# Graphical method to calculate power

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1. Nov 12, 2014

### Nicaragua

1. The problem statement, all variables and given/known data
I have been asked to show a graphical, more accurate method to calculate power used when running up a flight of stairs. The method I have used previously is measuring the height of the stairs, recording my weight in Newtons, timing how long it takes to run from the bottom to the top, then using the power equation.

2. Relevant equations
When asked to come up with a more accurate, graphical method, my tutor gave me some hints: independent and dependent variable, y=mx + c. I have thought very hard but can't seem to come up with an answer. Power = Force x Displacement / time : or in this case, P = mgh/ t.

3. The attempt at a solution
As the equation used is effectively mgh/t, time would be on the x axis, and Gravitational Potential Energy on the y axis. The steady gradient would represent Power as you would divide mgh by time.

This is my best attempt, but it still leaves some points open. Why is this more accurate? I do not know.

If anyone who understands this more than I do could help me out a little, I'd be very thankful to learn.

2. Nov 12, 2014

### rude man

You could do several runs (at last 20 or so) with different heights. Then you could graph h on the x axis and t on the y axis. You could do a least squares fit of the data and get the fit line t = mh + c. m is the slope, not your mass.

Then, using only the fit line, you compute power at several data pairs (hi,ti) and take the average using P = Wh/t where W is your weight.

Be sure to get enough rest between runs or the data will be meaningless.