Week 7 Recitation Problems PDF

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Carnegie Mellon University 33-141 Recitation

Physics Department Tuesday Week 7

Problem X.7.1) A block is moving in the positive x-direction along a frictionless, horizontal table. Someone exerts a horizontal force on the block which does positive work. (a) What can you say about the direction of the force? (b) Is the block speeding up, slowing down, or moving at constant speed? If the force instead does negative work (c) What can you say about the direction of the force? (d) Is the block speeding up, slowing down, or moving at constant speed? If there are two forces, with force 1 doing positive work (W1 > 0) and force 2 doing negative work (W2 < 0), determine if the net-work (Wnet = W1 + W2) is positive, negative, or zero for the following cases (e) The block speeds up. (f) The block slows down. (g) The block maintains constant speed.

Problem X.7.2) A block is pushed from the bottom to the top of a frictionless incline as shown below. The speed increases at a constant rate.

(a) Draw a free body diagram for the block. Make sure the label for each force indicates the types of force, the object on which the force is exerted, and the object exerting the force. (b) What is the direction of the net force on the block? (c) State whether the following quantities are positive, negative, or zero. Explain your reasoning. i) the work done on the block by the hand ii) the work done on the block by the Earth iii) the work done on the block by the incline (d) Is there work done on the hand by the block? Is it positive, negative, or zero? Explain. (e) How does the work done by the hand on the block relate to the work done by the block on the hand? Is this always true for interacting objects? I.e. could we say that, in general, work done by A on B is equal to work done by B on A? Can you think of a counterexample? Under what conditions would the statement be true? (f) The work energy theorem states that the net work done on a rigid body is equal to the change in its kinetic energy. Explain how your answers in part (c) are consistent with this theorem. (g) If the block were pushed up the incline at constant speed, would your answers in part (c) be different? What would be the net-work on the block?

Problem 6.3) A factory worker pushes a crate of mass m a distance d along a level floor at constant velocity by pushing horizontally on it. The coefficient of kinetic friction between the crate and the floor is μk. (a) What magnitude of force must the worker apply? (b) How much work is done on the crate by this force? (c) How much work is done on the crate by friction? (d) How much work is done on the crate by the normal force? By gravity? (e) What is the total work done on the crate?

Problem X.7.3) A mass m is tied to the end of a string of length L and swung in a vertical circle. (a) During one complete circle, starting anywhere, calculate the total work done on the ball by (i) the tension in the string, and (ii) gravity. (b) Repeat part (a) for motion along the semicircle from the lowest to the highest point on the path.

Problem X.7.4) You throw a rock of mass m vertically into the air from initial position yi. You observe that when it reaches position yf, it is traveling at velocity vf upward. Use the work–energy theorem to find (a) the rock’s speed just as it left the ground and (b) its maximum height.

Problem 6.75) A small block with a mass m is attached to a cord passing through a hole in a frictionless, horizontal surface (Fig. P6.75). The block is originally revolving at a distance of d from the hole with a speed vi = v. The cord is then pulled from below, shortening the radius of the circle in which the block revolves to d/4. At this new distance, the speed of the block is observed to be vf = 4v. (a) What is the tension in the cord in the original situation when the block has speed v? (b) What is the tension in the cord in the final situation when the block has speed 4v? (c) How much work was done by the person who pulled on the cord?

Carnegie Mellon University 33-141 Recitation

Physics Department Thursday Week 7

Problems from: University Physics, 13th edition, by H. D. Young & R. A. Freedman, Pearson Addison Wesley, 2012. Problem 6.46) An ingenious bricklayer builds a device for shooting bricks up to the top of the wall where he is working. He places brick on a vertical compressed spring with force constant k and negligible mass. When the spring is released, the brick is propelled upward. If the brick has mass m and is to reach a maximum height of h above its initial position on the compressed spring, what distance must the bricklayer compress the spring initially?

Problem 6.80) The spring of a spring gun has force constant k and negligible mass. The spring is compressed d, and a ball with mass m is placed in the horizontal barrel against the compressed spring. The spring is then released, and the ball is propelled out the barrel of the gun. The barrel is d long, so the ball leaves the barrel at the same point that it loses contact with the spring. The gun is held so the barrel is horizontal. (a) Calculate the speed with which the ball leaves the barrel if you can ignore friction. (b) Calculate the speed of the ball as it leaves the barrel if a constant resisting force of FR acts on the ball as it moves along the barrel. (c) For the situation in part (b), at what position along the barrel does the ball have the greatest speed, and what is that speed? (In this case, the maximum speed does not occur at the end of the barrel.)

X.7.5) A skier (mass m) is moving with velocity vi on a frictionless, horizontal plateau when she encounters a rough patch d long. The coefficient of kinetic friction between the rough patch and the skis is μk. After skiing over the rough patch and returning to the frictionless surface, she skis down a hill of height h. (a) What is the velocity of the skier at the bottom of the hill? (b) If the skier then turns around (without losing any energy) and heads back up the hill, and across the rough patch, what is her final velocity?

Problem 6.57) A ski tow operates on a slope of angle θ, and length l. The rope moves at speed v and provides power for 50 riders at one time, with a combined mass m. Estimate the power required to operate the tow.

Problem 6.97) It takes a force of 53 kN on the lead car of a 16-car passenger train with mass 9 .110 5 kg to pull it at a constant 45 m/s on level tracks. (a) What power must the locomotive provide to the lead car? (b) How much more power to the lead car than calculated in part (a) would be needed to give the train an acceleration of 1.5 m/s2 at the instant that the train has a speed of 45 m/s on level tracks? (c) How much more power to the lead car than that calculated in part (a) would be needed to move the train up a 1.5% grade (slope angle α = arctan 0.015 ) at a constant 45 m/s?

Problem 6.44) Half of a Spring. (a) Suppose you cut a massless ideal spring in half. If the full spring had a force constant k, what is the force constant of each half, in terms of k? (Hint: Think of the original spring as two equal halves, each producing the same force as the entire spring. Do you see why the forces must be equal?) (b) If you cut the spring into three equal segments instead, what is the force constant of each one, in terms of k?...