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CHAPTER 10 SIMPLE HARMONIC MOTION AND ELASTICITY CONCEPTUAL QUESTIONS 4 . REASONING AND SOLUTION Simple harmonic motion is the oscillatory motion that occurs when a restoring force of the form of Equation 10.2, F = - kx , acts on an object. The force changes continually as the displacement x changes. A steel ball is dropped onto a concrete floor. Over and over again, it rebounds to its original height. During the time when the ball is in the air, either falling down or rebounding up, the only force acting on the ball is its weight, which is constant. Thus, the motion of the bouncing ball is not simple harmonic motion. 7 . REASONING AND SOLUTION The time required for a particle in simple harmonic motion to travel through one complete cycle (the period) is independent of the amplitude of the motion, even though at larger amplitudes the particle travels further. This is possible because, at larger amplitudes, the maximum speed of the particle is greater. Thus, even though the particle must cover larger distances at larger amplitudes, it does so with greater speeds. ______________________________________________________________________________________ ______ 9 . REASONING AND SOLUTION The elastic potential energy that a spring has by virtue of being stretched or compressed is given by Equation 10.13: PE elastic = (1/2) kx 2 , where x is the amount by which the spring is stretched or compressed relative to its unstrained length. The amount of stretch or compression appears squared, so that the elastic potential energy is positive and independent of the sign of x . Therefore, the amount of elastic potential energy stored in a spring when it is compressed by one centimeter is the same as when it is stretched by the same amount. ______________________________________________________________________________________ ______ 13 . REASONING AND SOLUTION The playground swing may be treated, to a good approximation, as a simple pendulum. The period of a simple pendulum is given by T = 2 π L / g . This expression for the period depends only on the length of the pendulum and the acceleration due to gravity; for angles less than 10° the period is independent of the amplitude of the motion. Therefore, if one person is pulled back 4° from the vertical while another person is pulled back 8° from the vertical, they will both have the same period. If they are released simultaneously, they will both come back to the starting points at the same time. ______________________________________________________________________________________ ______
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15. REASONING AND SOLUTION The amount of force F needed to stretch a rod is given by Equation 10.17: F = Y ( L / L 0 ) A , where A is the cross-sectional area of the rod, L 0 is the original length, L is the change in length, and Y is Young's modulus of the material. Since the cylinders are made of the same material, they have the same Young's
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This note was uploaded on 12/28/2011 for the course PHY 2053 taught by Professor Darici during the Spring '09 term at FIU.

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