Mechanics II. Which of the following relations among the forces W, k, N, and F must be true?

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1 Mechanics II 1. By applying a force F on a block, a person pulls a block along a rough surface at constant velocity v (see Figure below; directions, but not necessarily magnitudes, are indicated). Which of the following relations among the forces W, k, N, and F must be true? (a) F = k and N = W (b) F = k and N > W (c) F > k and N < W (d) F > k and N = W (e) None of the above. 2. A small metal cylinder of mass 0.10 kg rests on a circular turntable which rotates at constant angular velocity. If the cylinder is 0.20 m from the center of the turntable, and the coefficient of static friction between cylinder and turntable surface is 0.12, then, if the cylinder is not to slip off the turntable, its linear velocity must lie within which of the following ranges? (a) 0 < v 0.5 m/s (b) 0.5 < v 1.0 m/s (c) 1.0 < v 1.5 m/s (d) 1.5 < v 2.0 m/s (e) 2.0 < v 2.5 m/s 3. Two disks, at rest on a frictionless table, are simultaneously pushed with equal forces in the same direction across the table. m 2 = 4m 1. Which disk will have the greater kinetic energy after they are both pushed a distance d? (a) 1 (c) The kinetic energies will be equal. 4. Two disks, at rest on a frictionless table, are simultaneously pushed with equal forces in the same direction across the table. m 2 = 4m 1. Which disk will reach a distance d first? (a) 1 (c) They will travel the same distance in the same time. 5. Two disks, at rest on a frictionless table, are simultaneously pushed with equal forces in the same direction across the table. m 2 = 4m 1. Which disk will have the greater momentum after they are both pushed a distance d? 1

2 (a) 1 (c) The momenta will be equal. 6. An object with mass m and velocity v directed to the left strikes a wall and rebounds with velocity v directed to the right. The change in the object s kinetic energy is (a) mv 2 (b) 1 2 mv2 (c) zero (d) 1 2 mv2 (e) mv 2 7. As a result of the collision described in the previous problem, the change in the object s momentum is (a) 2mv directed to the left (b) mv directed to the left (c) zero (d) mv directed to the right (e) 2mv directed to the right 8. A ball, initially at rest at t= 0 seconds, rolls with constant acceleration down an inclined plane 10 meters long. If the ball rolls 1 meter in the first 2 seconds, how far will it have rolled at t= 4 seconds? (a) 2m (b) 3m (c) 4m (d) 5m (e) 8m 9. A ball of mass m is thrown vertically upward. Air resistance is not negligible, but rather exerts a force of magnitude proportional to the velocity. At the highest point, the ball s acceleration is: (a) 0 (b) less than g downward (c) g downward (d) greater than g downward (e) upward 10. A train traveled due north at 80 km/h for 320 km and then at 100 km/h for 320 km. What was its average velocity for the entire trip? (a) 84 km/h (b) 89 km/h (c) 90 km/h (d) 91 hm/h (e) 95 km/h 2

3 11. The graph below shows an object s position as a function of time. Which segment corresponds to an interval when the object undergoes only negative acceleration? (a) A (b) B (c) C (d) D (e) E 12. An object is projected straight upward from ground level with a velocity of 50 m/s. Ignoring air resistance, it will return to ground level in approximately: (a) 2.5 s (b) 5 s (c) 7.5 s (d) 10 s (e) 15 s 13. Starting from rest at time t = 0, a car moves in a straight line with an acceleration given by the graph below. What is the velocity of the car at t = 3 s? (a) 1.0 m/s.0 m/s (c) 6.0 m/s (d) 10.5 m/s (e) 12.5 m/s 14. The system shown in the figure below is free to rotate about a frictionless axis through its center, perpendicular to the page. 3

4 Each force is exerted tangent to the rim. The magnitude of the net torque acting on the system is: (a) 1.5 F R (b) 1.9 F R (c) 2.3 F R (d) 2.5 F R (e) 3.5 F R 15. A rigid rod of mass M and length L has moment of inertia 1/12 ML 2 about its center of mass. A sphere of mass m and radius R has moment of inertia 2/5 mr 2 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 Figure below). What is the moment of inertia of the combined system about the axis shown? (a) I = 1/12 ML 2 + 2/5 mr 2 (b) I = 1/12 ML 2 + 2/5 mr 2 + ml 2 (c) I = 1/3 ML 2 + 2/5 mr 2 + ml 2 (d) I = 1/12 ML 2 + ml 2 (e) I = 1/3 ML 2 + ml The driver of a 1000 kg car tries to turn through a circle of radius 100 m on an unbanked curve at a speed of 10 m/s. The maximum frictional force between the tires and the slippery road is 900 N. The car will: (a) Slide into the inside of the curve. (b) Make the turn. (c) Slow down due to the centrifugal force. (d) Make the turn only if it speeds up. (e) Slide off to the outside of the curve. 17. A roller coaster travels with velocity of magnitude v A at point A. Point B is a height H above point A. Assuming no frictional losses and no work done by a motor, what is the roller coaster s magnitude of the velocity at point B? (a) v 2 A 2gH (b) v A 2gH 4

5 (c) v 2 A 2gH (d) v A + 2gH (e) v 2 A + 2gH 18. A uniform ladder of mass m and length L rests against a smooth frictionless wall at an (inner) angle θ with the floor. The floor is rough, and the coefficient of static friction between it and the ladder is µ. If the ladder is just about to slip, what, in terms of the quantities given, is the angle θ? (a) θ = µ/l (b) tan θ = 2µ (c) tan θ = 1/2µ (d) sin θ = 1/µ (e) cos θ = µ 19. Two ice skaters, a 200-lb man and a 120-lb woman, initially at rest next to each other on a frictionless level ice surface. The push off from each other, and ten seconds later they are 8.0 m apart. How far has the woman moved in that time? (a) 8 m (b) 6.5 m (c) 5 m (d) 4 m (e) 3 m 20. When a 1.53-kilogram mass is placed on a spring with a spring constant of 30.0 newtons per meter, the spring is compressed meter. How much energy is stored in the spring? (a) 3.75 J (b) 7.5 J (c) 15 J (d) 23 J (e) 30 J 5

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