Question

(a) You wish to determine the height of the smokestack of a local coal burning power plant. You convince a member of the maintenance crew to mount the support for a simple pendulum at the top of the stack and you suspend a 1.00 kg mass that just misses the ground at its lowest point from the pendulum cord. If the period of the pendulum is 30.7 s, determine the height of the smokestack. (b) If you had the ability to take this pendulum to the moon, where the acceleration due to gravity is 1.67 m/s2, what would you expect the period of the pendulum to be?

Answer 1

(a)

Use formula $T=2\pi \sqrt{\frac{L}{g}}$ , where $L$ is the length of the smokestack

$\frac{T}{2\pi }=\sqrt{\frac{L}{g}}$

$(\frac{T}{2\pi })^{2}=\frac{L}{g}$

$\frac{T^{2}}{4\pi^{2} }*g=L$

$\frac{(30.7s)^{2}}{4\pi^{2} }*9.81m/s^{2}=L$

$\frac{30.7^{2}}{4\pi^{2} }*9.81=L$

ANSWER: ${\color{Red} L=234.2m}$

======================

(b)

Use formula $T=2\pi \sqrt{\frac{L}{g}}$

$T=2\pi \sqrt{\frac{234.2m}{1.67m/s^{2}}}$

$T=2\pi \sqrt{\frac{234.2}{1.67}}$

ANSWER: ${\color{Red} T=74.41s}$

========================