PhysicsLAB AAPT Quiz
2015 net F = ma Contest

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Use g = 10 N/kg in ALL problems, #1-#50.

1. A 600 meter wide river flows directly south at 4.0 m/s. A small motor boat travels at 5.0 m/s in still water and points in such a direction so that it will travel directly east relative to the land. The time it takes to cross the river is closest to
2. A car travels directly north on a straight highway at a constant speed of 80 km/hr for a distance of 25 km. The car then continues directly north at a constant speed of 50 km/hr for a distance of 75 more kilometers. The average speed of the car for the entire journey is closest to
3. The force of friction on an airplane in level flight is given by Ff = kv2, where k is some constant, and v is the speed of the airplane. When the power output from the engines is Po, the plane is able to fly at a speed vo. If the power output of the engines is increased by 100% to 2Po, the airplane will be able to fly at a new speed given by
4. A 2.0 kg box is originally at rest on a horizontal surface where the coefficient of static friction between the box and the surface is µs and the coefficient of the kinetic friction between the box and the surface is µk = 0.90 µs. An external horizontal force of magnitude P is then applied to the box. Which of the following is a graph of the acceleration of the box a versus the external force P?
5. A 470 gram lead ball is launched at a 60 degree angle above the horizontal with an initial speed of 100 m/s directly toward a target on a vertical cliff wall that is 150 meters away as shown in the figure. Ignoring air friction, by what distance does the lead ball miss the target when it hits the cliff wall?
6. Three trolley carts are free to move on a one dimensional frictionless horizontal track. Cart A has a mass of 1.9 kg and an initial speed of 1.7 m/s to the right; Cart B has a mass of 1.1 kg and an initial speed of 2.5 m/s to the left; cart C has a mass of 1.3 kg and is originally at rest. Collisions between carts A and B are perfectly elastic; collisions between carts B and C are perfectly inelastic. What is the velocity of the center of mass of the system of the three carts after the last collision?
The next two questions share the same information Base your answers to questions 7 and 8 on the information and diagram below.


Carts A, B, and C are on a long horizontal frictionless track. The masses of the carts are m, 3m, and 9m. Originally cart B is at rest at the 1.0 meter mark and cart C is at rest on the 2.0 meter mark. Cart A is originally at the zero meter mark moving toward the cart B at a speed of vo
7. Assuming that all collisions are completely inelastic, what is the final speed of cart C?
8. Assuming that all collisions are completely elastic, what is the final speed of cart C?

The next two questions share the same information Base your answers to questions 9 and 10 on the information and diagram below.

A 0.650 kg ball moving at 5.00 m/s collides with a 0.750 kg ball that is originally at rest. After the collision, the 0.750 kg ball moves of with a speed of 4.00 m/s, and the 0.650 kg ball moves of at a right angle to the final direction of motion of the 0.750 kg ball.
9. What is the final speed of the 0.650 kg ball?
10. Let the change in total kinetic energy in this collision be defined by ΔK = Kf - Ki, where Kf is the total final kinetic energy, and Ki is the total initial kinetic energy. Which of the following is true?

11. A sphere floats in water with 2/3 of the volume of the sphere submerged. The sphere is removed and placed in oil that has 3/4 the density of water. If it floats in the oil, what fraction of the sphere would be submerged in the oil?

The next two questions share the same information Base your answers to questions 12 and 13 on the information and diagram below.

A pendulum consists of a small bob of mass m attached to a fixed point by a string of length L. The pendulum bob swings down from rest from an initial angle θmax < 90 degrees.
12. Which of the following statements about the pendulum bob's acceleration is true?

13. Consider the pendulum bob when it is at an angle  θ max on the way up (moving toward max). What is the direction of the acceleration vector?

The next two questions share the same information Base your answers to questions 14 and 15 on the information and diagram below.

A 3.0 meter long massless rod is free to rotate horizontally about its center. Two 5.0 kg point objects are originally located at the ends of the rod; they are free to slide on the frictionless rod and are kept from flying off the rod  by an inflexible massless rope that connects the two objects. Originally the system is rotating at 4.0 radians per second; assume the system is completely frictionless; and ignore any concerns about instability of the system.
14. Calculate the original tension in the rope.
15. The rope is slowly tightened by a small massless motor attached to one of the objects. It is done in such a way as to pull the two objects closer to the center of the rotating rod. How much work is done by the motor in pulling the two objects from the ends of the rod until they are each 0.5 meters from the center of rotation?

16. Shown below is a graph of potential energy as a function of position for a 0.50 kg object.

Which of the following statements is NOT true in the range 0 cm < x < 6 cm?

17. A flywheel can rotate in order to store kinetic energy. The flywheel is a uniform disk made of a material with a density ρ and tensile strength σ (measured in Pascals), a radius r, and a thickness h. The flywheel is rotating at the maximum possible angular velocity so that it does not break. Which of the following expression correctly gives the maximum kinetic energy per kilogram that can be stored in the  flywheel? Assume that σ is a dimensionless constant.
18. Shown below are three graphs of the same data. Which is the correct functional relationship between the data points? Assume a and b are constants.


The next two questions share the same information Base your answers to questions 19 and 20 on the information and diagram below.

A U-tube manometer consists of a uniform diameter cylindrical tube that is bent into a U shape. It is originally filled with water that has a density ρw. The total length of the column of water is L. Ignore surface tension and viscosity.
19. The water is displaced slightly so that one side moves up a distance x and the other side lowers a distance x. Find the frequency of oscillation.
20. Oil with a density half that of water is added to one side of the tube until the total length of oil is equal to the total length of water. Determine the equilibrium height difference between the two sides.

21. An object launched vertically upward from the ground with a speed of 50 m/s bounces off of the ground on the return trip with a coefficient of restitution given by CR = 0:9, meaning that immediately after a bounce the upward speed is 90% of the previous downward speed. The ball continues to bounce like this; what is the total amount of time between when the ball is launched and when it finally comes to a rest? Assume the collision time is zero; the bounce is instantaneous. Treat the problem as ideally classical and ignore any quantum effects that might happen for very small bounces.
22. A solid ball is released from rest down inclines of various inclination angles θbut through a fixed vertical height h. The coefficient of static and kinetic friction are both equal to µ. Which of the following graphs best represents the total kinetic energy of the ball at the bottom of the incline as a function of the angle of the incline?
23. A 2.0 kg object falls from rest a distance of 5.0 meters onto a 6.0 kg object that is supported by a vertical massless spring with spring constant k = 72 N/m. The two objects stick together after the collision, which results in the mass/spring system oscillating. What is the maximum magnitude of the displacement of the 6.0 kg object from its original location before it is struck by the falling object?
24. The speed of a transverse wave on a long cylindrical steel string is given by

where T is the tension in the string, M is the mass, and L is the length of the string. Ignore any string stiffness, and assume that it does not stretch when tightened.

Consider two steel strings of the same length, the first with radius r1 and a second thicker string with radius r2 = 4r1. Each string is tightened to the maximum possible tension without breaking. What is the ratio f1 = f2 of the fundamental frequencies of vibration on the two strings?
25. Two identical carts A and B each with mass m are connected via a spring with spring constant k. Two additional springs, identical to the first, connect the carts to two fixed points. The carts are free to oscillate under the effect of the springs in one dimensional frictionless motion.
Under suitable initial conditions, the two carts will oscillate in phase according to 

where xA and xB are the locations of carts A and B relative to their respective equilibrium positions. Under other suitable initial conditions, the two carts will oscillate exactly out of phase according to

Determine the ratio of ω2/ω1

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