Mechanics: 14 Problems related to force and motion.

1. In a college homecoming competition, 16 students lift a sports car. While holding the car off ground, each student exerts an upward force of 400 N. (a) What is the mass of the car in kilograms? (b) What is its weight in pounds?
2. A person pushes on a block of wood that has been placed against a wall. Draw a free-body diagram and identify the reaction forces to all the forces on the block.
3. A packing crate is placed on a 20º inclined plane. If the coefficient of static friction between the crate and the plane is 0.65, will the crate slide down the plane? Justify your answer.
4. A student could either pull or push, at an angle of 30º from the horizontal, a 50-kg crate on a horizontal surface, where the coefficient of kinetic friction between the crate and surface is 0.20. The crate is to be moved a horizontal distance of 15 m. (a) Compared with pushing, pulling requires the student to do (1) less, (2) the same, or (3) more work. (b) Calculate the minimum work required for both pulling and pushing.
5. A particular force is described by the equation F=(60 N/m)x x^. How much work is done when this force pushes a box horizontally between (a) xo = 0 and x = 0.15m, and (b) xo = 0.15 m and x = 0.25 m?
6. A 3.0-g bullet traveling at 350 m/s hits a tree and slows down uniformly to a stop while penetrating a distance of 12 cm into the tree's trunk. What was the force exerted on the bullet in bringing it to rest?
7. A 60-kg woman runs up a staircase 15 m high (vertically) in 20 s. (a) How much power does she expend? (b) What is her horsepower rating?
8. A 0.20-kg billiard ball traveling at a speed of 15 m/s strikes the side rail of a pool table at an angle of 60º. If the ball rebounds at the same speed and angle, what is the change in its momentum?
9. A 2.0-kg mud ball drops from rest at a height of 15 m. If the impact between the ball and the ground lasts 0.50 s, what is the average net force exerted by the ball on the ground?
10. A 1.0-kg ball is thrown horizontally with a velocity of 15 m/s against a wall. If the ball rebounds horizontally with a velocity of 13 m/s and the contact time is 0,020s, what is the force exerted on the ball by the wall?
11. To get off a frozen, frictionless lake, a 70.0-kg person takes off a 0.150-kg shoe and throws it horizontally, directly away from the shore with a speed of 2.00 m/s. If the person is 5.00 m from the shore, how long does it take for him to reach it?
12. A projectile that is fired from a gun has an initial velocity of 90.0 km/h at an angle of 60.0º above the horizontal. When the projectile is at the top of its trajectory, an internal explosion causes it to separate into two fragments of equal mass. One of the fragments falls straight downward as though it had been released from rest. How far from the gun does the other fragment land?
13. In a pool game, a cue ball traveling at 0.75 m/s hits the stationary eight ball. The eight ball moves off with a velocity of 0.25 m/s at an angle of 37º relative to the cue ball's initial direction. Assuming that the collision is inelastic, at what angle will the cue ball be deflected, and what will be its speed?
14. The centers of a 4.0-kg sphere and a 7.5-kg sphere are separated by a distance of 1.5 m. Where is the center of mass of the two-sphere system?

See attached file for full problem description.