1993 Physics Olympiad Screening Test (1-20)

1. A ball of mass m is thrown vertically upward. Air resistance is not negligible. Assume the force of air resistance has magnitude proportional to the velocity, and direction opposite to the velocity's. At the highest point, the ball's acceleration is

A. 0
B. less than g
C. g
D. greater than g
E. upward

2. A train is moving forward at a velocity of 2.0 m/s. At the instant the train begins to accelerate at 0.8 m/s², a passenger drops a quarter which takes 0.50 s to fall to the floor. Relative to a spot on the floor directly under the quarter at release, it lands:

A. 1.1 m toward the rear of the train
B. 1.0 m toward the rear of the train.
C. 0.10 toward the rear of the train.
D. directly on the spot.
E. 0.90 m toward the front of the train.

3, The dropped quarter in the preceding question (#2) is viewed by an observer standing next to the tracks. Relative to this observer, the quarter moves _____ before landing.

A. forward 1.1 m
B. forward 1.0 m
C. forward 0.10 m
D. straight down
E. backward 0.10 m

4. The accompanying graph of position x versus time t represents the motion of a particle.

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If b and c are both positive constants, which of the following expressions best describes the acceleration a of the particle?

A. a = 0
B. a = +b
C. a = - c
D. a = b + ct
E. a = b - ct

5. In the system shown to the right, a force F pushes on block A, giving the system an acceleration a. The coefficient of static friction between the blocks is m. The correct equation for block B not to slip is:

1993ques5.gif (1200 bytes)

A. a > mg
B. a < mg
C. a > g
D. a >g / m
E. a < g / m

6. A block of mass m starts at rest at height h on a frictionless inclined plane. The block slides down the plane, travels a total distance d across a rough surface with coefficient of kinetic friction m and compresses a spring with force constant k a distance x before momentarily coming to rest. Then the spring extends and the block travels back across the rough surface, sliding up the plane.

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The correct expression for the maximum height h that the block reaches on its return is:

A. mgh' = mgh - 2mmgd
B. mgh' = mgh + 2mmgd
C. mgh' = mgh + 2mmgd + kx²
D. mgh' = mgh - 2mmgd - kx²
E. mgh' = mgh - 2mmgd - kx² - ˝ mv²

7. Air track car A has mass m and velocity v. Air track car B has mass 2m and velocity 3v. The same constant force F is applied to each car until it stops. Car A is brought to rest in time t. The time required to stop car B is:

A. 2t
B. 3t
C. 6t
D. 9t
E. 18t

8. In the preceding question (#7), car A travels a distance d before coming to rest. The distance traveled by car B before coming to rest is:

A. 2d
B. 3d
C. 6d
D. 9d
E. 18d

9. Three air track cars are initially placed as shown in the accompanying figure.

Car A has mass m and initial velocity v to the right. Car B with mass m and car C with mass 4m are both initially at rest. Car A collides elastically with car B, which in turn collides elastically with car C. After the collision, car C has a velocity of 0.4v to the right. The final velocities of cars A and B are:

A.	Car A: 0.6v to the left	Car B: at rest
B.	Car A: 1.4v to the left	Car B: at rest
C.	Car A: v to the left	Car B: 0.6v to the left
D.	Car A: 0.4v to the left	Car B: v to the left
E.	Car A: 1.6v to the left	Car B: v to the right

10. Three cylinders, all of mass M, roll without slipping down an inclined plane of height H. The cylinders are described as follows:

I. hollow of radius R
II. solid of radius R/2
III. solid of radius R

if all cylinders are released simultaneously from the same height, reaching the bottom first is (are);

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

11. The system shown below is free to rotate about a frictionless axis through its center and perpendicular to the page. All three forces are exerted tangent to their respective rims.

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The magnitude of the net torque acting on the system is:

A. 1.5 FR
B. 1.9 FR
C. 2.3 FR
D. 2.5 FR
E. 3.5 FR

12. Two identical disks are positioned on a vertical axis. The bottom disk is rotating at angular velocity w_o and has rotational kinetic energy K_o. The top disk is initially at rest. It is allowed to fall, and sticks; to the bottom disk.

1993ques12.gif (1144 bytes)

What is the rotational kinetic energy of the system after the collision?

A. ź K_o
B. ˝ K_o
C. K_o
D. 2K_o
E. 4K_o

13. If the sun were suddenly replaced by a black hole of one solar mass, what would happen to the earth's orbit immediately after the replacement?

A. The earth would spiral into the black hole.
B. The earth would spiral out away from the black hole.
C. The radius of the earth's orbit would be unchanged, but the period of the earth's motion would increase.
D. Neither the radius of the orbit nor the period would change
E. The radius of the earth's orbit would be unchanged, hut the period of the earth's motion would decrease.

14. A hypothetical planet has density p, radius R, and surface gravitational acceleration g. If the radius of the planet were doubled, but the planetary density stayed the same, the acceleration due to gravity at the planet's surface would be.

A. 4g
B. 2g
C. g
D. ˝g
B. źg

15. An ideal organ pipe resonates at frequencies of 50 Hz, 150Hz, 250 Hz The pipe is:

A. open at both ends and of length 1.7m.
B. open at both ends and of length 3.4 m.
C. open at both ends' and of length 6.8 m.
D. closed at one end, open at the other, and of length 1.7 m.
E. closed at one end, open at the other, and of length 3.4 m.

16. A porpoise, whistle-clicking at a frequency f_o, swims toward an underwater vertical cliff at a velocity that is 1.0% of the velocity of sound in sea water. The reflected frequency experienced by the swimming porpoise is:

A. 0.98 f_o
B. 0.99 f_o
C. f_o
D. 1.01 f_o
E. 1.02 f_o

17. Three processes compose a thermodynamic cycle shown in the accompanying pV diagram. Process 1Ž2 takes place at constant temperature. Process 2Ž3 takes place at constant volume, and process 3Ž 1 is adiabatic. During the complete cycle, the total amount of work done is 10 J. During process 2Ž3, the internal energy decreases by 20 J; and during process 3Ž 1, 20 J of work is done on the system.

	Q	W	DU
1Ž2
2Ž3			- 20 J
3Ž 1		- 20 J
cycle		+ 10 J

How much heat is added to the system during process 1Ž2

A. 0
B. 10 J
C. 20 J
D. 30 J
B. 40 J

18. The root mean square velocity of oxygen gas is v at room temperature. What is the root mean square velocity of hydrogen gas at the same temperature?

A. 16 v
B. 4v
C. v
D. v/4
B. v/16

19. Monochromatic light of wavelength l is shone on a grating consisting of six equally spaced slits. The first order interference maximum occurs at an angle of 0.00100 radians. If the outer two slits are covered, the first order maximum will occur at _____ radians.

A. 0.00025
B. 0.00067
C. 0.00100
D. 0.00150
E. 0.00400

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.