MS.RAJA ELGADY/FORCE /PAPER 3 - …€¦ · MS.RAJA ELGADY/FORCE /PAPER 3 1-Fig. 4.1 shows a heavy...

MS.RAJA ELGADY/FORCE /PAPER 31- Fig. 4.1 shows a heavy ball B of weight W suspended from a fixed beam by two ropes P and Q.

beam

P30 N

Q30 N

45° 45°B

W

Fig. 4.1

P and Q are both at an angle of 45° to the horizontal. The tensions in P and Q are each 30N.

(a) In the space below, draw a scale diagram to find the resultant of the tensions in P and Q. Usea scale of 1.0cm to represent 5.0N. Label the forces and show their directions with arrows.

resultant = ............................................... [4]

(b) State the direction of the resultant. ...................................................................................... [1]

(c) State the magnitude of W. magnitude of W = ............................................... [1]

[Total: 6]

MS.RAJA ELGADY/FORCE /PAPER 32 (a) (i) Mass is a scalar quantity.

State another scalar quantity.

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

(ii) Force is a vector quantity.

State another vector quantity.

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

(b) A boat is floating on still water.

The mass of the boat is 290000kg. A resultant force of 50kN acts on the boat.

Calculate the acceleration of the boat.

acceleration = ...........................................................[3]

(c) Fig. 2.1, not to scale, shows the view from above of the boat, now on a fast-flowing river. Theboat accelerates.

Two forces are shown acting on the boat. The resultant of these forces is at right angles to theriver banks.

river bank

direction offorce on boat

from rivercurrent

direction offorce from

engine

boat

direction ofriver current

river bank

Fig. 2.1 (not to scale)

23

© UCLES 2011 0625/31/M/J/11 [Turn over© UCLES 2011 0625/31/M/J/11

MS.RAJA ELGADY/FORCE /PAPER 3Fig. 2.2 is an incomplete vector diagram of the forces acting on the boat.

resultant force

force from river current

Fig. 2.2

The force from the river current is 80kN.

(i) Determine the scale that has been used in the vector diagram.

scale is ...............................................................

(ii) On Fig. 2.2, complete the vector diagram to determine the magnitude and direction of theforce from the engine. Measure the angle between the direction of the current and theforce from the engine.

magnitude of force from engine = ...............................................................

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

[Total: 9]

33


MS.RAJA ELGADY/FORCE /PAPER 3

3- In a laboratory, an experiment is carried out to measure the acceleration of a trolley on a horizontaltable, when pulled by a horizontal force.

forcetrolley

Fig. 1.1

The measurements are repeated for a series of different forces, with the results shown in the tablebelow.

force /N 4.0 6.0 10.0 14.0

accelerationm/s2

0.50 0.85 1.55 2.25

43


MS.RAJA ELGADY/FORCE /PAPER 3(a) On Fig. 1.2, plot these points and draw the best straight line for your points. [2]

16

force / N

12

8

4

00 0.5 1.0 1.5 2.0

accelerationm / s2

2.5

Fig. 1.2

53


MS.RAJA ELGADY/FORCE /PAPER 3(b) The graph shows that below a certain force there is no acceleration.

(i) Find the value of this force. ............................................................................................ [1]

(ii) A force smaller than that in (b)(i) is applied to the stationary trolley. Suggest what happensto the trolley, if anything.

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

(c) Show that the gradient of your graph is about 5.7.

gradient = ...........................................................[1]

(d) (i) State the equation that links resultant force F, mass m and acceleration a.

[1]

(ii) Use your gradient from (c) to find the mass of the trolley.

mass = ...........................................................[2]

(e) On Fig. 1.3, sketch a speed/ time graph for a trolley with constant acceleration.

speed

00time

Fig. 1.3[1]

[Total: 9]

63


MS.RAJA ELGADY/FORCE /PAPER 34- The period of the vertical oscillations of a mass hanging from a spring is known to be

constant.

(a) A student times single oscillations with a stopwatch. In 10 separate measurements, thestopwatch readings were:

1.8s, 1.9s, 1.7s, 1.9s, 1.8s, 1.8s, 1.9s, 1.7s, 1.8s, 1.8s.

What is the best value obtainable from these readings for the time of one oscillation?Explain how you arrive at your answer.

best value = ......................................................................................... ............................

explanation ......................................................................................................................

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

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

(b) Describe how, using the same stopwatch, the student can find the period of oscillationmore accurately.

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

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

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

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

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

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

............................................................................................................................. ........ [4] [Total: 5]

6- (a) (i) Write down the names of three man-made devices in everyday use that depend,for their action, upon the moments of forces.

1. ............................................................................................................... ................

2. ........................................................................................................................... ....

3. ...................................................................................................... .........................[2]

73


MS.RAJA ELGADY/FORCE /PAPER 3F

F

(ii) Fig. 3.1 shows a uniform rod AB acted upon by three equal forces F.For

Examiner’sUse

F

A B

Fig. 3.1

State two reasons why the rod is not in equilibrium.

1. ........................................................................................................................... ....

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

83


MS.RAJA ELGADY/FORCE /PAPER 3(b) Fig. 3.2 shows a uniform rod PQ, supported at its centre and held in a horizontal position.

The length of PQ is 1.00m.For

Examiner’sUse

0.30 m1.00 m

P Q

12 N S

Fig. 3.2

A force of 12N acts at a distance of 0.30m from the support. A spring S, fixed at itslower end, is attached to the rod at Q.

(i) Calculate the force exerted on PQ by the spring.

force = .................................................. [2]

(ii) Explain why it is not necessary to know the weight of PQ.

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

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

[Total: 7]

93


MS.RAJA ELGADY/FORCE /PAPER 37- (a) A certain volume of water at room temperature and the same volume of ice in a freezer

are each heated through the same temperature rise.

Which of them will have the greater expansion, and why?

Which? .............................................................................................................................

Why? .......................................................................................................................... [1]

(b) For strength, concrete pillars are usually reinforced with metal rods, which are embeddedin the concrete before it sets.

The list below shows how much a length of 1m of each material expands when thetemperature rises by 1°C.

ForExaminer’s

Use

aluminium 0.03 mm

concrete 0.01mm

steel 0.01mm

Use this information to decide which metal should be used to reinforce concrete, why itis suitable, and why the other metal is not suitable.

Which metal should be used? ..........................................................................................

Why is it suitable? ............................................................................................................

Why is the other metal unsuitable? ..................................................................................

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

[Total: 4]

103

© UCLES 2011 0625/31/O/N/11 [Turn over© UCLES 2011 0625/31/O/N/11

MS.RAJA ELGADY/FORCE /PAPER 38- (a) State the two conditions required for the equilibrium of a body acted upon by a number of

forces.

1. ............................................................................................................................. ..................

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

2. ................................................................................................... ............................................

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

(b) Fig. 3.1 shows a diagram of an arm with the hand holding a weight of 120N.

F

2 cm

P

15 cm 20 N33 cm

120N

Fig. 3.1

The 20 N force is the weight of the forearm, acting at its centre of mass. F is the force in themuscle of the upper arm. P is the point in the elbow about which the arm pivots. The distancesof the forces from point P are shown.

(i) By taking moments about point P, calculate the force F.

force F = ...........................................................[3]

(ii) A force acts on the forearm at point P. Calculate this force and state its direction.

113


MS.RAJA ELGADY/FORCE /PAPER 3force = ...............................................................

direction = ...........................................................[2]

[Total: 7]

123


MS.RAJA ELGADY/FORCE /PAPER 39- Fig. 2.1 shows a steam safety valve. When the pressure gets too high, the steam lifts the

weight W and allows steam to escape.Examiner’s

Use

0.2 m

pivot

W

force ofsteam

Fig. 2.1

(a) Explain, in terms of moments of forces, how the valve works.

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

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

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

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

(b) The moment of weight W about the pivot is 12Nm. The perpendicular distance of theline of action of the force of the steam on the valve from the pivot is 0.2m.

The area of the piston is 0.0003m2.

Calculate

(i) the minimum steam force needed for the steam to escape,

force = ................................................ [2]

(ii) the minimum steam pressure for the steam to escape.

133


MS.RAJA ELGADY/FORCE /PAPER 3pressure = ................................................ [2]

[Total: 6]

143


MS.RAJA ELGADY/FORCE /PAPER 310- Fig. 2.1 shows a steam safety valve. When the pressure gets too high, the steam lifts the

weight W and allows steam to escape.

Examiner’sUse

0.2 m

pivot

W

force ofsteam

Fig. 2.1

(a) Explain, in terms of moments of forces, how the valve works.

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

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

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

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

(b) The moment of weight W about the pivot is 12Nm. The perpendicular distance of theline of action of the force of the steam on the valve from the pivot is 0.2m.

The area of the piston is 0.0003m2.

Calculate

(i) the minimum steam force needed for the steam to escape,

force = ................................................ [2]

(ii) the minimum steam pressure for the steam to escape.

153


MS.RAJA ELGADY/FORCE /PAPER 3pressure = ................................................ [2]

[Total: 6]

163


MS.RAJA ELGADY/FORCE /PAPER 311- (a) A spring of original length 3.0cm is extended to a total length of 5.0cm by a forceof

8.0N.

Assuming the limit of proportionality of the spring has not been reached, calculate theforce needed to extend it to a total length of 6.0 cm.

force = ................................................ [3]

(b) Fig. 3.1 shows the arrangement for an experiment on moments.

Examiner’sUse

pivotspring

F

173


MS.RAJA ELGADY/FORCE /PAPER 3metre rule

Fig. 3.1

The spring exerts a force F on the metre rule.

(i) On Fig. 3.1, mark another quantity which must be measured to find themoment of the force F.[1]

(ii) State how the moment of the force F is calculated.

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

.................................................................................. .......................................... [1] [Total: 5]

12- A student sets up the apparatus shown in Fig. 2.1 in order to find the resultant of the twotensions T1 and T2 acting at P. When the tensions T1, T2 and T3 are balanced, the anglesbetween T1 and the vertical and T2 and the vertical are as marked on Fig. 2.1.

ForExaminer’s

Use

pulley

pulley T1 = 6.0 N T2 = 8.0 N44°

verticalboard

183


MS.RAJA ELGADY/FORCE /PAPER 369°

P

T3

Fig.2.1

In the space below, draw a scale diagram of theforces T1 and T2. Use the diagram to find theresultant of the two forces.

State

(a) the scale used,

scale = ........................................ (b) the value of

the resultant, value =

........................................ (c) the direction of the

R

193


MS.RAJA ELGADY/FORCE /PAPER 3resultant. direction =

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

13- A mass of 3.0 kg accelerates at 2.0 m/s2 in a straight line.

(a) State why the velocity and the acceleration are bothdescribed as vector quantities.

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

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

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

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

(b) Calculate the force required to accelerate the mass.

force = ………………. [2]

(c) The mass hits a wall.The average force exerted on thewall during the impact is 120 N. Thearea of the mass in contact with thewall at impact is 0.050 m2.Calculate the average pressure that the mass exerts onthe wall during the impact.

pressure = ………………. [2]

203


MS.RAJA ELGADY/FORCE /PAPER 314- Fig. 2.1 shows apparatus for investigating moments offorces. For

Examiner’sUse

springbalance horizontally balanced

metre rule

0 10 20 30 40 50 60 70 80 90 100

6.0 Nweight

horizontal pivot

Fig. 2.1

The uniform metre rule shown in Fig. 2.1 is in equilibrium.

(a) Write down two conditions for the metre rule to be in equilibrium.

condition 1 .................................................................................................................. ......

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

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

condition 2 ........................................................................................ ................................

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

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

(b) Show that the value of the reading on the spring balance is 8.0 N. [2]

(c) The weight of the uniform metre rule is 1.5 N.

Calculate the force exerted by the pivot on the metre rule.

magnitude of force = …………………………………

direction of force ………………………………… [2]


MS.RAJA ELGADY/FORCE /PAPER 315-Fig 3-1 show hydrolic

car support

hydraulic fluid

4 pistons, eachof area 0.02 m2

piston A, area 0.01m2

Fig. 3.1

The hydraulic fluid transmits the pressure, caused by piston A, equally to each of the four pistonsholding up the car supports. The pressure throughout the fluid is the same.

A force of 1000N on piston A is just enough to raise the car.

(a) Using values from Fig. 3.1, find

(i) the pressure caused by piston A on the fluid,

pressure = ......................................................... [2]

(ii) the total upward force caused by the fluid.


MS.RAJA ELGADY/FORCE /PAPER 3force = ......................................................... [3]


MS.RAJA ELGADY/FORCE /PAPER 3(b) The weight of each of the two car supports is 1000N.

Calculate the mass of the car.

mass = ......................................................... [2] [Total: 7]

3


MS.RAJA ELGADY/FORCE /PAPER 316-A student investigated the stretching of a spring by hanging various weights from it and

measuring the corresponding extensions. The results are shown below.For

Examiner’sUse

weight /N 0 1 2 3 4 5

extension /mm 0 21 40 51 82 103

(a) On Fig. 3.1, plot the points from these results. Do not draw a line through the points yet.[2]

120

100

extension / mm

80

60

40

20

00 1 2 3 4 5 6

weight / N

Fig. 3.1


MS.RAJA ELGADY/FORCE /PAPER 3(b) The student appears to have made an error in recording one of the results.

Which result is this?

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

ForExaminer’s

Use

(c) Ignoring the incorrect result, draw the best straight line through the remaining points.[1]

(d) State and explain whether this spring is obeying Hooke’s Law.

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

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

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

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

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

(e) Describe how the graph might be shaped if the student continued to add several moreweights to the spring.

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

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

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

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

(f) The student estimates that if he hangs a 45N load on the spring, the extension will be920mm.

Explain why this estimate may be unrealistic.

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

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

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

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

[Total: 8]



45° A

B

17- (a) In an accident, a truck goes off the road and into a ditch. Two breakdown vehicles Aand

B are used to pull the truck out of the ditch, as shown in Fig. 4.1.

ForExaminer’s

Use

road

breakdownvehicles

ditch

Fig. 4.1




MS.RAJA ELGADY/FORCE /PAPER 3At one point in the rescue operation, breakdown vehicle A is exerting a force of 4000Nand breakdown vehicle B is exerting a force of 2000N.

(i) Using a scale of 1cm = 500N, make a scale drawing to show the resultant force onthe truck.

[4]

(ii) Use your diagram to find the magnitude and direction of the resultant force on thetruck.

magnitude of resultant force = ......................................................

direction of resultant force = ............................... to direction of road [2]

(b) (i) State why the resultant force is an example of a vector quantity.

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

(ii) Give an example of a vector quantity that is not a force.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.


MS.RAJA ELGADY/FORCE /PAPER 3..........................

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

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

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

[Total: 8]

18- Fig. 1.1 shows apparatus used to find a relationship between the force applied to a trolleyand the acceleration caused by the force.

ForExaminer’s

Use

string trolleyticker-tape

ticker-tapetimer roll of tape

hanging mass runway

Fig. 1.1

For each mass, hung as shown, the acceleration of the trolley is determined from the tape.Some of the results are given in the table below.

weight of the hanging mass /N acceleration of the trolleym/s2

0.20 0.25

0.40 0.50

0.70

0.80 1.0

(a) (i) Explain why the trolley accelerates.

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

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

(ii) Suggest why the runway has a slight slope as shown.

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

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

(b) Calculate the mass of the trolley, assuming that the accelerating force is equal to theweight of the hanging mass.



mass = ................................................ [2]




MS.RAJA ELGADY/FORCE /PAPER 3(c) Calculate the value missing from the table. Show your working.

value = ................................................ [2]

(d) In one experiment, the hanging mass has a weight of 0.4N and the trolley starts fromrest.

Use data from the table to calculate

(i) the speed of the trolley after 1.2s,

speed = ................................................ [2]

(ii) the distance travelled by the trolley in 1.2s.

distance = ................................................ [2] [Total: 11]

2

F

i

g

.

2

.

1

s

h

o

w

s

a


MS.RAJA ELGADY/FORCE /PAPER 319- circular metal

disc of mass 200

g, freely pivoted

at its centre. pivot

Fig. 2.1

Masses of 100g, 200g, 300g, 400g, 500g and 600g are available, but only one of eachvalue. These may be hung with string from any of the holes. There are three small holes oneach side of the centre, one at 4.0cm from the pivot, one at 8.0cm from the pivot and one at12.0cm from the pivot.

The apparatus is to be used to show that there is no net moment of force acting on a bodywhen it is in equilibrium.

(a) On Fig. 2.1, draw in two different value masses hanging from appropriate holes. Thevalues of the masses should be chosen so that there is no net moment. Alongside themasses chosen, write down their values. [2]

(b) Explain how you would test that your chosen masses give no net moment to the disc.

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

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

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

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

(c) Calculate the moments about the pivot due to the two masses chosen.

m

o

m

e

n

t

d

u

e

t

o

f

i

r

s

t

m

a

s

s


MS.RAJA ELGADY/FORCE /PAPER 3= ..................................................... moment due to second mass

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

ForExaminer’s

Use


MS.RAJA ELGADY/FORCE /PAPER 320- In an experiment, forces are applied to a spring as shown in Fig. 2.1a. The results of this

experiment are shown in Fig. 2.1b.For

Examiner’sUse

16RR

QQ

ruler

spring

force/N

12

8.0 PP

4.0

weights

00 2.0 4.0 6.0

extension/mm


MS.RAJA ELGADY/FORCE /PAPER 3Fig. 2.1a Fig. 2.1b

(a) What is the name given to the point marked Q on Fig. 2.1b?

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

(b) For the part OP of the graph, the spring obeys Hooke’s Law.State what this means.

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

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

(c) The spring is stretched until the force and extension are shown by the point R on thegraph. Compare how the spring stretches, as shown by the part of the graph OQ, withthat shown by QR.

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

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

(d) The part OP of the graph shows the spring stretching according to the expression

F = kx.

Use values from the graph to calculate the value of k.

k =..................................[2]


MS.RAJA ELGADY/FORCE /PAPER 3(d) Calculate the force on the pivot when the two masses chosen are hanging from

the disc.

force = ................................................ [2] [Total: 7]


MS.RAJA ELGADY/FORCE /PAPER 321- Fig. 2.1 shows a simple pendulum that swings backwards and forwards between P andQ.

support

string

ForExaminer’s

Use

P QR pendulum bob

Fig. 2.1

(a) The time taken for the pendulum to swing from P to Q is approximately 0.5 s.

Describe how you would determine this time as accurately as possible.

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

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

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

(b) (i) State the two vertical forces acting on the pendulum bob when it is at position R.

1. ........................................................................................................................... ....

2. .......................................................................................................................... [ 1]

(ii) The pendulum bob moves along the arc of a circle. State the direction of theresultant of the two forces in (i).

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

(c) The mass of the bob is 0.2 kg. During the swing it moves so that P is 0.05 m higherthan R.

Calculate the increase in potential energy of the pendulum bob between R and P.

potential energy = ………………. [2]


MS.RAJA ELGADY/FORCE /PAPER 322- (a) State Hooke’s law.

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

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

(b) Fig. 1.1 shows a graph of the stretching force F acting on a spring against the extensionx of the spring.

ForExaminer’s

Use

250

200

F / N

150

100

50

00 10 20 30 40 50 60 70 80

x /mm

Fig. 1.1

(i) State the features of the graph that show that the spring obeys Hooke’s law.

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

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

(ii) Calculate k, the force per unit extension of the spring.


MS.RAJA ELGADY/FORCE /PAPER 3k = ................................................... [3]



MS.RAJA ELGADY/FORCE /PAPER 3(iii) The limit of proportionality of the spring is reached at an extension of 50mm.

Continue the graph in Fig. 1.1 to suggest how the spring behaveswhen the stretching force is increased to values above 125N.

[1]

(iv) Another spring has a smaller value of k. This spring obeys Hooke’slaw for extensions up to 80mm.

On the grid of Fig. 1.1, draw a possible line of the variation of F withx for this spring.

[1]

[Total: 7]

MS.RAJA ELGADY/FORCE /PAPER 323- (a) A force acting on an object causes the object to accelerate.

In which direction is the acceleration?

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

(b) Any object moving in a circle has a force acting on it towards the centre of thecircle.

What does this force do to the object?

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

....... [1]

(c) A woman of mass 60kg is standing in a lift at a shopping centre.

(i) The lift is at rest.

1. State the value of the weight of the woman.

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

2. State the value of the force exerted on the woman by the floor of thelift.

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

....... [1]

(ii) Calculate the force required to accelerate a mass of 60kg at 2.5m/s2.

force = ................................................ [2]

(iii) The lift accelerates upwards at 2.5m/s2.

Calculate the force exerted on the woman by the floor when the lift isaccelerating.

force = ................................................ [1]

(iv) The lift reaches a steady upward speed.

MS.RAJA ELGADY/FORCE /PAPER 3State the value of the force exerted on the woman by the floor atthis steady speed.

............................................................................................................................ [1] [Total:

8]


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MS.RAJA ELGADY/FORCE /PAPER 3 - …€¦ · MS.RAJA ELGADY/FORCE /PAPER 3 1-Fig. 4.1 shows a heavy...

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