Problem 4: A ball of mass m is connected to two rubber bands of length L, cach under tension T, as shown in the Figure. Assume the tension does not change. (a) The ball of mass m is in equilibrium. Draw a free-body diagram on m. (b) Since the ball of mass m is in equilibrium, Eety=0. Use Fnet.y 0 to find the equilibrium position for the ball yo. Hint: sin 0 yo/L, Answer: o = mgL/(27'). T T. L L. т (c) The ball of mass m is now displaced slightly from equilibrium, as shown in the figure below. Draw a free-body diagram on m. (d) Use Newton's 2nd Law: Fnet.y = ma = n to show that the motion of m satisfies the SHM differential equation + wu = 0, where u = y - yo and w = since the downward gravitational force on the ball is larger than the two upward tension forces on the ball. Hint: sin 0 = y/L. Also, from part (b), yo = mgL/(2T). We can rewrite this expression as mg = 2T(yo/L). Use this expression to substitute for mg in Newton's 2nd Law: Fnet.y = -ma = -m 2T For this problem we use a = V mL dt2 -- y T L T. m

Problem 4: A ball of mass m is connected to two rubber bands of length L, cach under tension T, as shown in the Figure. Assume the tension does not change. (a) The ball of mass m is in equilibrium. Draw a free-body diagram on m. (b) Since the ball of mass m is in equilibrium, Eety=0. Use Fnet.y 0 to find the equilibrium position for the ball yo. Hint: sin 0 yo/L, Answer: o = mgL/(27'). T T. L L. т (c) The ball of mass m is now displaced slightly from equilibrium, as shown in the figure below. Draw a free-body diagram on m. (d) Use Newton's 2nd Law: Fnet.y = ma = n to show that the motion of m satisfies the SHM differential equation + wu = 0, where u = y - yo and w = since the downward gravitational force on the ball is larger than the two upward tension forces on the ball. Hint: sin 0 = y/L. Also, from part (b), yo = mgL/(2T). We can rewrite this expression as mg = 2T(yo/L). Use this expression to substitute for mg in Newton's 2nd Law: Fnet.y = -ma = -m 2T For this problem we use a = V mL dt2 -- y T L T. m

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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