Practice Test 3, No. 1

1. A simple pendulum has a frequency of 6 Hz. For a simple pendulum, it is known that the angular acceleration is related to the angular displacement through the relationship (angular acceleration) = - (g/L) times (angular displacement), where L is the length of the pendulum. To increase its frequency to 12 Hz, you should (a) increase its length by a factor of 4. (b) increase its length by a factor of 2. (c) decrease its length by a factor of 2. (d) decrease its length by a factor of 4. (e) increase its mass by a factor of 4.

2. In simple harmonic motion, the magnitude of the acceleration is least when the (a) displacement is zero. (b) displacement is maximum. (c) velocity is a minimum. (d) force is the greatest. (e) None of the above.

3. A string is attached horizontally between two supports. A wave is created in the string such that three antinodes are observed in the resulting standing wave pattern. The wave desribed is a (a) fundamental. (b) first overtone. (c) second overtone. (d) third overtone. (e) fourth overtone.

4. A weight, suspended from a spring, oscillates up and down. If the amplitude of the oscillation is doubled, the period will (a) remain the same. (b) double. (c) halve. (d) increase by a factor of SQRT(2). (e) decrease by a factor of SQRT(2).

5. A sound wave is a (a) longitudinal wave. (b) transverse wave. (c) standing wave. (d) shock wave. (e) none of these.

6. A typical tape using Dolby noise reduction has a "signal to noise ratio" of 62 db. If Is is the intensity of the signal, and In is the intensity of the noise, the 62 db signal to noise ratio is calculated rom which of the following? (a) 62*62 (b) 10 E 62. (c) Log (Is/In). (d) 10 Log (Is/In). (e) e E Log(10+3).

7. If glass had a higher coefficient of thermal expansion than mercury, then the column of mercury in a mercury thermometer would rise when the temperature (a) increases. (b) decreases. (c) The level of the mercury would remain fixed over all temperatures. (d) It depends upon the cross sectional area of the thermometer. (e) None of the above.

8. Two containers of equal volume contain different ideal gases at equal pressure and temperature. It follows that (a) both containers hold the same number of gas molecules. (b) the total mass of gas in the two containers is equal. (c) the average speed of the gas molecules in the containers is equal. (d) the density of the two gases is equal. (e) one container is red, the other is blue.

9. A bimetallic bar is a bar made of two strips of different metals and is commonly used in thermostats. When a bar made of copper and iron is heated, the bar bends towatd the iron strip. The reason for this is (a) iron gets hotter before copper. (b) copper gets hotter before iron. (c) the coefficient of linear expansion is larger for iron than copper. (d) the coefficient of linear expansion is larger for copper than iron. (e) None of the above.

10. Hydrogen and oxygen molecules in a sample of gas have the same temperature. This means that the hydrogen molecules, on the average, have the same (a) speed, and the smae kinetic energry. (b) speed, but more kinetic energy. (c) speed, but less kinetic energy. (d) kinetic energy, but more speed. (e) kinetic energy, but less speed.

11. The rate of heat flow through a slab is H. If the slab thickness is doubled, its cross-sectional area is halved, and the temperature difference across it is doubled, then the rate of heat flow becomes (a) 2H. (b) H/2. (c) H. (d) H/8. (e) 8H.

12. Temperatueres in both the Fahrenheit and Celsius scales can be negative, but they cannot be negative in the Kelvin (absolute) scale. Why? (a) Because the Kelvin scale sets zero to be the lowest physically realizabel temperature. (b) Because Fahrenhet and Celsius used up all the coupons for negative temperatures. There were none left for Kelvin. (c) Because negative temperatures on the Kelvin scazle would be a violation of the Third Law of Thermodynamics. (d) Because negative temperatures would imply negative momentum. This cannot happen. (e) Temperatures on the Kelvin scale can be negative.

13. When 100 grams of copper at 100oC is added to 100 grams of water at 20oC, the resulting temperature of the mixture will be (a) between 20oC and 60oC. (b) 60oC. (c) between 60oC and 100oC. (d) dependent on the heat of vaprization of the water. (e) There is not enough information provided to answer this question.

14. In which of the following processes is the heat transfer primarily by conduction? (a) The heating of the earth by the sun. (b) A metal rod is heated at one end and eventually beomes hot at the other end. (c) The motion of material from the interior to the exterior of the sun transfers the heat. (d) The warmth a person feels while standing near a fire. (e) None of the above.

15. An object executes simple harmonic motion at the end of a spring of spring constant 4 N/m.. The amplitude is 5 cm and the frequency is 2 Hz. At t = 0, the object is at its equilibrium position. What is the equation of motion for this object (all numbers are in mks)? (a) x = 0.05 cos(4 pi t). (b) x = 0.05 sin(4 pi t). (c) x = 0.05 cos(2t). (d) x = 0.05 sin(2t). (e) None of the above.

16. The total energy of the object in the previous question is (a) 0.001 J. (b) 0.002 J. (c) 0.003 J. (d) 0.004 J. (e) 0.005 J.

17. A block is slid across a frictionless, level table top. It strikes a horizontal spring, and as a result, the spring is compressed .02 m before the block comes to rest. The spring constant is 10 N/m. What was the kinetic energy (in Joules) of the block before it collided with the spring? Assume no losses due to heat. (a) 0.001. (b) 0.002. (c) 0.02. (d) 0.1. (e) 0.2.

18. A balloon is filled with helium until it reaches a volume of 1 m3. If the temperature of the helium is now lowered until the balloon is half its original volume, how much work has been done by the helium (in atm-m3)? Assume that the process occurs at a pressure of 1 atm. Also assume that helium is an ideal gas. (a) -1.0. (b) -0.5. (c) 0.0. (d) 0.5. (e) 1.0.

19. An ideal gas is at 1 atm, 20 oC, and is contained in a container of fixed volume. In order to double the pressure, the temperature should be changed to (a) 0oC. (b) 40oC. (c) 273oC. (d) 313oC. (e) 586oC.

20. One mole of an ideal gas expands slowly and isothermally at temperature T until its volume is doubled. The work done during this process is 5 J. The change in entropy of this gas for this process is (everything is in SI units) (a) 25/T2. (b) 5/T. (c) zero. (d)5T. (e) 25T2.

21. A flagpole is attached rigidly to a vertical wall, in such a way that the pole is horizontal. The length of the pole is 4 m. (a) Sketch the shape of the fundamental and first 3 overtones associated with the possible standing wave patterns which can be produced in the pole (identify which is which). In each case, what is the wavelength for each standing wave? (B) If the wave velocity for the pole is 10 m/sec, what is the frequency for each pattern, and what is the GENERAL rule governing the frequencies?

22. Two samples of ideal gas are originally at the same temperatue and pressure. They are each compressed reversibly from a volume V to a volume V/2, one isothermally and the other adiabatically. (a) For which sample will the final pressure be greater? Explain. (b) determine the change in entropy for the gas in each process.

ANSWER KEY: 1.D 2.A 3.C 4.A 5.A 6.D 7.B 8.A 9.D 10.D 11.B 12.A 13.A 14.B 15.B 16.E 17.B 18.D 19.D 20.B

Practice Test 3, Number 2

1. A spring is compressed through some distance. The work done by the person compressing the spring will be (a) zero. (b) positive. (c) negative. (d) vertical. (e) horizontal.

2. The frequency of a spring undergoing simple harmonic motion can be increased by (a) increasing the spring constant. (b) decreasing the spring constant. (c) increasing the mass. (d) decreasing the mass. (e) Both (a) and (d).

3. Two waves run into each other, and it is observed that the waves dissapear during the collision. This is an example of (a) wave intensity. (b) resonance. (c) constructive interference. (d) destructive interference. (e) forced vibration.

4. A wave is created in water. As the wavelength of the wave increases, the wave velocity (a) increases. (b) decreases. (c) remains the same. (d) The answer depends upon the direction in which the wave is traveling. (e) The answer depends upon the amplitude of the wave.

5. A string vibrates at a frequency of 1 Hz. The length of the string is 25 m, and the wave velocity of the wave is 100 m/sec. Using your understanding of harmonics, which of the following boundary conditions is most apprpriate for this string? This question is not an easy question; good luck! (a) Node-node. (b) Node-antinode. (c) Antinode-antinode. (d) There is not enough information given. (e) All of the above.

6. A string vibrates at a frequency of 1 Hz. The length of the string is 25 m, and the wave velocity of the wave is 100 m/sec. This string is appearently vibrating in which of the following modes? This question is not an easy question; good luck! (a) The fundamental mode of vibration. (b) The first overtone. (c) The second overtone. (d) The third overtone. (e) The fourth overtone.

7. If you wanted to know how high the mercury in a thermometer would rise for a givewn temperature increase, which of the following would be most useful to know (in addition to the dimensions of the thermometer)? (a) The coefficient of linear expansion ofr mercury. (b) The specific heat of mercury. (c) The thermal conductivity of mercury. (d) The melting point of mercury. (e) The density of mercury.

8. The specific heat of copper is 0.093 kcal/kg-oC while the specific heat of water is 1.00 kcal/kg-oC. A piece of copper and an amount of water both have the same mass and are at the same temperature. If they are heated so that the same amount of heat is transfered into each, which will have the higher temperature? (a) The water. (b) The copper. (c) Both will have the same final temperature. (d) It dependes upon the number of moles of each. (e) Not enough information given.

9. When a metal ring is heated, the hole becomes (a) Frank Sinatra. (b) Bigger. (c) Smaller. (d) The hole remains the same size. (e) All of the above.

10. When 100 grams of copper at 100oC is added to 100 grams of water at 20oC, the resulting temperature of the mixture will be (a) between 20oC and 60oC. (b) 60oC. (c) between 60oC and 100oC. (d) dependent on the heat of vaprization of the water. (e) There is not enough information provided to answer this question.

11. A container contains an ideal gas. What force (on the average) is extered on the wall perpendicular to an axis perpendicular to the wall (the x-axis) by a particle in the gas? (a) mv. (b) ( m vx2)/L (c) ½mv2. (d) 6. (e) zero.

12. Two different samples have the same mass and temperature. Equal quantities of heat are added to each. Their final temperatures will be different if the samples have different (a) thermal conductivity. (b) coefficient of expansion. (c) density. (d) volume. (e) specific heats.

13. The temperature of a solid is increased until the solid begins to melt. While the solid is melting (A) it's temperature remains constant. (b) it's temperature continues to increase. (c) the temperature actulaay decreases because some heat is lost in the form of latent heat. (d) the temperature goes up and down and all around. (e) There is not enough information given to answer this question.

14. The real efficiency of an engine is given by (TL is the temperature at the exhaust end of the engine, TH is thetemperature at the input end, W is the work done, QL is the exhaust heat, and QH is the input heat) (A) TL/TH. (b) 1 - (TL/TH). (c) 1 - (TH/TL). (d) W/QL. (e) W/QH.

15. One mole of an ideal gas expands slowly and adiabatically until its volume is doubled. The change in entropy of this gas for this process is (everything is in SI units) (a) 4/T2. (b) 2/T. (c) zero. (d)2T. (e) 4T2.

16. A floating leaf oscillates up and down two complete cycles in one second as a water wave passes by. The wave's wavelength is 10 meters. What is the wave's speed? (a) 2 m/s. (b) 10 m/s. (c) 20 m/s. (d) 40 m/s. (e) more than 40 m/s.

17. A mass on the end of a spring executes simple harmonic motion with an amplitude of 10 cm and angular frequency of 3 Hz. At t = 0, the mass is at 5 cm. Which of the following equations of motion best describes the motion? (a) x = vot+at^2. (b) x = (10 cm) cos (3t). (c) x = (10 cm) sin (3t). (d) x = (10 cm) cos (3t + 60) (e) x = (10 cm) cos (3t + 30).

18. An ideal gas is at 1 atm, 20 oC, and is contained in a container of fixed volume. In order to double the pressure, the temperature should be changed to (a) 0oC. (b) 40oC. (c) 273oC. (d) 313oC. (e) 586oC.

19. A tank is filled with an Ideal gas. The pressure of the gas is 10 N/m , and the temperature is 100 C. If the temperature of the gas is increased to 200 C, what is the new pressure (in N/m )? (a) 10. (b) 20. (c) 30. (d) 40. (e) None of the above.

20. By what factor will the rms speed of an ideal gas be increased if the temperature of the gas is changed from 10 C to 1000 C? (a) 1.85 (b) 3.16 (c) 10 (d) 100 (e) None of the above.

21. A vertical spring stretches 0.150 m when a 0.300 kg mass is hung from it. The spring is then stretched an addtional 0.100 m from it's equilibrium point and released. (A) What is the spring constant? (B) What is the amplitude of hte oscillation? (c) What is the maximum velocity? (D) What is the total energy of the oscillation?

22. An ideal gas is carried through a cycle quasistatically. The gas starts at state "a," is expanded isobarically to state "b," the pressure is then lowered at constant volume to state "c," the volume is then decresed isobarically to state "d,' and then the pressure is increased at constant volume back to state "a." A diagram might help in this. Use the following information: Pa = 4 x 105 Pa. Pc = 2 x 105 Pa. Va = 1.5 x 10-6 m3. Vb = 4 x 10-6 m3. (a) What is the net amount of work done in the cycle ABCDA? (b) How much heat is transfered in the cycle? Is the heat added or extracted from the gas? (c) Which point (A, B, C, or D) is atthe lowest temperature? Which is at the highest temperature? Explain why CLEARLY. (d) What is the Carnot efficiency for this cycle?

ANSWER KEY: 1.B 2.E 3.D 4.C 5.B 6.A 7.A 8.B 9.B 10.A 11.B 12.E 13.A 14.E 15.C 16.C 17.D 18.D 19.E 20.E