A pendulum is composed of a mass m suspended from the ceiling by a massless string of length L.The mass is pulled back,raised and released.If the tension in the string at the bottom of the swing is 2mg,how high was the the mass raised above the bottom of the swing?
A)0.33 L
B)0.25 L
C)0.10 L
D)0.50 L
E)0.67 L

Question

Quizplus · Accepted Answer

At the bottom of the swing, the tension in the string is the sum of the centripetal force needed to keep the mass moving in a circular path and the gravitational force acting on the mass. The tension is given as $2mg$, which means the centripetal force component is $mg$, since the gravitational force $mg$ is also acting on the mass. The centripetal force can be equated to the change in potential energy, which is $mgh$, where $h$ is the height raised. Since the centripetal force is $mg$, and it equals $mgh$, we have $mg = mgh$, which simplifies to $h = \frac{1}{2}L$, indicating the mass was raised to a height of $0.5L$ above the bottom of the swing.

A Pendulum Is Composed of a Mass M Suspended from the Ceiling