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MSU Physics 231 Fall 2012 1 Physics 231 Final Exam Review Session Wade Fisher Dec 5-7 2012
MSU Physics 231 Fall 2012 1
Physics 231
Final Exam Review Session
Wade Fisher
Dec 5-7 2012
MSU Physics 231 Fall 2012 2
Review Problems Chapters 1-5
MSU Physics 231 Fall 2012 3
From Exam 1 A pitcher throws a ball horizontally with a speed of 39 m/s to a catcher 18.5 m away. When the ball is caught, the height has decreased by X m. Find X.
MSU Physics 231 Fall 2012 4
Same Problem Reworded A pitcher throws a ball with a speed of 39 m/s to a catcher some distance away. When caught, the ball’s height has decreased by 0.57 m. How far away is the catcher?
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And another example…
Calculate how far the ball goes.
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0.5 kg
A
20o
Is there a value for the static friction of surface A for which these masses do not slide? If so, what is it?
1 kg n Ffriction
Fg
T
T
Fg
Example
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Conservation of mechanical energy What is the speed of m1 and m2 when
they pass each other?
M2
3 kg
5 kg
M1
4.0 m
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Friction (non-conservative) The pulley is now not frictionless. The friction force equals 5 N. What is the speed of the objects when they pass?
M2
3 kg
5 kg
M1
4.0 m
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Question
A boat is trying to cross a 1-km wide river in the shortest way (straight across). Its maximum speed (in still water) is 10 km/h. The river is flowing with 5 km/h. 1) At what angle does the captain have to steer the boat the go straight across? 2) How long does it take for the boat to cross the river? 3) If it doesn’t matter at what point the boat reaches the other side, at what angle should the captain steer to cross in the fastest way?
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Question
A ball of 1 kg rolls up a ramp, with initial velocity of 6 m/s. It reaches a maximum height of 1 m (i.e., the velocity is 0 m/s at that point). How much work is done by friction?
a) 0. b) 8.2 J c) 9.8 J d) 18 J e) 27.8 J
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Review Problems Chapters 6-9
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From Exam 2 The motor for a toy Ferris wheel creates a torque of 15 Nm. The wheel requires 31 seconds to reach its design frequency of one revolution per 12 seconds. What is the moment of inertia of the wheel?
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Same Problem Reworded The motor for a toy Ferris wheel with moment of inertia 1181 kgm2 creates a torque of 15 Nm. The wheel has a design frequency of one revolution per 12 seconds. How long does it take to reach this frequency?
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Ballistic Pendulum
Mblock=1 kg
Mbullet=0.1 kg Vbullet=20 m/s
h
How high will the block go?
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An Example
A mass of 1 kg is hung from a spring. The spring stretches by 0.5 m. Next, the spring is placed horizontally and fixed on one side to the wall. The same mass is attached and the spring stretched by 0.2 m and then released. What is the acceleration upon release?
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An Example
d
h A block with mass of 200 g is placed over an opening. A spring is placed under the opening and compressed by a distance d=5 cm. Its spring constant is 250 N/m. The spring is released and launches the block. How high will it go relative to its rest position (h)? (the spring can be assumed massless)
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Conical motion
What is the speed of the mass undergoing conical motion if the mass is 1 kg and =20o? The length of the string swinging the mass is 1 m.
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Example
A monocycle (bicycle with one wheel) has a wheel that has a diameter of 1 meter. The mass of the wheel is 5 kg (assume all mass is sitting at the outside of the wheel). The friction force from the road is 25 N. If the cycle is accelerating with 0.3 m/s2, what is the force applied on each of the paddles if the paddles are 30 cm from the center of the wheel?
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There is a s=0.5 coef of friction between the wall and the 4.0 meter bar (weight w). What is the minimum x where you can hang a weight w for which the bar does not slide?
37o
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An Example
A
B star
Two planets are orbiting a star. The orbit of A has a radius of 108 km. The distance of closest approach of B to the star is 5x107 km and its maximum distance from the star is 109 km. If A has a rotational period of 1 year, what is the rotational period of B?
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Review Problems Chapters 10-14
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An Example An architect wants to design a 5m high circular pillar with a radius of 0.5 m that holds a bronze statue that weighs 1.0E+04 kg. He chooses concrete for the material of the pillar (Y=1.0E+10 Pa). How much does the pillar compress?
5m
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Another one An air mattress 2m long 0.5m wide and 0.08m thick and has a mass of 2.0 kg. A) How deep will it sink in water? B) How much weight can you put on top of the mattress before it sinks? water=1.0E+03 kg/m3
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Example
A police car using its siren (frequency 1200Hz) is driving west towards you over Grand River with a velocity of 25m/s. You are driving east over grand river, also with 25m/s. a)What is the frequency of the sound from the siren that you hear? b) What would happen if you were also driving west (behind the ambulance)? vsound=343 m/s
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An Example ?? N
1 kg of water inside thin hollow sphere
A) ?? N
7 kg iron sphere of the same dimension as in A)
B)
Two weights of equal size and shape, but different mass are submerged in water. What are the weights read out?
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And another! An airbubble has a volume of 1.50 cm3at 950 m depth (T=7oC). What is its volume when it reaches the surface (water=1.0x103 kg/m3)?
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Heating your Home A house has a floor area of 190 m2 and 2.3-m ceilings. (A)What energy (in kWh) is required to raise the air
temperature by from 20°C to 21°C at constant pressure? (specific heat of air cP=30 J/mol°C and 1 mol of air = 24 L)
(B)At $0.16/kWh, what’s the cost to heat this air by 1°C? (assume a 80% heating efficiency)
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Testing an Unknown Substance A block of unknown substance with a mass of 8 kg, initially at T=280K is thermally connect to a block of copper (5 kg) that is at T=320 K (ccopper=0.093 cal/g
0C). After the system has reached thermal equilibrium the temperature T equals 290K. What is the specific heat of the unknown material in cal/goC?
????
copper
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Examples for this chapter
One mole of an ideal gas initially at 00C undergoes an expansion at constant pressure of one atmosphere to four times its original volume. a) What is the new temperature? b) What is the work done on the gas?
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Question An ideal monatomic gas is
taken around the cycle ABCDA
as shown below.
What is the amount of energy
removed by heat during one
cycle?
a. 0
b. P1V1
c. 2P1V1
d. 4P1V1
e. Impossible to determine
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Another Example The efficiency of a Carnot engine is 30%. The engine absorbs 800 J of energy per cycle by heat from a hot reservoir at 500 K. Determine a) the energy expelled per cycle and b) the temperature of the cold reservoir. c) How much work does the engine do per cycle?
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A new powerplant is designed that makes use of the temperature difference between sea water at 0m (200) and at 1-km depth (50). A) What would be the maximum efficiency of such a plant? B) If the powerplant produces 75 MW, how much energy is absorbed per hour? C) Is this a good idea?
A New Powerplant
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Although the water is indeed hot, it releases only 1 cal/g of heat as it
cools. The steam, however, first has to undergo a phase change into
water and that process releases 540 cal/g, which is a very large amount of
heat. That immense release of heat is what makes steam burns so
dangerous.
Hot Water
Which will cause more severe burns
to your skin: 100°C water or 100°C
steam?
a) water
b) steam
c) both the same
d) it depends...
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Aluminum is the only material that has a larger b value than the
steel ring, so that means that the aluminum rod will expand more
than the steel ring. Thus, only in that case does the rod have a
chance of reaching the top of the steel ring.
Thermal Expansion
Coefficient of volume expansion b (1/°C )
Glass Hg Quartz Air
Al Steel
a) aluminum
b) steel
c) glass
d) aluminum and steel
e) all three
A steel ring stands on edge with a rod of
some material inside. As this system is
heated, for which of the following rod
materials will the rod eventually touch the
top of the ring?
