Conservation Of Energy

Pendulum Problem - Angular Momentum and Kinetic Energy

A pendulum consists of a bob of mass and a massless, inextensible string of length . It is suspended from a fixed point at a height above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse is imparted to the bob at some instant.

After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. We are tasked with finding the magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off, and the kinetic energy of the pendulum just after the lift-off.

Solution:

The given values are:

• Mass of bob,
• Length of string,
• Impulse imparted,
• Height from which the bob is suspended,

Since the bob is lifted after the string becomes taut, it will gain potential energy, and we can use the work-energy theorem. The total mechanical energy of the system just after the lift-off will consist of the kinetic energy and potential energy.

From the conservation of mechanical energy and the information provided, the kinetic energy of the pendulum just after the lift-off is given by:

Answer:

The value of is .