1998 Physics Olympiad Screening Test (1-20)

1. The graph to the right is a plot of position versus time. For which labeled region is the velocity positive and the acceleration negative?

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A. A
B. B
C. C
D. D
E. E

2. A child left her home and started walking at a constant velocity. After a time she stopped for a while and then continued on with a velocity greater than she originally had. All of a sudden she turned around and walked very quickly back home. Which of the following graphs best represents the distance versus time graph for her walk?

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3. In a rescue attempt, a hovering helicopter drops a life preserver to a swimmer being swept downstream by a river current of constant velocity v. The helicopter is at a height of 9.8 m. The swimmer is 6.0 m upstream from a point directly under the helicopter when the life preserver is released. It lands 2.0 m in front of the swimmer. How fast is the current flowing? Neglect air resistance.

A. 13.7 m/s
B. 9.8 m/s
C. 6.3 m/s
D. 2.8 m/s
E. 2.4 m/s

4. A child tosses a ball directly upward. Its total time in the air is T. Its maximum height is H. What is its height after it has been in the air a time T/4? Neglect air resistance.

A. (1/4) H
B. (1/3) H
C. (1/2) H
D. (2/3) H
E. (3/4) H

5. A whiffle ball is tossed straight up, reaches a highest point, and falls back down. Air resistance is not negligible. Which of the following statements are true?

I. The ball’s speed is zero at the highest point.
II. The ball’s acceleration is zero at the highest point.
III. The ball takes a longer time to travel up to the highest point than to fall back down.

A. I only
B. II only
C. I & II only
D. I & III only
E. I, II, & III

6. A pendulum is attached to the ceiling of an elevator car. When the car is parked, the pendulum exhibits a period of 1.00 s. The car now begins to travel upward with an upward acceleration of 2.3 m/s² . During this part of the motion, what will be the approximate period of the pendulum?

A. 0.80 s
B. 0.90 s
C. 1.00 s
D. 1.10 s
E. 1.20 s

7. Two identical blocks of weight W are placed one on top of the other as shown below. The upper block is tied to the wall. The lower block is pulled to the right with a force F. The coefficient of static friction between all surfaces in contact is m. What is the largest force F that can be exerted before the lower block starts to slip?

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A. mW
B. (3/2) mW
C. 2 mW
D. (5/2) mW
E. 3 mW

8. An object placed on an equal arm balance requires 12 kg to balance it. When placed on a spring scale, the scale reads 120 N. Everything (balance, scale, set of masses, and the object) is now transported to the moon where the gravitational force is one-sixth that on Earth. The new readings of the balance and the spring scale (respectively) are:

A. 12 kg, 20 N
B. 12 kg, 120 N
C. 12kg, 720 N
D. 2 kg, 20 N
E. 2 kg, 120 N

9. A large spool of rope lies on the ground. See the diagram below. The end, labeled X, is pulled a distance S in the horizontal direction. The spool rolls without slipping. The distance the spool’s center of mass moves is

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A. 2S
B. S
C. S/2
D. S/3
E. S/4

10. Air track car Z of mass 1.5 kg approaches and collides with air track car R of mass 2.0 kg. See the accompanying diagram. Car R has a spring attached to it and is initially at rest. When the separation between the cars has reached a minimum, then:

A. car R is still at rest.
B. car Z has come to rest.
C. both cars have the same kinetic energy.
D. both cars have the same momentum.
E. the kinetic energy of the system has reached a minimum.

11. Two ice skaters, a 200 lb man and a 120 lb woman, are initially hugging on a frictionless level ice surface. Ten seconds after they push off from each other, they are 8.0 m apart. How far has the woman moved in that time?

A. 8.0 m
B. 6.5 m
C. 5.0 m
D. 4.0 m
E. 3.0 m

12. The diagram below shows the velocity-time graph for two masses R and S that collided elastically. Which of the following statements is true?

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I. R and S moved in the same direction after the collision.
II. The velocities of R and S were equal at the mid-time of the collision.
III. The mass of S was greater than the mass of R.

A. I only
B. II only
C. I & II only
D. II & III only
E. I, II, & III

Questions 13 and 14 refer to the motion of two blocks along a frictionless level track. Block #1 (mass m₁) is initially moving with speed v_o. It collides with and sticks to an initially stationary block (#2) of mass m₂ = 9 m₁.

13. What is the speed of the two blocks after the collision?

A. v_o
B. (9/10) v_o
C. (8/9) v_o
D. (1/9) v_o
E. (1/10) v_o

14. What fraction of the initial kinetic energy of the system is converted to other forms (heat, sound, ...) as a result of the collision?

A. 1 %
B. 10 %
C. 50 %
D. 90 %
E. 99 %

15. Three identical objects of mass M are fastened to a massless rod of length L as shown. The array rotates about the center of the rod. Its rotational inertia is

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A. (1/2) ML²
B. ML²
C. (5/4) ML²
D. (3/2) ML²
E. 3 ML²

16 A length of rope is wrapped around a spool of weight W with inner radius r and outer radius R as shown in the accompanying diagram. The rope is pulled with a tension T at an angle q. Which of the following conditions must be satisfied for the spool to slide uniformly without rolling?

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A. cosq = r / R
B. sinq = r / R
C. T = W
D. T = W sinq
E. T = W cosq

17. Two identical bricks of length L are piled one on top of the other on a table. See the diagram below. What is the maximum distance S the top brick can overlap the table with the system still balanced?

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A. (1/2) L
B. (2/3) L
C. (3/4) L
D. (7/8) L
E. L

18. A gas contains a mixture of ⁴He and ²⁰Ne atoms. If the average speed of the ⁴He atoms is vo, what is the average speed of the ²⁰Ne atoms?

19. One end of a metal rod of length L and cross-sectional area A is held at a constant temperature T₁ . The other end is held at a constant T₂ . Which of the following statements about the amount of heat transferred through the rod per unit time are true?

I. The rate of heat transfer is proportional to 1/(T₁ - T₂ ).
II. The rate of heat transfer is proportional to A.
III. The rate of heat transfer is proportional to L.

A. II only
B. III only
C. I and II only
D. I and III only
E. II and III only

20. On all the pV diagrams shown below the lighter curve represents an isothermal process, a process for which the temperature remains constant. Which dark curve best represents an adiabatic process, a process for which no heat enters or leaves the system?

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