As the captain of the scientific team sent to Planet Physics, one of your tasks
ID: 1277678 • Letter: A
Question
As the captain of the scientific team sent to Planet Physics, one of your tasks is to measure g. You have a long, thin wire labeled 1.66g/m and a 1.24kg weight. You have your accurate space cadet chronometer but, unfortunately, you seem to have forgotten a meter stick. Undeterred, you first find the midpoint of the wire by folding it in half. You then attach one end of the wire to the wall of your laboratory, stretch it horizontally to pass over a pulley at the midpoint of the wire, then tie the 1.24kg weight to the end hanging over the pulley. By vibrating the wire, and measuring time with your chronometer, you find that the wire's second harmonic frequency is 200Hz . Next, with the 1.24kg weight still tied to one end of the wire, you attach the other end to the ceiling to make a pendulum. You find that the pendulum requires 314s to complete 100 oscillations. Pulling out your trusty calculator, you get to work.
What value of g will you report back to headquarters?
Please explain your answer. Thank you
Explanation / Answer
T = mg = 1.24*9.8 = 12.152 N
u = 1.66g/m = 0.00166 kg/m
l = L/2
V = sqrt(T/u) = 85.5 m/s
f2 = nV/2l
200 = 2*85.5/2l
l = 0.4275
L = 2l = 0.855m
T = 314/100 =3.14s
T = 2*pi*sqrt(L/g)
g = 4*pi^2*L/T^2
g = 3.42 m/s^2
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