# Homework Help: Only for genius people: jumping stilts on a trampoline.

1. Dec 7, 2005

### rossero-NL

At school, my teacher asked us a question, where he didn't know the answere on too. The other teachters were not agreed to eachother about the answere.

This is the question:

A trampoline jumper jumps with jumpingstilts ( http://www.tanomi.com/shop/images_item/poweriser_01.jpg ) (shoes whith suspension) off of a stair one time from one meter hight. He tries to get as high as possible, and pushes himself as far as he can. And now the question is: when does he get OBVIOUS higher?

a: With the stilts on his feet
b: With the stilts in a backpack. (means same weight)
or
c: Doesn't make any difference, with or without the suspension-stilts.

Thanks!!!

2. Dec 7, 2005

b.
totally.

3. Dec 7, 2005

### Pengwuino

I don't understand the question here...

Are you saying he jumped off the stairs with the stilts in his backpack and then he tried again using them to jump off the stairs?

I'm pretty sure its A because you put energy into the springs when you compress them and assuming you "push off" with the same force you did without the stilts, the added energy stored in the springs should create a higher jump height.

And i do not think this would be considered "Advanced physics".

Last edited: Dec 7, 2005
4. Dec 7, 2005

### rossero-NL

He won't use them when they're in a backpack, and thats just the question. Will he get higher with, or without the stilts? And emptymaximum, do you have provement that he will get higher with the springs in his bag?

5. Dec 7, 2005

provement?

6. Dec 7, 2005

### rossero-NL

My english is not the best:p But an explication why it will be b.
Because that were my first thoughts too, but I can't prove that it's true. And i need somebody who can prove that one of the statements is true.

7. Dec 7, 2005

### Pengwuino

hmm im actually not sure now. I think it depends on if your foot touches the ground using the stilts or if all the work is done on the spring. If your foot touches the ground, you add your own jumping force to add to the spring force i believe. If not, its completely the spring's force and whatever energy you put into it, you'll get back out and the simple fact that the stilts make you higher before-hand is the reason you would jump higher with the stilts.

8. Dec 7, 2005

### rossero-NL

Yes, that's true

But I've thought of that too, and find out that if you don't use the stilts, but only the trampoline, the trampoline does the same thing. All you put in, you get back.

But, will the jumpstilts oppose the energy of the trampoline (so without stilts you get higher) Or, because of the stilts, you have longer contact with the trampoline and you're able to give more energy, and you'll get higher with the stilts.

Or, last but not least, with or without stilts, you put the same energy into the trampoline, so you will get the same energy back. Means, it doesn't matter whether you're wearing the stilts, or not.

So every answere can be good, but witch one IS good?

can anybody help me?

9. Dec 7, 2005

### Pengwuino

ohhh hes jumping on a trampoline...

ugh, its 3am, i can't think.

10. Dec 7, 2005

### Tide

If I understand the question correctly, he jumps higher wearing the stilts because his center of mass is higher.

11. Dec 7, 2005

### emptymaximum

interesting. trick question then eh?

i think maybe the question is supposed to be asking in which situation will the centre of mass have the greatest displacement between z = 0 and z = zmax?

Last edited: Dec 7, 2005
12. Dec 7, 2005

### emptymaximum

think about it for a bit and you'll see it's b. the stilts work like the shocks on a car. they'll absorb the energy from the restoring force onn the trampoline, and when the kid gets launched into the air, the stilts decompreess, but there's nothing for them to push on so they don't do any lifting.

in the idealised system, the kid would stay where he was.

13. Dec 8, 2005

### rossero-NL

But if you think more, the sto springs (trampoline and stilts) will hold eachother in balance. So at the deepest point they both hold 100% potential force. At the top, they will have decompressed equally till 0%. In the fases between, they allways have to keep up with eachother, so the stilt won't just opposit the trampoline, but only uses the power of it.

So after a few thinking, I concluded that it can't be b, because they work together as one spring. The only difference left is how much harder can the jumper push down the trampoline with or without the stilts.

If his max is in both situations the same, and the system is totally elastic, means no energy lost, he will get in both situations the same hight.

But if he can add more energy with or without stilts, than in the other situation, he will get higher. Because there can't be energy lost, so all energy will rest in hight.

So my final question is: Can he, or can't he add more energy in one of the two situations, and if so, can it be proved with formules witch one it is?

thanks

14. Dec 8, 2005

### rossero-NL

And Tide, back to your answere, it's not correctly, because when he starts his centre of mass is distance "a" higher. But the second he touches the trampoline, his centre is the same distance "a" higher, then when he touches the trampoline without the things.

Or is there something i didn't see?

15. Dec 8, 2005

### Tide

rossero,

No, there's nothing you're not seeing. I was a little too hasty in sizing up the problem.

16. Dec 8, 2005

### Cyrus

W/springs, He will be launched up just the same as with them in his backpack, the only difference is that when he is launched with the springs on his feet, the will decompress AFTER he leaves contact with the trampoline and thus do him no good! Its like an elevator, as he comes down on the tramp. (no pun, oh thats a bad one), his springs are being compressed due to deceleration. But once the trampoline changes directions, his inertia wants to still go down, which means the trampoline will push UP on him, and thus keep his springs compressed still or further compress them. Once he looses contact then and only then can the springs uncompress. Id say keep them in your backpack so you dont break your neck, cuz thats all there good for.

On second thought, I belive this system can be modeled by two springs in series, which means that the spring constant now goes down, and the tramp. can do less work to the acrobat, but still, springs seem to be bad.

Last edited: Dec 8, 2005
17. Dec 8, 2005

### CarlB

The whole purpose of the jumping stilts is to store up kinetic energy and then give it back. That's also the whole purpose of the trampoline.

So the problem really amounts to the question of should one put two springs in parallel or instead just use one of them.

From the point of view of conservation of energy, if one assumes that both the trampoline and the stilts are perfect, it doesn't matter what one does. But that's probably not a reasonable assumption.

From the point of view of avoiding a trip to the hospital, I say put stilts in the backpack, and then tell the person who wants you to jump that you can hear your mother calling you and it is time for you to go home.

Now if the trampoline and or the stilts are not perfect, but instead have some friction, we must make some sort of assumption of how that friction is related to how they are used. Only by doing this can we answer the problem.

Carl

18. Dec 8, 2005

### rossero-NL

Also is said: when does he obvious jump higher. And ovbious is not the couple centimeters he's missing because of the extra friction by the stilts.

I've made an drawning of what happens after my opinion. I don't have a clue, or its true or not, but that is what I'm asking you. I've send the drawning with the reply.

The weight (nr 1) is the weight of the man. (hight energy), the bound spring (nr 2) is the possible power of the man to push himself up at the lowest point (potential energy). The third spring (3) is the trampoline, without energy. The fourth one (4), only in situation 2, is the stilt, also without energy in the first fase. This is the starting situation.

Fase 2 is the second the man touches the tramp. The springs 2 and 3 are still out of ballast, and the weight (1) has kinetic energy and hight energy.

In fase 3, all springs are pushed in, and all under influence of the same force and energy. They all hav at this point potential energy, but th weight is out of ballast and has zero energy, and spring 4 (man's power), is ready to decompress in sit. 2.

In fase 4 all springs (including in sit. 2 the man's legs) are decompressed and have zero energy left. The weight gets back height and kinetic energy, and moves up.

In fase 5 all is up, the spring don't have potential energy, and the weight reaches his heighest point, and has only hight energy left.

My conclusion is that the 4th spring doesn't have any influence, because it is only in action in fase 3, were it works together with the tramp (3) like one spring. Although it is an weaker spring, the spring will be totally elastic and will give back as many kinetic energy as it took.

So my conclusion: it doesn't matter if he has or hasn't the stilts on his feet.

And for the funniest guys, i've seen a sample of a movie where acrobatics jump with jumping stilts on a tramp. It is possible. (although I think it's hard to learn, but they didn't look like they've broken their neck before.)

19. Dec 8, 2005

### rossero-NL

I saw that the add of an figure didn't work, so i've made a page on my site. the link is: www.rosserobertolli.4t.com/veren.html . Can annyone tell my when my explennation is correct or incorrect? thaks

20. Dec 8, 2005

### emptymaximum

the trampoline slows you down then you stop, that's when it will start to launch you up. the stilts work like a damper. the stilts make you jump higher on the ground because the ground is 'solid'. when they push on the trampoline, their energy goes into deforming the trampoline not boosting you up.

b.
totally.

21. Dec 8, 2005

### Cyrus

I agree with empty on this one.

22. Dec 9, 2005

### Hermite

I agree, the answer is (b) - he gets higher without the stilts. Here's why I think so:

Think of the man at the very bottom of the jump (on the trampoline). The springs are compressed by the man's weight and by the restoring force of the trampoline. As the trampoline pushes the man upward, the restoring force of the trampoline decreases (because it's proportional to the trampoline's downward displacement) and the effective 'weight' of the man against the springs decreases because he's given an upward momentum. This means that the springs are able to decompress mid-jump which allows them to work against the trampoline. Thus, the man's centre-of-mass displacement won't be as great as it would be without the springs (stilts).

Let me know what you all think.

I tried to put this into equations but couldn't (sorry).

23. Dec 9, 2005

### rossero-NL

Thats just the question. Does the springs work against the trampoline?

I think no, and thats why I think it can be any answere, without b. Nom my explenation.

You think the springs will have at some point more potential force downwards than the tramp upwards. If thats true, you say, the stilts will push the tramp back. Means, they trade energy. So the trampoline will give the man all the energy back, becaus in an ideal situation, the tramp has no mass, and wil come up with an endless speed. So it wil never lose contact and they give every part of energy back.

But I don't think they will have at some point an other potential energy level, because they will keep up to eachother. For example, you have two different springs, witch you push together with some force. They both keep eachother in balance. As the left is wearing double the energy as the right one, the left one will push to the right untill they have the same power. From this view, you can see the trampoline with stilts like one spring. With an lower constant. but in a ideal situation, that doesn't affect at all.

Then the man pushing down, I think he'll push the tramp down, more likely then he pushes himself up. But he gives all the energy to the trampline. And this one will give it all back. So if he pushes in both situations with the same strenght, he will get in the same situations the same hight.

So after long thinking, I think it will be, "it doesnt matter"

Can anybody tell me who he's thinking is right?

And cyrusabdollahi, with who did you argee? Me or emptymaximum?

24. Dec 9, 2005

### rossero-NL

And emptymaximum, you've said that "their energy goes into deforming the trampoline not boosting you up". But the effect of deforming an trampoline ís that he'll push you up.

Or am I thinking wrong?

25. Dec 9, 2005

### Hermite

I'm not sure what you mean by 'endless speed'. It doesn't matter how light the trampoline is, it cannot have an infinite speed. The trampoline's 'ability to push upward' depends on its initial displacement furthermore (since it has no mass) it will be very easy to change the trampoline's velocity. The more the trampoline rises, the smaller its restoring force thus the stilts will be able to push back i.e. they will NOT experience the same force between them at all times.
If the restoring force of the trampoline is opposed then it will have a lesser affect on the man.
As far as I can tell, it does make a difference.