ME 261Solution to Test 2 Spring 2008

# ME 261Solution to Test 2 Spring 2008 - ME 261 Spring 2008...

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ME 261 - Spring 2008 - Test 1 Problem 1 Two identical pendulums consist of a mass of 500 g at the end of a 1.5 m long string. At rest, the two strings are vertical and the two masses are touching. Pendulum A is then released from rest at an angle of 60 o . Find the maximum angle B will reach after impact. The coefficient of restitution is 0.8. Solution: The entire event consists of three phases: (1) A will swing down by an angle of 60 o ; (2) A will impact B; (3) B will swing out until it stops and starts moving back. During the first phase, A starts from rest and moves down following a circular path as shown in Figure 1.b. When it reaches the vertical, its velocity will be V A . The velocity V A can be determined applying the work-energy principle 1 2 12 T T U - = to mass A. To determine 12 U , the work done by the external forces, we consider the free body diagram (Fig. 1.c) which shows two forces: the weight mg and T, the tension in the string. As mass A moves on a circle, the tension T is always directed in the radial direction. Since the tension is always perpendicular to the direction of the motion, it does not do any work. The work done by the weight mg is equal to mg(L-L’). The initial

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ME 261Solution to Test 2 Spring 2008 - ME 261 Spring 2008...

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