1994 Physics Olympiad Screening Test (1-20)

1. A motorist travels 320 km at 80 km/h and then 320 km at 100 km/h. What is the average speed of the motorist for the entire trip?

A. 84 km/h
B. 89 km/h
C. 90 km/h
D. 91 km/h
E. 95 km/h

2. A sports car is stopped at a light. At t = 0 the light changes and the sports car accelerates at a constant 2.0 m/s² . At t = (10/3) seconds a station wagon traveling at a constant 15 m/s in the same direction passes the stop light. When does the station wagon catch up to the sports car?

A. never
B. t = 5.0 s
C. t = 7.5 s
D. t = 12 s
E. t = 21 s

3. A ball is thrown from ground level with an initial velocity of v_o in the upward direction. It reaches a maximum height y and returns to ground level at time t seconds after it was thrown. If its initial velocity is doubled, it will be in the air _____ seconds and reach a maximum height _____.

A. t, 4y
B. 2t, y
C. 2t, 2y
D. 2t, 4y
E. 4t, 2y

4. The ball in the preceding question (#3) is taken to Mars where the acceleration due to gravity is approximately 4 m/s² (0.4 g_E). It is thrown from ground level with the same initial velocity as it originally had on Earth, v_o in the upward direction. On Mars, it will be in the air _____ seconds and reach a maximum height _____.

A. 0.4 t, 2.5 y
B. 0.4 t, 6.25 y
C. 2.5 t, 2.5y
D. 6.25 t, 2.5 y
E. 6.25 t, 6.25 y

5. A top is spinning in the direction shown in the accompanying figure. Its axis of rotation makes an angle of 15º with the vertical. Assume friction can be neglected.

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The magnitude of the top’s angular momentum will _____ while its direction will _____.

A. increase, precess in the counterclockwise direction when seen from above.
B. increase, not precess
C. remain the same, not precess
D. remain the same, precess in the clockwise direction when seen from above.
E. remain the same, precess in the counterclockwise direction when seen from above.

6. Three air track cars, shown in the accompanying figure, all have the same mass m. Cars 2 and 3 are initially at rest. Car 1 is moving to the right with speed v. Car 1 collides with car 2 and sticks to it. The 1-2 combination collides elastically with car 3. Which of the following is most nearly the final speed of the 1-2 combination?

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A. 0.17 v
B. 0.50 v
C. 0.67 v
D. 0.80 v
E. 1.0 v

7. A cube with mass M starts at rest at point 1 at a height 4R, where R is the radius of the circular part of the track. The cube slides down the frictionless track and around the loop. The force that the track exerts on the cube at point 2 is most nearly _____ times the cube’s weight Mg.

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A. 1
B. 2
C. 3
D. 4
E. 5

8. An astronaut with weight W on Earth lands on a planet with mass 0.1 times the mass of Earth and radius 0.5 times the radius of Earth. The astronaut’s weight is _____ on the planet.

A. 0.02 W
B. 0.04 W
C. 0.2 W
D. 0.4 W
E. W

9. A horizontal force F, represented by the arrow in the figure to the right, is used to push a block of weight mg up an inclined plane making an angle of q with the horizontal. The coefficient of friction between the plane and the block is m.

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The magnitude of the frictional force acting on the block is:

A. m mg cosq
B. m mg/( cosq )
C. m ( mg cosq + F sinq )
D. m ( F cosq – mg sinq )
E. m F cosq

10. A child of mass M stands on the edge of a merry-go-round of radius R and moment of inertia I. Both the merry-go-round and child are initially at rest. The child walks around the circumference with speed v with respect to the ground. What is the magnitude of the angular velocity of the merry-go-round with respect to the ground?

11. A rigid rod of mass M and length L has moment of inertia ¹/₁₂ ML² about its center of mass. A sphere of mass m and radius R has moment of inertia ²/₅ MR² about its center of mass. A combined system is formed by centering the sphere at one end of the rod and placing an axis at the other (see accompanying figure).

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What is the moment of inertia of the combined system about the axis shown?

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12. A rocket is launched from the surface of a planet with mass M and radius R. What is the minimum velocity the rocket must be given to completely escape from the planet’s gravitational field?

13. A uniform rod of length L and weight W_R is suspended as shown in the accompanying figure.

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A weight W is added to the end of the rod. The support wire is at an angle q to the rod. What is the tension T in the wire?

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14. A hollow vertical cylinder of radius R is rotated with angular velocity w about an axis through its center.

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What is the minimum coefficient of static friction necessary to keep the mass M suspended on the inside of the cylinder as it rotates?

15. A block of mass M is attached to a relaxed spring with force constant k, placed on a frictionless inclined plane as shown in the accompanying figure, and released.

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What is the maximum extension of the spring?

16. A simple pendulum of length L and mass m is attached to a moving support. In order for the pendulum string to make a constant angle q with the vertical, the support must be moving to the:

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A. right with constant acceleration a = g tanq.
B. left with constant acceleration a = g tanq.
C. right with constant acceleration a = g sinq.
D. right with constant velocity
E. left with constant velocity

17. A Carnot cycle takes in 1000 J of heat at a high temperature of 400 K. How much heat is expelled at the cooler temperature of 300 K?

A. 0
B. 250 J
C. 500 J
D. 750 J
E. 1000 J

18. An ideal gas is expanded at constant pressure from initial volume V_i and temperature T_i to final volume V_f and temperature T_f . The gas has molar heat capacity C_P at constant pressure. The amount of work done by n moles of the gas during the process can be expressed:

19. The average translational kinetic energy of any ideal gas depends only on:

A. the absolute (Kelvin) temperature.
B. the mass of the gas.
C. the pressure of the gas.
D. the amount of the gas.
E. whether the gas is monatomic or diatomic.

20. A soap film of thickness t is surrounded by air. It is illuminated at near normal incidence by monochromatic light which has wavelength l in the film.

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A film thickness of _____ will produce maximum brightness of the reflected light.

A. ¼ l
B. ½ l
C. 1 l
D. 2 l
E. 4 l