Explain why the percentage of the rod submerged in water will be more than 50% when the

string is cut.


23 | P a g e

2010 AJC H2 P3 Q5

12 a (i) Define linear momentum.

(ii) State Newton’s second law.

(iii) Use your answer in (i) and (ii) to show that F = m a where F is the force, m is the mass and a is the

acceleration.

(iv) State the principle of conservation of momentum.


24 | P a g e

(b) A firework of mass 0.30 kg is launched with an initial velocity v of 8.0 m s-1

at an angle of 60°to the

ground, which is horizontal. Fig. 5.1 shows the path of the firework from the point of projection O to the

point of maximum height P.

At the instant when the firework is at P, an internal explosion separates it into two parts, A and B. The mass

of A is 0.2 kg and the mass of B is 0.1 kg. Immediately after the

explosion, part A is momentarily at rest and part B moves horizontally. Parts A and B then move on

different paths and strike the ground. It is assumed that all effects of air

resistance are negligible for the whole process.

(i) Calculate the momentum of the firework just before the explosion.

(ii) Calculate the momentum of part B immediately after the explosion.

(iii) Determine the additional kinetic energy supplied to parts A and B by the explosion.


25 | P a g e

(iv) Sketch on Fig. 5.1 the paths followed by parts A and B after the explosion. Label

these paths as A and B clearly.

(v) Calculate the time for part A to reach the ground.

(vi) Suggest and explain whether part B will take lesser, same or greater time to reach

the ground than your answer in (b)(v).

(vii) Determine the distance apart of parts A and B when they strike the ground.


26 | P a g e

(c) (i) If the firework in part (b) fails to explode and air resistance is not negligible, will the

firework reach a point lower, same or higher than point P? Explain.

(ii) Sketch on Fig. 5.2 the path of the firework when it fails to explode where

1. air resistance is negligible. Label the path as R.

2. air resistance is not negligible. Label the path as S.

2010 SRJC H2 P2 Q2

13 (a) A uniform plank of mass 40.0 kg and length 2.0 m is held horizontally by two identical supports at

points A and B. Point B is 0.5 m away from end of beam at point C as shown in Fig. 2.1.

(i) On Fig. 2.1, draw the three forces acting on the plank. [1]


27 | P a g e

(ii) Calculate the force provided by the support at point A.

(iii) Consider another scenario where a person pushes the support at point A towards the middle of

the plank steadily. With the aid of clear calculations and/or explanations, state how the force on

the plank at point B changes as the support at point A is shifted. [2]

(b) Fig. 2.2 shows a variable force acting on a 200 kg object travelling in a straight line with an initial

velocity, in the positive direction along the same line as the line of action of the force , of 15 m s-1

at t = 0 s.

Calculate the magnitude of the final velocity of the object at t = 30.0 s.


28 | P a g e

(c) Fig. 2.3 shows a wooden block Z resting on block X. Block X and Z are connected by an inelastic string

which goes around a fixed smooth pulley. The mass of block X is 20 kg and the mass of block Z is 2.0 kg.

The friction between blocks X and Z is 11.0 N. Block X is pulled at a constant velocity by a 100.0 N force.

All strings are of negligible mass.

Calculate the frictional force between X and the table.

END

H2 Physics/ 2012/ Year 1/ Revision/ WEP Source: 2010 Prelim Questions

1 | P a g e

2010 NYJC H2 P2 Q2

1 The question is about reverse bungee jumping.

Fig. 2.1 shows the set up of a reverse bungee jumping. A capsule is connected by two identical elastic

cords each attached to a tower 30.0 m tall. The mass of the capsule when fully loaded with three

passengers has a total mass of about 300 kg. When released, the capsule will shoot up at high speed.

(a) The original length of each of the elastic cords is 25.0 m with an elastic constant of 19 000 N

m-1

and the capsule has an effective diameter of 2.0 m. Prove that the total elastic potential

energy at the ground level = 510 kJ when the cord length is 30.2 m.

[1]

(b) Fill in the blanks in the table below to determine the various amounts of energy when the

capsule starts from the ground level and shoots up to its highest point.

Total elastic

potential energy /kJ

Gravitational

potential energy of

capsule /kJ

Kinetic energy of

capsule /kJ

Ground level 510 0 0

30 m above the

ground

Highest point 174

[2]

30.0 m

10.0 m

Elastic

cords

capsule

Fig. 2.1

Ground level


2 | P a g e

(c) Use the value in (a) to determine the speed reached by the capsule when the cords first become

loose.

speed = m s-1

[2]

(d) State and explain the position where the apparent weight of the passenger will be the greatest.

[2]

2010 SAJC H2 P2 Q2

2 A system of two bodies A and B are connected by an inextensible cord over a frictionless pulley

and are resting on inclined planes as shown in Fig. 2.1. Body A of mass 2.00 kg and body B of mass

5.00 kg move, in the directions as indicated, a distance of 0.500 m and each experiences a frictional

force of 3.00 N.

Fig. 2.1

(a) Calculate the change in gravitational potential energy of the system.

change in gravitational potential energy = …………………… J [2]

A B

40° 50°


3 | P a g e

(b) Determine the final speed of system after travelling 0.500 m.

final speed = …………………………….m s−1

[3]

(c) On the axes of Fig. 2.2, sketch a clearly labelled graph of the variation with time of the

gravitational potential energy Ep, kinetic energy Ek and work done against frictional forces

Wf. [3]

Fig. 2.2

Energy

Time 0


4 | P a g e

2010 ACJC H2 P3 Q4

3 A metal spring of natural length 20.0 cm fixed to the ceiling such that the bottom end is at a height of

30.0 cm from the ground as shown in Fig 4.

(a) When the box of mass 5.00 kg hangs in equilibrium, the bottom end of the spring is at a distance

of 25.0 cm from the ground. Determine the spring constant of the spring.

Spring constant = …………….. N m [3]

(b) The box was then brought to a higher point, such that the bottom of the spring was 40.0 cm

above the ground. The box was subsequently released from rest.

(i) Calculate the speed of the box when the bottom of the spring is 30.0 cm above the ground.

Speed = ……………… m s [3]

30.0 cm

20.0 cm

Fig 4


5 | P a g e

(ii) Determine the nearest distance of the bottom of the spring from the ground.

Distance = ……………… m [3]

(c) Explain why in practice, we expect the answer obtain in (b)(ii) to be larger.

2010 CJC H2 P3 Q5

4 (a) Explain how an object travelling in a circle with constant speed has an acceleration.

What is the direction of this acceleration?

[3]

(b) (i) State the principle of conservation of momentum.

[2]

(ii) A particle of mass m moving with speed v makes a head-on collision with an

identical particle which is initially at rest. Determine the subsequent motion of

the particles after they had made a completely inelastic collision.

[2]


6 | P a g e

(iii) A bullet of mass 0.025 kg is travelling horizontally with a speed of 150 m s-1

when it strikes the centre of a vertical face of a cubical block of mass 2.0 kg

which is hanging at rest from vertical strings. If the bullet embeds itself in the

block, calculate the vertical height risen by the block and bullet.

Height raised =…………….. m

[4]

(c) A railway truck of mass 22 000 kg and moving at a speed of 3 m s-1

catches up and collides

with a truck of mass 66 000 kg moving at 1 m s-1

moving in the same direction.

The graph shows the speeds of the trucks before, during and after the collision.

22 000 kg 66 000 kg

3 m s-1 1 m s-1

Spring buffers


7 | P a g e

(i) Use the information in the graph to show that the collision is elastic.

[3]

(ii) Calculate the change in the total kinetic energy between the instant halfway through the

collision and after the collision. Suggest a reason for this change.

Change in Kinetic Energy = ………………………… J

[3]

(iii) Calculate the magnitude of the impulse exerted by the lighter truck on the heavier truck.

Impulse = ………………………… N s

[2]

V/ m s-1

3

2

1

0

0.000 0.100 0.200 time/ s


8 | P a g e

(iv) Explain whether or not this impulse changes in value if the collision remains elastic but

takes half the time.

[1]

2010 HCI H2 P2 Q2

5.

Daniel decides to have his first attempt at bungee jumping. He falls from rest from the top of a

tall cliff with an elastic rope tied to his feet. The force constant of the rope is 100 N m-1

, and the

rope's unstretched length is 20.0 m. Daniel's mass is 80.0 kg. Assume that the average drag

force by the air on Daniel during his jump is 300 N, and that g = 10 m s-2

.

H cliff


9 | P a g e

(a) Determine the lowest height H Daniel reaches in his jump.

H = ____________ m [3]

(b)

Calculate the tension in the rope at the instant when Daniel is at his lowest height.

tension = ____________ N [1]

(c) Hence, determine Daniel's acceleration at this instant.

Magnitude of acceleration = ____________ m s-2

Direction of acceleration = _________________ [3]


10 | P a g e

(d) Sketch a graph of the tension in the rope against the height which Daniel falls through,

from the time when he jumps to the instant when he is at the lowest height

[1]

Tension in rope

Height Daniel falls through 0


11 | P a g e

2010 HCI H2 P2 Q3

6.

A small cube of mass m slides down along a spiraled path round a cone as shown in

Figure 3a. The path is always inclined at an angle to the horizontal at any point.

There is a smooth wall along the outer edge of the spiraled path to prevent the cube from

falling out of the path (see Figure 3b). This wall is inclined such that it always exerts a

horizontal contact force on the cube as it spirals down. All frictional forces are

negligible.

(a) Label all the forces acting on the cube in Figure 3b. [3]

Inner Wall

Outer Wall

Cube

Cone

Spiraled Path

Figure 3a

Spiral Path taken by cube

Figure 3b

cube


12 | P a g e

(b)

Based on the answer in (a), describe the motion of the cube.

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

___________________________________________________________________[2]

(c)

(i)

State the work done by the horizontal contact force on the cube as it spirals down

the plane.

________________________________________________________________

______________________________________________________________[1]

(ii) Derive an expression for the rate of change of kinetic energy of this cube in

terms of m, and its instantaneous speed v.

[2]

2010 SRJC H2 P2 Q8

7. A small boat is powered by an outboard motor of variable power output P. Fig. 8.1 shows the variation

with speed v of P when the boat is carrying different loads.


13 | P a g e

The masses shown are the total mass of the boat plus passengers.

(a) For the boat having a steady speed of 2.00 m s−1

and with a total mass of 250 kg,

(i) use the graph in Fig. 8.1 to determine the power of the engine.

(ii) calculate the resistive force acting on the boat.


14 | P a g e

(b) Consider the case of the boat of mass 350 kg moving with a speed of 2.50 m s-1

.

(i) By using data from the graph, estimate the total amount of energy which the motor provides in order for

the boat to travel for a total of 30 minutes.

(ii) The amount of energy given off when 1.00 kg of fuel is mixed with oxygen in the air is 45.0 MJ. The

efficiency of the motor in converting the energy released by the combination of oxygen and the fuel is

40.0%. Determine for the case in (i) the total amount of fuel which would be expended.

(iii) Hence, explain if the estimate in (i) is a reasonable one. [2]

(c) Fig. 8.2 shows how the speeds of 2 boats of equal mass vary with respect to time. Boat A starts from rest

while boat B travels at a constant speed.

(i) Boat A and boat B both travel the same distance at t = 900 s. State the velocity V of boat A at t = 900 s.

[1]

(ii) Explain which boat, if any, would expend a greater amount of petrol at the end of 900 s.

[3]

END

H2 Physics/ 2012/ Year 1/ Revision/ Thermal Physics Source: 2010 Prelim Questions

1 | P a g e

2010 NYJC H2 P3 Q7

1 (a) Explain what is meant by the internal energy of a system.

[2]

(b) State what is meant by saying a temperature is on an absolute scale.

[1]

(c) A cake of mass 0.90 kg is cooked in an oven at a temperature of 180°C. It is

taken out of the baking tin onto a rack to cool in a kitchen of 20°C.

(i) State the final temperature of the cake.

final temperature = K [1]

(ii) Calculate the energy released from the cake in cooling. Take the

specific heat capacity of the cake to be 990 J kg-1

K-1

.

energy released = J [2]


2 | P a g e

(d) The oven of volume 0.10 m3 cools down from 180°C to 25°C.

een the two

temperatures. The pressure in the oven remains at an atmospheric pressure of

1.0 x 105 Pa. Assume that air behaves ideally. [Relative molecular mass of air

= 0.030 kg mol-1

]

kg [4]

(e) Air is mainly made up of nitrogen and oxygen. The mass of 1 nitrogen

molecule is 28 u while the mass of 1 oxygen molecule is 32 u.

Find the ratio

average speed of oxygen molecule at 180 C

average speed of nitrogen molecule at 25 C

ratio = [3]


3 | P a g e

(f) The gas in the cylinder of a diesel engine can be considered to undergo a cycle

of changes of pressure, volume and temperature. One such cycle, for an ideal

gas, is shown in Fig. 7.1.

The table below shows the increase in internal energy which takes place

during each of the changes A to B, B to C, C to D and D to A.

Section of cycle Heat supplied

to gas / J

Work done

on gas / J

Increase in

internal energy

of gas / J

A to B 0 - 300 - 300

B to C - 450 0 - 450

C to D 0 650 650

D to A

Using Fig. 7.1, fill in the missing values in the table above. [3]

(g) In a continuous flow method for determining the specific heat capacity a liquid, the

liquid flows through the tube at 0.15 kg min-1

, while the heater provides

power at 25 W. The temperatures of the liquid at the inlet and outlet are 15 oC

and 19 oC, respectively.

With the inlet and outlet temperatures unchanged, the flow rate is increased to

0.23 kg min-1

and the power of the heater is increased to 37 W.

(i) Explain why it is necessary for the inlet and outlet temperatures to

remain unchanged.

Fig. 7.1


4 | P a g e

[1]

(ii) Determine the rate of heat loss of the liquid.

rate of heat loss = W [3]

2010 PJC H2 P3 Q6

2 (a) State what is meant by saying that a temperature is on an absolute scale.

....................................................................................................................................

................................................................................................................................. [1]

(b) Explain what is meant by

(i) an ideal gas,

..................................................................................................................................

........................................................................................................................... [1]

(ii) absolute zero on the Kelvin scale,

..............................................................................................................................

........................................................................................................................... [1]


5 | P a g e

(iii)the internal energy of a gas.

[2]

(c) A car tyre has a fixed internal volume of 0.0160 m3. On a day when the

temperature is 27°C, the pressure in the tyre has to be increased from 51076.2

Pa to 51091.3 Pa.

(i) Assuming that the air is an ideal gas, calculate the amount of air which has to

be supplied at constant temperature.

amount of air = ........................................ mol [3]

(ii) A portable supply of air used to inflate tyres has a volume of 0.0117 m3 and is

filled with air at a pressure of 610165.1 Pa. Show that, at 27°C, there is

more than enough air in it to supply four tyres, as in (c)(i), without the

pressure falling below 51000.4 Pa.

[3]


6 | P a g e

(iii) Show that the internal energy of a molecule of air at a temperature of 27°C is 211021.6 J. Assume that the air behaves as a monatomic ideal gas.

[2]

(iv) Hence, calculate the internal energy of one mole of the air at a temperature of 27°C.

internal energy = ........................................ J [1]

(d) In order to study the sudden compression of a gas, some dry air is enclosed in a

cylinder fitted with a piston, as shown in Fig. 6.1.

Fig. 6.1

The mass of air in the cylinder is constant. The material of the cylinder and the

piston is an insulator so that no thermal energy enters or leaves the air.

The volume and pressure of air are measured. The piston is then moved suddenly

to compress the air and the new volume and pressure are measured.

cylinder piston


7 | P a g e

The variation with volume V of the pressure p of the air is shown in Fig. 6.2.

Fig. 6.2

It may be assumed that the dry air behaves as an ideal gas.

(i) By considering the pressure and volume of the dry air at points A and B, and

using the equation of state for an ideal gas, show that the temperature of the

air increases when the air is compressed.

[3]

(ii) The dry air then goes through two more processes.

Process 1: The gas is cooled while keeping the piston at the same position.

Process 2: The gas then expands, while kept at constant temperature, to

return to its original state.

On Fig. 6.2, draw and label the p-V graphs of the two processes described

above. [3]

1.0

A

B

V / 10−3

m3 5.0 4.0 3.0 2.0 1.0 0

p / 105 Pa

2.0

3.0

4.0


8 | P a g e

2010 RI H2 P2 Q1

3 (a) Explain what is meant by internal energy of a gas.

[1]

(b) A cylinder fitted with a piston contains 0.20 mole of an ideal gas. Initially the volume and

pressure of the gas are 3 35.0 10 m and 51.0 10 Pa respectively.

(i) Calculate the initial temperature of the gas.

Initial temperature = K [2]

(ii) The gas is

(1) heated at constant volume to twice its initial temperature

(2) cooled at constant pressure to its initial temperature, and finally

(3) expanded isothermally to its initial volume.

Sketch the above changes on a clearly labelled p-V diagram.

V/ 103 m

3

0

p/ 105 Pa

2.5 5.0

1.0

2.0

[4]


9 | P a g e

2010 RVHS H2 P2 Q3

4 A small immersion electrical heater, operating at a constant power, was used to heat 64 g of

water in a thin plastic cup. The mass of the cup was negligible. The temperature of the water

was recorded at regular intervals for 30 minutes and a graph of temperature against time is

drawn as shown in Fig. 3.1 below.

60

50

40

30

200 5 10 15 20 25 30

Time / minutes

Temperature / °C

Fig. 3.1

(a) (i) Use the graph to determine the initial rate of temperature rise of the water.

rate of temperature rise = ………………………… C min–1

[2]

(ii) The specific heat capacity of water is 4200 J kg–1

K–1

. Determine the rate at

which energy was supplied to the water by the heater.

Time / minutes

Temperature / C


10 | P a g e

rate of energy supply = ………………………… J min–1

[2]

(b) After 26 minutes the rate of temperature rise became very small. Explain why.

……………………………………………………………………………………………

……………………………………………………………………………………… [1]

(c) The experiment was repeated using the same mass of water in a thick ceramic mug.

The initial temperature of the water was the same and the water was heated for the

same length of time.

(i) On Fig 3.1, sketch a possible graph of temperature against time for the water in

the thick ceramic mug. [1]

(ii) Explain your reasoning for your graph.

……………………………………………………………………………………

……………………………………………………………………………... [2]

2010 SAJC H2 P3 Q6

5 (a) (i) There is no attraction between the molecules of an ideal gas. Use

this information to explain why the internal energy of an ideal gas

is proportional to its temperature.

………………………………………………………………………

………………………………………………………………………

………………………………………………………………………

………………………………………………………………………

………………………………………………………………………

………………………………………………………………………

[3]


11 | P a g e

(ii) Hence, explain how this relationship between the internal energy

of an ideal gas and the absolute temperature, gives rise to the

concept of an absolute zero of temperature.

………………………………………………………………………

………………………………………………………………………

………………………………………………………………………

………………………………………………………………………

[2]

(b) Fig. 6.1 represents how the temperature of a small mass of water changes

when it is heated steadily from room temperature to above its boiling point

in a large sealed container.

Fig. 6.1

Describe and explain the features of the graph in terms of the changes

which occur to the separation of the molecules and to their potential and

kinetic energies. Three distinct sections of the graph have been labelled to

aid your description.

(i) A to B

………………………………………………………………………

………………………………………………………………………

………………………………………………………………………[2]


12 | P a g e

(ii) B to C

………………………………………………………………………

………………………………………………………………………

………………………………………………………………………[2]

(iii) C to D

………………………………………………………………………

………………………………………………………………………

………………………………………………………………………[2]

(c) This question is about the atmosphere treated as an ideal gas.

(i) The equation of state of an ideal gas is pV = nRT. Data about gases

are often given in terms of density ρ rather than volume V. Show

that the equation of state for a gas can be written as

p = ρRT

M

where M is the mass of one mole of gas.

[2]


13 | P a g e

(ii) One simple model of the atmosphere assumes that air behaves as

an ideal gas at a constant temperature. Using this model the

pressure p of the atmosphere at a temperature of 20 °C varies with

height h above the Earth’s surface as shown in Fig. 6.2.

Fig. 6.2

Use data from the graph to show that the variation of pressure with

height follows an exponential relationship.

[ 3 ]

(iii) The ideal gas equation in (c)(i) shows that, at constant temperature,

pressure p is proportional to density ρ. Use data from Fig. 6.2 to

find the density of the atmosphere at a height of 8.0 km. (Density ρ

of air at h = 0 m is 1.3 kg m–3

)

ρ = .............................................. kg m–3

[2]


14 | P a g e

(iv) In the real atmosphere the density, pressure and temperature all

decrease with height. At the summit of Mt. Everest, 8.0 km above

sea level, the pressure is only 0.30 of that at sea level. Take the

temperature at the summit to be –23 °C and at sea level to be 20 °C.

Calculate, using the ideal gas equation, the density of the air at the

summit.

(Density ρ of air at sea level = 1.3 kg m–3

)

ρ = ............................................. kg m–3

[2]

2010 TJC H2 P2 Q4

6 (a) State, in words, the relation between the increase in internal energy of a gas, the work done by

the gas, and the heat supplied to the gas.

[1]

(b) A scuba diver releases an air bubble, of diameter 3.0 cm, from a depth of 14 m below the sea

level. Assume that air behaves as an ideal gas and the temperature of water is constant at 25 C.

(i) Given that the density of water is 1000 kg m-3

and the atmospheric pressure is 1.0 x 105

Pa, show that the pressure of the water at a depth of 14 m is 2.4 x 105 Pa.

[1]


15 | P a g e

(ii) Hence calculate the volume of the air bubble when it reaches the surface of water.

volume of air bubble = m3 [3]

(iii) Sketch a clearly labeled graph in Fig. 4.1 showing the variation of pressure P with

volume V of the air bubble as it rises from the sea.

[2]

(iv) Use the relation stated in (a) to deduce whether heat is added or removed from the air

bubble as the bubble rises.

P/Pa

V/m3 Fig. 4.1


16 | P a g e

2010 YJC H2 P3 Q2b

7(b) (i) Fig. 2.1 shows data for ethanol.

Density 0.79 g cm-3

Specific heat capacity of liquid ethanol 2.4 J g-1

K-1

Specific latent heat of fusion 110 J g-1

Specific latent heat of vaporisation 840 J g-1

Melting point -120 oC

Boiling point 78 oC

Fig 2.1

Use the data in Fig. 2.1 to calculate the thermal energy required to

convert 1.0 cm3 of ethanol at 20

oC into vapour at its normal boiling

point. [3]

Thermal energy required = ………..…….. J

(ii) Suggest why there is a considerable difference in magnitude between its

specific latent heat of fusion and vaporization.

[1]

………..……………………………………………………………………………………

………..……………………………………………………………………………………

………..……………………………………………………………………………………


17 | P a g e

2010 SRJC H2 P3 Q7

8 (a) The following statements were made with regard to various thermal processes.

Using kinetic theory, comment on the validity of the statements and elaborate on the reasoning.

(i) Energy must be supplied to a sample of pure liquid to maintain constant temperature during

boiling because it is needed to maintain the amount of internal energy of the sample. [3]

(ii) More energy is needed for boiling of pure water than melting of pure ice of the same mass

under the same environmental conditions because ice has a lower density than water and therefore

less energy is needed. [2]

(b) Using kinetic theory, explain why evaporation occurs at all temperature and is accompanied

by cooling. [3]

(c) The setup in Fig. 7.1 is used for the electrical method of determining the specific heat capacity,

c of a solid material X of mass m1.


18 | P a g e

The temperature of the solid increased from θ1 to θ2 in time t1 when the voltmeter and ammeter

reading remained constant at V1 and I1.

The following equation was used to determine c.

(i) State and explain whether the calculated c value, based on the above equation, is an

underestimate, overestimate or accurate reflection of the true value of c. [2]

(ii) Describe and explain how the accuracy of c can be improved with the same setup, with

accompanying

(d) An ideal monatomic gas in an enclosed space obeys the two equations

(i) Derive an expression for the relationship between average random translational

kinetic energy of the gas atom and the temperature of the gas. [1]

(ii) Two samples of the same gas, X and Y of 3.0 mol and 4.5 mol respectively are at

temperature 100 °C and 200 °C.

Determine the ratio of the root mean square speeds of X to Y.

ratio = ..................... [1]


19 | P a g e

(iii) Two samples of ideal gas P and Q of 1.0 mol each are at the same temperature.

Determine the ratio of root mean square speeds of P to Q, when the ratio of the relative molecular

mass of P to Q is 3:2.

ratio = ………………… [2]

2010 TPJC H2 P3 Q1

9. In a heat engine, the working substance is an ideal monatomic gas with 3.0 moles of

molecules. The gas undergoes a cycle of thermodynamic processes ABCDA as it drives the

engine, as shown in Fig. 1.

(a) Determine the thermodynamic temperature of the gas at B. [2]

(b) If the average kinetic energy of a molecule of a gas at temperature T is given by 3kT/2,

determine the change in internal energy of the gas in the process BC. [3]


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(c) Determine the work done by the gas in the process BC. [2]

(d) Determine the heat absorbed by the gas in the process in BC. [2]

2010 ACJC H2 P3 Q2

10 (a) Explain what is meant by an elastic collision.

[2]

(b) An ideal gas is contained in a thermally insulated cylinder by means of a piston as

shown in Fig 2.1. An atom of the gas collides with the piston, as illustrated.

The piston in (b) is lowered so that the volume of the gas is reduced.

(i) Explain the difference in the speed of an atom of ideal gas after an elastic

collision with a moving piston and with a stationary piston (assume mass of

piston much greater than mass of an atom of the gas). and hence use the kinetic

Fig

2.1


21 | P a g e

theory to explain the changes to the temperature of the gas as the piston is

lowered.

[4]

(ii) Use the 1st law of thermodynamics to support your answer obtained in (i).

[3]

(c) Sketch on Fig 2.2, with the help of the two isotherms given, the variation in the

pressure of the gas in the cylinder as its volume is decreased.

Pressure

Volume


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2010 CJC H2 P3 Q2

11 (a) State what is meant by the internal energy of a system.

.......................................................................................................................................

......................................................................................................................................

[2]

(b) An ideal gas in a cylinder can be considered to undergo a cycle of changes of pressure, volume and

temperature as shown on the graph of Fig. 2.1.

The temperature of the gas at A and C are 623 K and 50 K respectively.

(i) Calculate the number of gas molecules in the cylinder.

Number of gas molecules = ……………………………..

[2]

Fig 2.1

7.5 x 10-3


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(ii) Calculate the volume of gas at C.

Volume of gas = ……………………….. m3

[2]

(iii) Calculate the net work done by the gas.

Net work done by gas = …………………….. J

[2]

(iv) State with a reason the total change in internal energy of the gas when it completes a cycle.

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

[2]


24 | P a g e

2010 HCI H2 P3 Q2

12 (a) State

(i) the first law of thermodynamics, [2]

_____________________________________________________________

_____________________________________________________________

_____________________________________________________________

(ii) the meaning of the term internal energy. [2]

_____________________________________________________________

_____________________________________________________________

_____________________________________________________________

(b) The diesel cycle is the thermodynamic cycle which approximates the pressure and

volume of the combustion chamber of the diesel engine, invented by Rudolph Diesel in

1897.

An ideal gas undergoes the diesel cycle which comprises 4 processes:

Process A - adiabatic compression

Process B - isobaric heating

Process C - adiabatic expansion

Process D - isovolumetric cooling

B C A

D

0.020 0.070 V / m3

11

P / 105 Pa


25 | P a g e

(i) Calculate the work done by the gas during process B.

work = ___________ J

[2]

(ii) Table 2.1 is a table of energy changes during one cycle. Complete the table with

appropriate values.

Process work done on

gas, W / kJ

heat supplied to

gas, Q / kJ

increase in internal

energy, ΔU / kJ

A + 201

B + 74

C - 185

D - 35 - 35

Table 2.1

[4]

2010 IJC H2 P3 Q2

13(a) (i) What is meant by the term internal energy of a system? [2]

(ii) Write down an equation representing first law of thermodynamics. Define the

symbols that you use. [2]


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(b) Some water in a saucepan is boiling.

(i) Explain why there is a change in internal energy as water changes to steam.

[2]

(ii) Explain why external work is done by the boiling water. [2]

(iii) With reference to your answers in (b)(i) and (b)(ii), show that thermal energy must

be supplied to the water during the boiling process.

[2]

2010 JJC H2 P3 Q2

14 A fixed mass of ideal gas undergoes a cycle of changes A → B → C → D → A as shown in Fig. 2.

Fig. 2


27 | P a g e

(a) Use Fig. 2 to determine the net work done by the ideal gas in a complete cycle. [2]

(b) Explain why the total change in the internal energy of the ideal gas in a complete cycle must

be zero. [2]

(c) If the thermodynamic temperature of the ideal gas at A is 600 K, what is the thermodynamic

temperature of the gas at B? [2]

(d) Can the thermodynamic cycle illustrated in Fig. 2 be found in a refrigerator or a petrol engine?

Explain your answer. [2]


28 | P a g e

2010 MI H2 P2 Q3

15. (a) Using the simple Kinetic Model of Matter, explain the following:

(i) the melting of ice takes place without a change in temperature.

……………………………………………………………………………………

……………………………………………………………………………………

…………………………………………………………………………………[2]

(ii) the specific latent heat of vaporisation of water is higher than its specific latent

heat of fusion.

……………………………………………………………………………………

……………………………………………………………………………………

………………………………………………………………………………...[2]

(b) An ideal gas at constant pressure has its volume directly proportional to its absolute

temperature.

Calculate the absolute temperature T when an ideal gas has volume 0.00825 m3,

assuming that the same mass of the ideal gas at the same pressure has volume

0.00424 m3 at a temperature of 273 K.

absolute temperature T =…………….K [2]


29 | P a g e

(c) (i) State the conversion formula from the Celsius scale (°C) to the thermodynamic

absolute scale (K)

[1]

(ii) Hence or otherwise, comment on whether the following statement is true:

“Today the temperature is 30 °C and yesterday it was 15 °C. Hence it is twice

as hot today as it was yesterday.” [1]

2010 NJC H2 P3 Q2

16 A monoatomic ideal gas is subject to a cycle of changes ABCA. Figure 2 shows a graph of

pressure p against volume V for one cycle of changes for the gas.

Figure 2

(a)(i) Using data from the graph, verify that process BC is isothermal. Show your workings clearly.

p /105 Pa

V /10 - 4

m3


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State an assumption of the gas you must make to support your verification.

(ii) Explain the term internal energy in relation to an ideal gas.

[1]

(b) Temperature of the gas at point C is 385 K. Calculate the temperature of the gas

in oC at point A.

[1]

(c)(i) Calculate the change in the internal energy of the gas during the process AB.

[2]

Temperature of the gas = ………..………….oC

Change in the internal energy = ……………….. J


31 | P a g e

(ii) Work is done by the gas in the change AB. State what must be done to the system

for this change to occur. Explain using the first law of thermodynamics.

[2]

(d) Use the Kinetic Theory of gases to explain why the pressure of an ideal gas

increases in the change BC when it contracts at constant temperature.

[2]

2010 CJC H2 P2 Q4

17 A student sets up the apparatus illustrated in Fig. 4.1 in order to determine a value for the specific

latent heat of fusion of ice.

A heater is placed in the funnel, surrounded by pure melting ice. The student measures the mass of

melted ice in the beaker at regular time intervals before and after switching on the heater. The

variation with time t of the mass m of melted ice in the beaker is shown in Fig. 4.2.

Fig 4.1


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During the heating process, the current is adjusted so that the readings on the ammeter and

voltmeter are constant.

(a) By reference to Fig. 4.2,

(i) Suggest a time at which the heater is switched on,

time = ………………….. minutes

[1]

Fig 4.2


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(ii) Determine the mass of ice melted in 1.0 minute

1. with the heater switched off,

mass = ……………………. kg

[1]

2. with the heater switched on.

mass = ……………………. kg

[1]

(b) The readings of the ammeter and the voltmeter are 5.2 A and 11.5 V respectively. Use your

answers in (a) to calculate a value for the specific latent heat of fusion of ice.

specific latent heat of fusion = ……………………….. J kg-1

[3]


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(c) State and explain the effect on your calculated value for the specific latent heat of fusion if

ice taken directly from a freezer were used to replace the ice in the funnel.

[2]

2010 MJC H2 P3 Q5

18 (a) Explain what is meant by internal energy of a system.

…………………………………………………………………………………………........

…………………………………………………………………………………………........

……………………………………………………………………………………...... [2]

(b) The temperature, T of an ideal gas at pressure p is defined by the equation p = nkT

(i) Identify the quantity n.

……………………………………………………………………………………......

[1]

(ii) State an equation relating k and R, molar gas constant.

……………………………………………………………………………………......

[1]

(c) State the process and give one practical example of each of the following :

(i) a process in which heat is supplied to a system without causing an increase in

temperature.

…………………………………………………………………………………………........

…………………………………………………………………………………………........

……………………………………………………………………………………...... [2]


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(ii) a process in which no heat enters or leaves a system but the temperature changes.

…………………………………………………………………………………………........

…………………………………………………………………………………………........

……………………………………………………………………………………......

[2]

2010 AJC H2 P2 Q3

19. A fixed mass of gas in a heat pump undergoes a cycle of changes of pressure, volume and

temper ature as illustrated in Fig. 3.1. The gas is assumed to be ideal.

a. Determine the number of moles of the gas.

b. Complete the table below indicating the energy changes in each stage of the cycle.

Increase in internal

energy / J

Heat supplied to gas /

J

Work done on gas / J

A to B 720 0

B to C -810

C to D -360 0

D to A

c. State one practical use of such a heat pump.

END

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H2 Physics 2012 - PBworks

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