11.2 - Personal Power Output

The experiment

Aim

To measure your own power output by finding how quickly you can do the work of lifting your own weight up a flight of stairs.

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Background

• Climbing stairs means lifting your weight, which takes work. Work done is the force multiplied by the distance moved in the direction of the force, $W=F\times d$.
• Here the force is your weight in newtons, which is your mass × gravitational field strength. The distance is the vertical height you climb, not the distance along the slope of the stairs.
• Power is how fast the work is done, $P=\frac{W}{t}$. Someone who runs up the stairs has a higher power output than someone who walks up, even though both do the same work.
• You can't measure power directly, but you can measure your mass, the height of the staircase, and the time you take.
• So in this practical you time yourself running up a staircase, work out the work done in lifting your weight, and divide it by the time.

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Variables

• Measurements - Your mass, the height of the staircase, and the time taken to run up it.
• Control variables - The same staircase and the same runner for every run.

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Method

1. Find your weight - Measure your mass in kilograms on bathroom scales, and multiply it by 10 N/kg.
2. Measure the risers - Measure the height of five different risers with a metre ruler, and find the mean.
3. Find the height of the staircase - Count the risers, multiply by the mean riser height, and convert to metres.
4. Time the run - On the longest flight you can find, a partner starts a stopwatch as your foot leaves the bottom step and stops it as you reach the top. To improve the timing, use light gates at the bottom and top step, which remove the timer's reaction time altogether.
5. Repeat - Rest, then run at least three times and find the mean time.
6. Calculate the power - Work done = weight × height, and power = work done ÷ time.

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Safety

• Clear stairs - Only run up the stairs, never down, and make sure they're clear of people and bags first.
• Your health - Hold the handrail if you need to, and don't take part if hard exercise isn't safe for you.

Worked example - Power output on a staircase

A student measured her own power output by running up a staircase. Take the gravitational field strength as 10 N/kg.

Calculate her power output, to an appropriate number of significant figures.

Common exam questions

Question 1

Why is the height of several risers measured and a mean taken, rather than measuring just one?

The risers aren't all exactly the same height, and one measurement could be a millimetre or two out. The mean is multiplied by the number of risers, so any error in it would be multiplied too.

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Question 2

Why is a long flight of stairs better than a short one?

The timer's reaction error is about the same whatever the flight. On a long flight taking several seconds, a two-tenths-of-a-second error is a small share of the time, but on a short flight it's a large share.

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Question 3

Two students run up the same staircase in the same time, but one has a greater mass. Which has the greater power output, and why?

The heavier student. They have a larger weight to lift through the same height, so they do more work, and more work in the same time means more power.

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Question 4

A student of mass 50 kg does 100 step-ups onto a step 0.25 m high in 200 s. Calculate her power output.

Her weight is 50 × 10 = 500 N. Each step-up does 500 × 0.25 = 125 J of work, so 100 of them do 12,500 J. The power is 12,500 ÷ 200 = 62.5 W.

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Question 5

Why is the power calculated smaller than the total power your body produces during the run?

Only the work done lifting your weight is counted. Your body also transfers energy to moving your arms and legs, and to your thermal energy store, which is why you get hot.