A pendulum?

Question

A pendulum consists of a 1.6 kg stone swinging on a 3.0 m string of negligible mass. The stone has a speed of 8.2 m/s when it passes its lowest point. (a) What is the speed when the string is at 59° to the vertical? (b) What is the greatest angle with the vertical that the string will reach during the stone's motion? (c) If the potential energy of the pendulum-Earth system is taken to be zero at the stone's lowest point, what is the total mechanical energy of the system?

Answer 1

The mechanical energy of a pendulum is conserved.

At the bottom of the swing, all of the energy is kinetic.
We'll take potential energy to be zero at the bottom of the swing.

So E = 1/2 m v^2 = 1/2 (1.6 kg)(8.2 m/s)^2

When the string is at 59 degrees, the height of the stone is
h = L - L cos 59

E = 1/2 m v^2 + mgh

You know everything execpt v; solve for v.

At the greatest angle t, the height is h = L - L cos t.

E = mgh

Solve for h, then solve for the angle t.

The total mechanical energy is E as calculated in the first part.