For multiple choice questions, circle the one best answer or letter (unless more
ID: 1516265 • Letter: F
Question
For multiple choice questions, circle the one best answer or letter (unless more than one answer is asked for). Show your work on free-response questions. Be sure to use proper units and significant figures in your final answers. Organization and neatness count, too. Do NOT use red ink - please reserve that color for grading. 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 5.00-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.) If you want the clock to be used on the surface of the Earth near sea level (g = 9.80 m/s^2), what length should you use for the pendulum arm? Show your work. Suppose that the temperature in the room gets much warmer, and the length of the pendulum's arm expands by 1.00%. By what multiplicative factor will the pendulum's period increase? Show your work. Express your final answer as either a decimal or a percentage (with appropriate sig.figs.). 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: moving the pendulum to the top of a (fictitiously) high mountain where g = 9.70 m/s^2 sticking some putty on the pendulum bob, thereby increasing its mass decreasing the amplitude of the pendulum's swingsExplanation / Answer
1)
a) we know,
T = 2*pi*sqrt(L/g)
T^2 = 4*pi^2*L/g
==> L = g*T^2/(4*pi^2)
= 9.8*2^2/(4*pi^2)
= 0.993 m
b) L' = L + 0.01*L
= 0.993 + 0.01*0.993
= 1.00293
T' = 2*pi*sqrt(L'/g)
= 2*pisqrt(1.00293/9.8)
= 2.01 s
T'/T = 2.01/2
T' = 1.005*T
c)
In case A only Time period would be increased.
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