Question

The lighthouse on Presque Isle is 21.0 m tall. You decide to verify this by attaching a pendulum mount to the top of the lighthouse and observing the pendulum as it swings. You use a rope that just barely misses the ground when it is hanging straight down.

(a) If you attach a 2.0 kg mass to the end of the rope, pull it back, and release it, how long will it take for the pendulum to complete one cycle?

(b) How long will one cycle take if you replace the 2.0 kg mass with a 4.0 kg mass?

(c) When you pull the pendulum back just prior to releasing it, the mass is at a height of 50 cm above its equilibrium position. After you release it, what is the speed of the mass as it passes through equilibrium?

Answer 1

A.) Time period of a pendulum, T=

                                                                    $\mathbf{2 \pi \sqrt{\frac{l}{g}}}$

                                 T= 2*3.14 (21/9.8)^1/2=9.19 s

B.) Since, time period is independent of mass of pendulum, so period will remain 9.19 s.

C.)

                  $\mathbf{V=\sqrt{2gh}}$

                       = 3.13 m/s