1997 Physics Olympiad Screening Test (1-20)

1	1. Starting from rest at time t = 0, a car moves in a straight line with an acceleration given by the accompanying graph. What is the speed of the car at t = 3 s? A. 1.0 m/s B. 2.0 m/s C. 6.0 m/s D. 10.5 m/s E. 12.5 m/s
2	2. A flare is dropped from a plane flying over level ground at a velocity of 70 m/s in the horizontal direction. At the instant the flare is released, the plane begins to accelerate horizontally at 0.75 m/s² . The flare takes 4.0 s to reach the ground. Assume air resistance is negligible. Relative to a spot directly under the flare at release, the flare lands A. directly on the spot. B. 6.0 m in front of the spot. C. 274 m in front of the spot. D. 280 m in front of the spot. E. 286 m in front of the spot.
3	3. As seen by the pilot of the plane (in question #2) and measured relative to a spot directly under the plane when the flare lands, the flare lands A. 286 m behind the plane. B. 6.0 m behind the plane. C. directly under the plane. D. 12 m in front of the plane. E. 274 m in front of the plane
4	4. A force F is used to hold a block of mass m on an incline as shown in the diagram. The plane makes an angle of q with the horizontal and F is perpendicular to the plane. The coefficient of friction between the plane and the block is m. What is the minimum force, F, necessary to keep the block at rest? A. m mg B. mg cosq C. mg sinq D. (mg/m) sinq E. (mg/m) ( sinq - m cosq )
5	5. You hold a rubber ball in your hand. The Newton’s third law companion force to the force of gravity on the ball is the force exerted by the A. ball on the Earth. B. ball on the hand. C. hand on the ball. D. Earth on the ball. E. Earth on your hand.
6	6. A ball of mass m is fastened to a string. The ball swings in a vertical circle of radius R with the other end of the string held fixed. Neglecting air resistance, the difference between the string’s tension at the bottom of the circle and at the top of the circle is A. mg B. 2 mg C. 4 mg D. 6 mg E. 8 mg
7	7. 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 car 3? A. 0.17 v B. 0.50 v C. 0.67 v D. 0.80 v E. 1.0 v
8	8. A point object of mass 2m is attached to one end of a rigid rod of negligible mass and length L. The rod is initially at rest but free to rotate about a fixed axis perpendicular to the rod and passing through its other end A second point object with mass m and initial speed v collides and sticks to the 2m object. What is the tangential speed v_t of the object immediately after the collision?
9	9. Two artificial satellites I and II have circular orbits of radii R and 2R, respectively, about the same planet. The orbital velocity of satellite I is v. What is the orbital velocity of satellite II?
10	10. The gravitational acceleration on the surface of the moon is 1.6 m/s². The radius of the moon is 1.7 x 10⁶ m. The period of a satellite placed in a low circular orbit about the moon is most nearly A. 1.0 x 10³ s B. 6.5 x 10³ s C. 1.1 x 10⁶ s D. 5.0 x 10⁶ s E. 7.1 x 10¹² s
11	11. A uniform ladder of length L rests against a smooth frictionless wall. The floor is rough and the coefficient of static friction between the floor and ladder is m. When the ladder is positioned at angle q, as shown in the accompanying diagram, it is just about to slip. What is q?
12	12. Three objects, all of mass M, are released simultaneously from the top of an inclined plane of height H. The objects are described as follows I. a cube of side R. II. a solid cylinder of radius R III. a hollow cylinder of radius R Assume the cylinders roll down the plane without slipping and the cube slides down the plane without friction. Which object(s) reach(es) the bottom of the plane first? A. I B. II C. III D. I & II E. II & III
13	13. A massless rod of length 2R can rotate about a vertical axis through its center as shown in the diagram. The system rotates at an angular velocity w when the two masses m are a distance R from the axis. The masses are simultaneously pulled to a distance of R/2 from the axis by a force directed along the rod. What is the new angular velocity of the system? A. w/4 B. w/2 C. w D. 2w E. 4w
14	14. A meter stick moves with a velocity of 0.60 c relative to an observer. The observer measures the length of the meter stick to be L. Which of the following statements is always true? A. L = 0.60 m B. L = 0.80 m C. 0.80 m ² L ² 1.00 m D. L = 1.00 m E. L ³ 1.00m
15	15. A glowing ember (hot piece of charcoal) radiates power P in watts at an absolute temperature T. When the temperature of the ember has decreased to T/2, the power it radiates is most nearly A. P B. P/2 C. P/4 D. P/8 E. P/16
16	16. Three processes compose a thermodynamic cycle shown in the accompanying pV diagram of an ideal gas. Process 1®2 takes place at constant temperature (300 K). During this process 60 J of heat enters the system. Process 2®3 takes place at constant volume. During this process 40 J of heat leaves the system. Process 3®1 is adiabatic. T₃ is 275 K. What is the change in internal energy of the system during process 3®1? A. -40 J B. -20 J C. 0 D. +20 J E. +40 J
17	17. What is the change in entropy of the system described in Question # 16 during the process 3®1? A. +5.0 K/J B. +0.20 J/K C. 0 D. -1.6 J/K E. -6.9 K/J
18	18. A wave is described by the equation: where x and y are in meters and t is in seconds. The +x direction is to the right. What is the velocity of the wave? A. 0.80 m/s to the left B. 1.25 m/s to the left C. 0.12 p m/s to the right D. 0.80 m/s to the right E. 1.25 m/s to the right
19	19. Two sources, in phase and a distance d apart, each emit a wave of wavelength l. Which of the choices for the path difference DL = L₁ – L₂ will always produce destructive interference at point P? A. d sinq B. x/L₁ C. d(x/L₂) D. l/2 E. 2l
20	20. You are given two lenses, a converging lens with focal length +10 cm and a diverging lens with focal length -20 cm. Which of the following would produce a virtual image that is larger than the object? A. Placing the object 5 cm from the converging lens. B. Placing the object 15 cm from the converging lens. C. Placing the object 25 cm from the converging lens. D. Placing the object 15 cm from the diverging lens. E. Placing the object 25 cm from the diverging lens.

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