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Unformatted text preview: Solution for Homework 17 Motion in a Plane I, Work problems Solution to Homework Problem 17.1() Problem: Can potential energy be associated between two elements if both are not within a system? Why or why not? Solution No. Potential energy always refers to the relative position of various parts of a system (between which there exists a conservative force), never to the position of various parts of a system relative to the environment. Total Points for Problem: 2 Points Solution to Homework Problem 17.2() Problem: An object moves in two dimensions. The objects acceleration vector is perpendicular to its velocity vector at all times. How is the objects velocity affected, both in magnitude and direction? Explain. Solution The objects speed is unchanged. Only the direction of the velocity vector changes. The component of acceleration that is parallel to velocity changes speed, while the component perpendicular to the velocity vector changes its direction. Since in this case acceleration is purely perpendicular to velocity, speed is unaffected. As we will learn later, this situation produces uniform circular motion. Total Points for Problem: 2 Points Solution to Homework Problem 17.3() Problem: Starting from rest, a car pulls a trailer along a road that climbs from sea level over a mountain and then back to sea level, where it continues to travel at a constant speed. Car and trailer have identical inertias. In the process of climbing, the cars engine heats up substantially; you may neglect the heating of the surrounding air. Using diagrams like the template in the figure, for each choice of system below draw work-energy diagrams for the initial and final states described in the problem. Make sure that the lengths of the bars in the diagrams for the different choices of system are consistent with one another. Briefly explain your diagram, and, if work is done on the system, indicate which forces do work and confirm the sign of the work. (a)System: car, trailer, and earth. (b)System: trailer only. (c)System: car only. E source K U E diss W Solution to Part (a) Source energy (fuel) is converted to kinetic energy and dissipated en- ergy. E source + K + E diss = 0 E source K U E diss W Grading Key: Part (a) 2 Points Solution to Part (b) The change in the kinetic energy of the trailer is half that of the car and trailer in part (a), since they have the same mass. In the system with only the trailer, this increase is due to work done by an external agent, the car. Since force and displacement are parallel, W > . E source K U E diss W Grading Key: Part (b) 2 Points Solution to Part (c) E source and E diss are the same as in part (a), but the kinetic energy of the car is only half that of the car and trailer. In this system the trailer does negative work on the car, since the force is opposite the direction of displacement. The work has the same magnitude as that in part b), since the force of the trailer on the car is exactly the same...
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