How to Solve a Tough Trampoline Problem?

[MrMath]

Tough trampoline problem...help?!

Hi there...i've recently been set a problem in one of my modules and need some help as to how to solve it, it goes as follows...a person jumps from a height (x) onto a trampoline, the person desires to bounce for 30 seconds without any effort of their own, but also their speed to not get too frightening. Assuming air resistance is proportional to speed, what should the trampolines properties be? What should the height of the platform be? And why?

Could someone please help me with this? Much appreciated!
MrMath

 

[denverdoc]

Welcome to PF. the forum guidelines ask that you do some work, or even at least post some remarks about your source of confusion. The trampoline is a big spring. Should it be a perfect spring, that is when there is no internal friction, would depend to the extent air resistance takes away enuf energy during the cycles in thirty seconds such that the last cycles landing doesn't stretch tramp enuf to impart enuf force to overcome weight? It can be calculated, but you might want to first do some research on falling bodies such as skydivers. We would need at least one other piece of info to even make a go of this problem.

 

[rcgldr]

Competition trampolines have very little wind resistance, usually they are like nets ("ozzie" / Australia beds), or the older style 1/4" canvas beds (1/4 inch wide strips with about 5/8 inch spacing between). Still, some energy is consumed with each bounce.

Even with 80% energy retension, 30 seconds would be a relatively long time to continue bouncing. I would suspect that a person's feet would no longer leave the surface of the tramp in much less time, although vertical motion would remain for quite a while longer after this.

 

[MrMath]

Sorry, previously i failed to mention that i have actually done some work and realize that conservation of energy is vital to the problem with PE, KE and Elastic E being the three main types, the energy is obviously lost to friction, wind resistance and deformation causing the person to not bounce to the same height each bounce. Given a height i can obviously work out the max speed the person reaches (just prior to point of contact with the trampoline) but from there if i guessed at a spring constant how would i go about modelling the trampoline? and how would i work out how far it would bounce the person back up?

 

[denverdoc]

well before getting too much into the trampoline itself, two problems maybe to consider would be a horizontal spring, which itself is fixed to the wall, and is struck by a block of mass M. Then you could add friction if desired as some fx of velocity, normally V^2 for air resistance. Then you could turn the problem over vertically to consider gravity. I'd do all this if you haven't already before thinking about the actual tramp.