A pendulum that was originally erected by Foucault at the Pantheon in Paris for the Paris Exhibition in 1851 was restored in 1995. It has a 28.0-kg sphere suspended from a 67.0-m light cable. How long would it take for the bob in this pendulum to move from the position of maximum displacement down to the equilibrium point?
A) 2.58 s
B) 21.5 s
C) 4.11 s
D) 32.2 s
E) 42.9 s

Question

A pendulum that was originally erected by Foucault at the Pantheon in Paris for the Paris Exhibition in 1851 was restored in 1995. It has a 28.0-kg sphere suspended from a 67.0-m light cable. How long would it take for the bob in this pendulum to move from the position of maximum displacement down to the equilibrium point?
A)  2.58 s
B)  21.5 s
C)  4.11 s
D)  32.2 s
E)  42.9 s

Quizplus · Accepted Answer

The time it takes for a pendulum to move from its maximum displacement to the equilibrium point is a quarter of its period. The period $T$ of a pendulum is given by $T = 2\pi\sqrt{\frac{L}{g}}$, where $L$ is the length of the pendulum and $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$). For a pendulum with a length of 67.0 m, the period is $T = 2\pi\sqrt{\frac{67.0}{9.8}}$. Calculating this gives a period of approximately 16.4 seconds. Since we are interested in the time to go from maximum displacement to equilibrium, we divide this period by 4, resulting in approximately 4.1 seconds.

A Pendulum That Was Originally Erected by Foucault at the Pantheon