# Measuring average power during a jump

1. Jul 6, 2009

### RoyalCat

1. The problem statement, all variables and given/known data
At your disposal are a scale and a measuring tape. You are not allowed to jump on the scale.
How would you go about measuring the average power you exert on the floor?

2. Relevant equations
$$P_{average}=\frac{\Delta E_{tot}}{\Delta t}$$

3. The attempt at a solution
I am honestly lost. Without a way to measure the time it takes to execute the jump, how am I supposed to calculate the average power? I mean, calculating the total energy difference is fairly straight-forward. Measure the height of the person's center of mass at the top of the jump (Momentary rest) and say that all you've gained is potential height energy (A good choice for a plane of reference here would be the height of the center of mass in the knees-bent position), and bam, you're done.

But how do I use that change in energy to calculate the average power?

A hint at the right way to approach this would be terrific.

Last edited: Jul 7, 2009
2. Jul 6, 2009

### LowlyPion

Well you can figure the impulse can't you from the height?

That gives you the I = F * T = Δmv

You can get the maximum force reading from the scale, ... maybe deduce the time from that?

3. Jul 6, 2009

### xavior13

Can't you use delta y= Vi(t)+at^2/2? Vi=0, a=9.8, delta y measured solve for t then multiply t times two for the whole trip then devide delta E by delta t? seems reasonable although i usually overlook some detail -_-. tell me when you solve it. good luck.

4. Jul 7, 2009

### RoyalCat

EDIT:
Maybe it's one of those 'think outside the box' exercises? I could measure the time by dropping the scales from a measured height, until the time it takes them to drop, matches the time it takes the jumper to straighten out, and from there, since I have the time it takes to transfer the energy, the rest of the calculations are trivial
?

xavior13, there is no way to measure the time it takes to execute the jump. And your acceleration during a jump is FAR from constant, and FAR from just free-fall.

LowlyPion, we're not allowed to jump on the scale. So it's only there to measure our mass (Or for some other creative use which I haven't figured out yet.)

Calculating $$\Delta mv$$ is tricky as well. I can't see how I can take care of the whole height energy conundrum. Would setting my plane of reference at the height of the center of mass when the jumper is on the tips of his toes do me any good? Would it be correct to claim, that at that point during his jump, all of his negative height energy has been converted into kinetic energy?
$$W=\Delta E_k$$
But that would still leave the problem of how long it took him to straighten out, though. >>

Last edited: Jul 7, 2009
5. Jul 7, 2009

### LowlyPion

I wasn't suggesting jumping on the scale.

I was suggesting to jump off the scale.

6. Jul 7, 2009

### RoyalCat

One of two things is eluding me here. It's either the irony, or the difference. Care to clarify?

7. Jul 7, 2009

### LowlyPion

If you stand on the scale and jump off observing the maximum deflection of the needle and determining the height that you jump, doesn't that give you a way to determine the impulse and the maximum force?

F * T = Δmv

8. Jul 7, 2009

### RoyalCat

I'd say no. You would only be able to measure the maximal deflection (Unless you have a video camera that can help you draw a graph of $$F(t)$$ which you would then integrate), and that's only if the scales can get to that reading at all, or fast enough (Don't you end up exerting several thousand Newtons during a jump?).

The maximal deflection doesn't tell us much about the average force.
And I'm fairly certain they meant jumping on (Or off. (: ) the scale in any sort of way is not allowed.

9. Jul 7, 2009

### xavior13

lol yeah i think Lowly is reading too much into technicalities.

try this: avg power= square root of 4.9 times mass times maximum height times 9.81

10. Jul 7, 2009

### davieddy

Measure how far you crouch down before you jump.
Assume constant acceleration, and you can calculate the time taken
and acceleration during the actual jumping (straightening the legs).

11. Jul 7, 2009

### RoyalCat

Interestingly enough, that's almost word-for-word what the full wording of the problem suggested I do (Minus the 'assume constant acceleration' bit), but I don't really understand how assuming constant acceleration lets me find the time taken.

All that does, is give me a complicated way to calculate the work done, and I think it's much better to just look at the crouched position compared to the top of the jump position to see what the work done was.

12. Jul 7, 2009

### xavior13

im sry i made a mistake.

solve it with this: avg power=sq root of 4.9 times mass times sq root of max height times 9.81

its very simple. potential energy at top=work= mgh. Avg power=mgh/time, time= sq of 2h/a then simplify to wat i typed above and solve. a=freefall acceleration.

tell me wat u get, and do u have the answer to the problem?

13. Jul 7, 2009

### davieddy

He crouches to a depth d, accelerates to speed v in time t and then ascends
under gravity to a height h.

mv^2/2=mgh
So we know v.

d=vt/2 so t=2d/v

Work done during jump = mv^2/2 + mgd

Power = work/t

14. Jul 7, 2009

### RoyalCat

Bleh, I thought that was the solution for a second, but all that tells us is the power of gravity, since we don't know how long it takes him to actually get from the initial state, the crouch at depth d, to the final state, the upright position with enough velocity to reach height h, we don't know how long it actually takes him to do the work.

I'm really starting to lean towards my idea of dropping the scale from such a height, so that the time it takes it to fall is equal to the time it takes the jumper to straighten out, and then we can find out the time during which he does work.

xavior, when you're jumping, you are NOT accelerating at free-fall acceleration. That solution is completely incorrect.

15. Jul 7, 2009

### xavior13

lol ok ok sheesh!

16. Jul 7, 2009

### davieddy

As I said t = 2d/v
You know v and d
What's the problem?

17. Jul 7, 2009

### RoyalCat

I do not understand that equation. Where did it come from, what does it mean? At what point does the jumper cover twice the depth of his crouch at the speed at which he leaves his crouch?

The jumper at no point moves at a constant velocity, I really can't make heads or tails of your equation.

18. Jul 7, 2009

### davieddy

d = (u+v)t/2 (area under v-t graph or average velocity * time)
u=0

19. Jul 7, 2009

### RoyalCat

Oooh, I think I see it now. Since I know that the initial speed is 0, and I can tell the final speed from the height at the top of the jump, I can see what the average acceleration is, since I know the distance over which the jumper accelerates, and from that, I can see how long it took as well.

Your equation still makes very little sense to me, though. Thanks anyway. :3

20. Jul 7, 2009

### davieddy

If you read Dr Al's "sticky" post on formulae,
you will see "average velocity = displacement / time"
and for constant acceleration,
"average velocity = (u+v)/2"

It follows that d = (u+v)/2 * t.
I don't know why he didn't include this in his list of constant acceleration
equations.
Perhaps he overestimated the intelligence of the average punter here :)

David
(with attitude)