1. You want to design a pendulum for a grandfather clock so that it has a...

1. You want to design a pendulum for a grandfather clock so that it has a period of 2.00 seconds (so that one “tick” plus one “tock” occur during one complete period). The pendulum has a heavy 8.00-kg bob. (Throughout this problem, assume an ideal simple pendulum: the pendulum’s arm has negligible mass, the bob can be approximated as a point-mass, the initial angle of displacement is small, and there is negligible friction.)

a.) If you want the clock to be used on the surface of the Earth near sea level (where g = 9.80 m/s2 ), what length should you use for the pendulum arm? Show your work. (Note: How many significant figures should your final answer have? Watch your rounding!)

b.) Suppose that the temperature in the room gets much warmer, and the length of the pendulum’s arm expands by 2.50%. By what percentage will the pendulum’s period increase? Show your work. Express your final answer as either a decimal factor or a percentage (with appropriate sig. figs.).

c.) Which one or more of the following changes would (when considered separately and individually) increase the period of the pendulum, thereby making the clock run “slower”? Circle ALL that apply:

A. moving the pendulum to the top of a (fictitiously) high mountain where g = 9.70 m/s2

B. sticking some putty on the pendulum bob, thereby increasing its mass

C. decreasing the amplitude of the pendulum’s swings

Solutions

Expert Solution

samet mamat answered 1 year ago

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