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 1.61 g/m and a 1.30 kg 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 1.30 kg 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 200 Hz . Next, with the 1.30 kg 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 318 s to complete 200 oscillations. Pulling out your trusty calculator, you get to work.

What value of g will you report back to headquarters?

Answer 1

Consider the length of the string is L and the wire is vibrating in the second harmonic Thus, the wavelength λ in terms of length of the string is. The speed v of the wave on the string in terms of tension and the reduced mass is, The tension in the string is, The speed of the wave after substituting the value of the tension is, mg The expression of the wavelength in terms of the speed and the frequency is, Substitute for v 2 Img The expression of the time-period of a pendulum is, (2.T)

Substitute for L and rearrange the expression for g 2mg (21) T4 4 m The gravity is, 1.30 kg 2 (2"(1.61x 10-3 kg/m (318/200 200 Hz -19.7 m/s