# The velocity of a very long pendulum

##### Demonstration

Measuring the velocity of a pendulum at different points along its swing to introduce discussions of acceleration and force.

#### Apparatus and materials

Massive pendulum

Electronic scaler/timer

Light gate, or photo-diode assembly and light souce

#### 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 beam must be suitable for anchoring the top of the wire.

The bob should be close to the floor or bench when at rest with a suitable cushion to catch it should the wire slip or break.

As the wire is under tension, it would be prudent to wear safety spectacles.

The pendulum: It’s best to use a massive pendulum bob such as a large brick or a 3 kg mass, but you could use a 5 cm steel sphere. To avoid timing difficulties caused by rotation, the bob should be a large sphere or should have a cardboard cylinder fixed round it like a collar. The bob should be suspended by steel wire and have a very rigid support, if possible the ceiling so that it is as long as possible.

If you use a photo-diode assembly, connect it to the red terminals of the scaler/ timer. The pre-focused bulb illuminates the photo-diode.

#### Procedure

a Position the pendulum and light gate so that when the bob is at its lowest point it passes through the gate. Connect the light gate to the timer.

b Draw the massive pendulum to one side. Release it to swing through the light gate. The timer will record the time taken, enabling its velocity to be calculated.

c Reposition the light gate and time the bob at several places in the swing. Calculate its velocity at each position.

#### Teaching notes

1 This experiment is only suited to more able students. Begin by asking: is the acceleration of a pendulum constant?

Help your students to appreciate that the acceleration is greatest where the velocity can only increase, at the top of the swing (here the velocity is zero). The acceleration is zero where the velocity cannot increase any more, at the bottom of the swing (here the velocity is a maximum).

To follow this discussion, students need to clarify in their own minds the relations between bob position, velocity and acceleration. Weaker students will easily become confused.

If the acceleration of a body is directly proportional to its distance from a fixed point, and is always directed towards that point, the motion is simple harmonic.

2 Sketch (or plot) a graph of velocity against time or displacement for a few oscillations. With more advanced students, you may want to compare a graph of velocity against time with a graph of displacement against time, to introduce the idea of a phase difference.

3 The force causing the acceleration is always directed inwards towards the centre of the swing. It is the vector sum of the weight of the bob and the tension in the string.