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The swinging pendulum

Energy and power · level 3, lesson 4 of 6

A question to start

Pull a swing back and let go, without pushing. It swings to the other side, almost as high, and back again. What is happening to its energy? And how would it swing on Mars?

The idea

A pendulum is a weight on a string or rod that swings freely: a swing, a clock pendulum, a conker on a string.

As it swings, its energy changes back and forth:

  • At each end, it stops for a moment at its highest point. All its energy is height energy.
  • In the middle, it is at its lowest point and moving fastest. All its energy is moving energy.

The total stays the same, apart from a little lost to air and friction at the top. That is why each swing goes back to almost the same height, and the pendulum slowly dies down.

all heightall heightall moving

On Mars, a pendulum still swings to the same height on each side: energy is still conserved. But weaker gravity pulls it back more gently, so it swings more slowly.

A pendulum 1 m long Mars Earth
Time for one swing there and back 3.3 s 2.0 s
Swings in a minute about 18 about 30

A pendulum clock brought from Earth would run slow on Mars, losing about 23 minutes every hour.

Worked examples

1. A swing. You start it 1 m above its lowest point. It rises to nearly 1 m on the other side, a little less each time as air slows it.

2. Pushing. A friend gives a small push at the right moment each swing. That adds just enough energy to make up for the losses, so the swing keeps going.

Try it

  1. Where in its swing does a pendulum move fastest?
  2. Where is all its energy height energy?
  3. Why does a pendulum slowly stop swinging?
  4. Would a pendulum on Mars swing faster or slower than the same one on Earth?
Answers
  1. At the bottom, in the middle of the swing.
  2. At each end, where it stops for a moment.
  3. Air resistance and friction turn a little of its energy into heat on each swing.
  4. Slower: weaker gravity pulls it back more gently.

Common mistake

"A pendulum on Mars would swing higher, because gravity is weaker." It swings to the same height it started from: energy is conserved. Only the speed changes.

Where it leads