Question

4. A Foucault pendulum is used to demonstrate the rotation of the Earth. They can usually be found in science museums. A certain pendulum has a 120-kg bob swinging on a 16.2-m-long wire with a maximum amplitude of 6.3°.

A. Sketch the pendulum at its maximum displacement and label all known quantities.

B. What is the difference in gravitational potential energy between the maximum displacement and the equilibrium point?

C. What is the maximum speed of the bob?

D. Where in the oscillation is the bob when it has its maximum speed?

E. What is the period and frequency of the oscillation?

Answer 1

solution 2 10- 6.80) here cose - H 16.2 H 16.2 l'os 6.3 nn0 HE 16.2.10363 H= 16.10 m hence h= 16.2 16.10 = 10.1 metus B. difference in ma lolx9 9 - 9.81 m/s potential energy = mgh = 190 X 9.61X 0) 17.42 Joule let maximum speed be Vmax det es consider the ero potential envigy at meon position here using conservation 9 enougy law the potential chogy at into maximum displacement is converted dinete enolgy at meon position Immax = 117.72 hence 117.72X2 VY may = 120 [Vmax. = 1.4 ms]

cut O E mean position period T- stje e 16:2m 9 = 9.81 m/s 2x 304 16.2 V9 81 T= 8,07 second] frequency V+ + $107 - 10.12. Hz)