# Power, Work and Energy

When work is done, energy is transferred.

Rub your hands together, hard. They get hot. There’s no way someone could tell whether you’d dipped your hands into hot water or applied a force against the frictional resistance of your palms – done mechanical work on them in other words – the result is the same. Hot hands.

Work = force x distance moved by the force along the same straight line

J = N x m (joules = newtons x metres)

If I clamber up a vertical ladder 4m high, I have moved my weight (800N) 4m against gravity. I have done 800×4 = 3200J of work to do this. Looking at it another way, I have acquired 3200J of gravitational potential energy.

Work done and energy transformed are two halves of the same coin.

One more thing. The route that I take makes no difference to the work that I do or the energy transferred. Walking up a spiral staircase to get to the top of the Eiffel Tower does exactly the same amount of work on me as if I’d used the elevator, since my weight is being transferred through the same vertical height. There are stern warnings about hurling objects – even small ones – off the summit of the Eiffel Tower. I wonder why….? You might try to work out how fast an object would be going at ground level, given that the top level is at a height of 276m. Plus or minus 15cm, depending on expansion due to temperature differences….Oh, forget about air resistance. I’ll post the answer, but do try to work it out for yourself.

Here’s a little problem:

For those who like exercise, you can walk almost up to the top.

The actual count of stairs includes 9 steps to the ticket booth at the base, 328 steps to the first level, 340 steps to the second level and 18 steps to the elevator platform on the second level. When exiting the elevator at the third level there are 15 more steps to ascend to the upper observation platform. Each step is 15cm high. If someone like me – my weight is 800N – walks at one step per second, work out how long it would take me, and also my average power (energy transformed per second). We can neglect the time in the elevator.

## One thought on “Power, Work and Energy”

1. esfscience says:

OK. Gravitational potential energy = mgh = kinetic energy gained = 1/2mv2.
m cancels – doesn’t matter how massive the object is when calculating how fast it is going.
Now do the algebra to get v on its own on 1 side of the equation:
v = sqrt[2gh]
=sqrt[2x10x276]
=sqrt[5520]
=74.3m/s
OR: 267km/h

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