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# work, energy and power :/ watch

1. a cyclist of mass 100kg produces a power of 72W.
a) if he maintains a steady speed of 4.0m/s along a level road, what resistance is he overcoming?
b) if this resistance remains comstant, what speed can be maintained up a slope of 1 in 40?

i'm not sure where to start here, i first thought about using force=power/velocity
to find the forward force, then if the speeds constant (which i think it is) the resistance=forward force.
but its more the b) part im stuck on, as i'm really not sure!

any help would be gratefull, also any correction if im going wrong on part a, thanks sarah xx
2. Your answer to part a) sounds fine to me. I would be clear in your answer that the cyclist is doing work against resistance only, and this accounts for the 72W of power.

For b), he now needs to do work against gravity as well as against resistance. If he were moving vertically he would have to do work against all of the gravitational force pulling him down. In fact, he is moving up a slope so he only works against a fraction of that force. Sketch the slope and work out what this fraction is. Add this to the resistance he is working against and put the sum in the expression linking power, velocity and force. You know the power he produces, so it is then simple to determine the speed maintained.
3. okay, so i got a) to equal 18N.

but with b) the fraction will be 1/40, so do i need to work out 1/40 from the gravity force, 9.8 m/s,?? then add that 18N?? thanks xx
4. That answer to a) looks fine.

In b), the question is almost certainly expecting you to use 1/40 as the fraction of the gravitational force, but I think you should be aware this is just an approximation that we can make because the slope is shallow. The exact fraction is 1/sqrt(40^2 + 1), but this is so close to 1/40 that 1/40 can be used instead.

9.8 is not the gravitational force, it is the acceleration due to gravity. As such it should have units of ms^-2 not m/s. The gravitational force is found by multiplying the acceleration due to gravity by the cyclist's mass (this is a statement of Newton's second law). Then multiply this by the fraction you have just found, add it to the resistance and you have the total force the cyclist must supply to stay at constant speed. Then put this and the power he supplies into the F=P/v equation to get v.

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Updated: December 1, 2011
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