Physics x141 Practice Final Exam Name: Partial credit will be awarded. However, you must show/explain your work. A correct answer without explanatory material will not receive full credit. Clearly indicate your final result with a box or circle. If you need more space, use the back and indicate with OVER. v f = v i + adt s f = s i + v i Dt + 1 2 a(dt)2 v f 2 = v i 2 + 2aDs F net = ma w = mg f s µ s n, f k = µ k n a r = v 2 r = rw 2 p = mv J = t f ò t i F dt = Dp = F avedt DK = W net = W c + W diss + W ext W c = -DU, W diss = -DE th DK + DU + DE th = W ext W F = F Dr = FDrcosq F,Dr (F const) U grav = mgy U spring = 1 2 k(ds)2 K = 1 mv 2 2 A B = ABcosa g = 9.8 m/s 2 s = rq, v = rw, a t = ra w f = w i + adt q f = q i + w i Dt + 1 2 a(dt)2 w f 2 = w i 2 + 2aDq t = rf sinf = rf t t net = Ia K rot = 1 2 Iw 2, v cm = Rw Problem 1 (10) Problem 2 (10) Problem 3 (15) Problem 4 (15) Problem 5 (15) Problem 6 (20) Problem 7 (15) Total (100)
Write your answer to the multiple-choice questions 1-10 in this box. This is not optional; your answers must be recorded in the box below, or you will receive zero points for this section. 1 2 3 4 5 6 7 8 9 10 Problem1 (10 parts) (10 pts.) 1. Two metal balls roll off a horizontal table with the same speed. One ball is twice as heavy as the other. In this situation: A) Both balls hit the floor at approximately the same horizontal distance from the base of the table. B) The heavier ball hits the floor at about half the horizontal distance from the table as does the lighter ball. C) The lighter ball hits the floor at about half the horizontal distance from the table as does the heavier ball. D) The heavier ball hits the floor considerably closer to the base of the table than the lighter ball, but not necessarily at half the distance. E) The lighter ball hits the floor considerably closer to the base of the table than the heavier ball, but not necessarily at half the distance. 2. A bowling ball accidentally falls out of the cargo bay of an airplane as it flies along in a horizontal direction. As observed by a person standing on the ground and viewing the plane in the figure at the right, which path would the bowling ball follow after leaving the airplane? Page 2 of 10
3. A boy throws a steel ball straight up. Consider the motion of the ball only after it has left the boy's hand but before it touches the ground. Assume that forces exerted by the air are negligible. The forces acting on the ball are: A) A downward force of gravity along with a steadily decreasing upward force. B) A steadily decreasing upward force from the moment it leaves the boy's hand until it reaches its highest point; on the way down, there is a steadily increasing downward force of gravity as the ball gets closer to the earth. C) An almost constant downward force of gravity along with an upward force that steadily decreases until the ball reaches its highest point; on the way down, there is only a constant downward force of gravity. D) An almost constant downward force of gravity. E) None of the above. The ball falls back to the ground because of its natural tendency to rest on the surface of the earth. 4. An elevator is being lifted upward at a constant speed by a steel cable. All frictional effects are negligible. In this situation: A) The upward force by the cable is greater than the downward force of gravity. B) The upward force by the cable is equal to the downward force of gravity. C) The upward force by the cable is less than the downward force of gravity. D) The upward force by the cable is greater than the sum of the downward force of gravity and a downward force due to the air. E) None of the above. The elevator goes up because the cable is being shortened. Page 3 of 10
8. A large truck has a dead battery. It is pushed to the garage by a small car. In the figure, the car is speeding up to get up to cruising speed. A) The amount of force with which the car pushes on the truck is equal to that with which the truck pushes on the car. B) The amount of force with which the car pushes on the truck is less than that with which the truck pushes on the car. C) The amount of force with which the car pushes on the truck is greater than that with which the truck pushes on the car. D) The car's engine is running, so the car pushes against the truck. But the truck's engine is not running, so the truck does not push back against the car. E) The truck is pushed forward simply because it is in the way of the car. 9. A ball rolls down the incline and off the horizontal ramp. Ignoring air resistance, what force or forces act on the ball as it moves through the air after leaving the ramp? A) The weight of the ball vertically down. B) A horizontal force that maintains the motion. C) A force whose direction changes as the direction of motion changes. D) The weight of the ball and a horizontal force. E) The weight of the ball and a force in the direction of motion. Page 4 of 10
Problem 2 (10 pts) Blocks A and B, with m B >m A, are connected by a string. A hand pushing on one side of A accelerates them along a frictionless surface. The string (S) is not massless. Use Newton s laws to rank order all of the horizontal forces from the largest to the smallest. Explain your reasoning. You will receive no credit if it appears as if you just guessed at your answers. Essay answers means you are guessing and will not be accepted. Use Newton s laws. B S hand A Page 5 of 10
Problem 3 (15 pts) A 1500 kg car is traveling at a speed of 30 m/s when the driver slams on the brakes and skids to a halt. Determine the stopping distance if the car is traveling on a level road. (For this situation µ s =1.00, µ k = 0.80 and you can ignore rolling friction.) Page 6 of 10
Problem 4 (15 pts) You are moving out of your dorm and use a compressed spring to shoot a 2-kg package of your stuff up a 1-m-high frictionless ramp onto a truck. The spring constant is 500 N/m and the spring is compressed 30 cm. a) What is the speed of the package as it reaches the truck? You must use conservation of energy to solve this problem. You must start the problem by drawing a proper energybar-chart (no bar-chart = no credit). b) You accidentally spill your soda on the ground and create a 50-cm-long sticky spot with a coefficient of friction 0.30. Will your next 2-kg package make it onto the truck? As before, use conservation of energy to solve this, and start by drawing an energy-bar-chart (no bar-chart = no credit). Page 7 of 10
Problem 5 (15 pts) A 2-kg block hangs from a string of length 1 m. A 5-gram bullet moving at 500 m/s is fired into the 2-kg block. The bullet rebounds with some unknown speed and the block swings to a height of 20 cm above the lowest position. a) What is the rebound speed of the bullet? Explain your reasoning. Write down the physical principle(s) you are applying, represent quantities using proper symbols, solve for the desired unknown(s), and use numbers to get the final answer(s). b) Is Mechanical Energy conserved during the collision? Justify your answer. Page 8 of 10
Problem 6 (20 pts) A 2.0 kg box is attached to a massless string that is wrapped around a 1 kg, 4 cm diameter cylinder. The cylinder rotates on an axle through its center. The block is released from rest 1.0 m above the floor. Note: I cylinder = 1. 2 MR2 a) What is the angular acceleration of the cylinder? b) How long does the cylinder take to complete one revolution? c) How long will it take the block to reach the ground? Page 9 of 10
Problem 7 (15 pts) An 80 kg construction worker sits on a 1450 kg steel beam. You will receive no credit on this problem if you do not start with a neat and useful free-body-diagram. a) What is the tension in the cable if the worker sits on the beam at a position 4.5 m from the wall? b) The beam is attached to the wall using a big hinge that exerts both horizontal and vertical forces on the beam. What are the horizontal and vertical components of the hinge force? Page 10 of 10