1. You want to design a pendulum for a grandfather clock so thatit has a period of 2.00 seconds (so that one “tick†plus one “tockâ€occur during one complete period). The pendulum has a heavy 8.00-kgbob. (Throughout this problem, assume an ideal simple pendulum: thependulum’s arm has negligible mass, the bob can be approximated asa point-mass, the initial angle of displacement is small, and thereis negligible friction.)
a.) If you want the clock to be used on the surface of the Earthnear sea level (where g = 9.80 m/s2 ), what length should you usefor the pendulum arm? Show your work. (Note: How many significantfigures 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 whatpercentage will the pendulum’s period increase? Show your work.Express your final answer as either a decimal factor or apercentage (with appropriate sig. figs.).
c.) Which one or more of the following changes would (whenconsidered separately and individually) increase the period of thependulum, thereby making the clock run “slower� Circle ALL thatapply:
A. moving the pendulum to the top of a (fictitiously) highmountain where g = 9.70 m/s2
B. sticking some putty on the pendulum bob, thereby increasingits mass
C. decreasing the amplitude of the pendulum’s swings
