# Massive pendulum

##### Demonstration

Energy transfers in a simple pendulum illustrate the principle of conservation of energy.

Massive pendulum

#### Health & Safety and Technical notes

Two persons are needed to fix the support to a ceiling beam: one to hold the ladder or steps and one to do the work. The bob should be close to the floor when at rest with a suitable cushion to catch it should the wire slip or break.

A 5 cm steel sphere will work. A more massive pendulum-bob such as a 3 kg mass is better. It should preferably be suspended by steel wire and should have a very rigid support, if possible from the ceiling, so that it is as long as possible.

If a light gate is used to measure the velocity of the bob, the bob should either be cylindrical or have a cardboard cylinder fixed round it.

For a similar experiment to this, see The swinging pendulum, which uses a small bob and a light gate.

#### Procedure

a Pull the pendulum to one side and release it, allowing it to swing.

b Measure the difference in height between the bob at the end and middle of its flight. Calculate the gravitational potential energy lost and hence the velocity at the lowest point.

c A good demonstration is to pull the pendulum so that it just touches one's knee. Let it go and stand still until it returns. Do not push the pendulum on release.

d A useful extension to the experiment is to measure the speed of the pendulum bob at its lowest point, using multiflash photography, a ticker-timer or an ultrasound position sensor.

#### Teaching notes

1 When the pendulum is pulled to one side its bob rises higher so there is a gravitational store of energy. There is no way in which energy can be transferred through the thread of the pendulum, unless its support is insecure, so all the energy is transferred to kinetic energy of the bob as it swings downward.

Hence 1/2mv2 = mgh

where m is the mass of the pendulum bob, v its maximum speed and h the vertical distance through which the bob has fallen.

2 If you find the maximum speed of the bob (using one of the methods suggested in d), you can compare the maximum values of gravitational potential energy and kinetic energy.

2 The use of multiflash photography is described in the guidance note Multiflash photography.

The use of a light gate is described in Investigating energy transfers in a pendulum.

If you use a ticker-timer, attach a length of tickertape to the pendulum-bob (using Sellotape) so that it is pulled through the ticker-timer.

This experiment was safety-checked in November 2005