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Homework Problems

 

HW#39   Ch 15: Oscillations

Instructions: Be sure to write formulas and show substitutions to earn full credit.

1.    In your rotating platform lab, you were asked to measure the moment of inertia of a rod and two brass weights at each end. Assume that the mass of the rod is m and each brass weight has mass M. The rod has a length L and the masses are placed at L/2 from the center of the rod. Instead of rotating in a horizontal circle, imagine that you drill a hole at L/4 from the end of the rod, and you swing the rod in a vertical plane as a physical pendulum. (see figure below.) What is the period of this physical pendulum?

Physical pendulum

2.    Write the equation for the angular displacement of a simple pendulum about its vertical if it makes 10 oscillations in 15.4 s and if its speed is zero at 2 s. Assume that the pendulum has length L and that the bob reaches a maximum height of L/6 above its lowest point. (More than one answer is acceptable.)

3.    A warm wad of gum of mass 10 g that has been freshly chewed is launched horizontally with speed 1.4 m/s. The gum sticks to a 100 g block that is initially at rest and attached to a spring with spring constant 5 N/cm. a) What is the resulting period of oscillation of the block and gum if the block rests on a frictionless surface? b) What is the amplitude of oscillation?