Re: How does waight affect how high you go on a trampoline?

Dear Anne,

While I think doing experiments to test scientific theories is a wonderful 
thing, it is always very important to make sure they are safe 
experiments.  Trampolines, unfortunately, can be very dangerous, 
especially if they are not surrounded with a safety net.  Many people end 
up in the emergency room with broken bones, or worse, for trampoline 
injuries.  How about doing this as a Gedanken experiment, which was one of 
Einstein’s ways of experimenting?  A Gedanken experiment is a “thought” 
experiment, that is, one that you do in your head.

You can think of a trampoline as a platform on a spring on which you are 
standing.  Please take a look at this website where I have drawn a diagram 
for you (http://www.gpc.edu/~jguinn/MadSci/Trampoline.pdf).  The strength 
of the spring (trampoline) can be described by the spring constant, “k”.  
The larger “k” is, the less the spring, or trampoline, will compress or 
stretch for a given weight.  A very tight trampoline (large “k” value) 
would stretch down only a little if you stood on it, a very loose 
trampoline (small “k” value) would stretch a lot.  The more weight you put 
on the trampoline, the more it will stretch.  We can measure the amount of 
stretch by the displacement, “x”, which is the distance the spring goes 
down.  These three quantities are roughly related by the equation

Weight equals Spring constant times Displacement , or

W = k x .

So what would happen if you put weights on a person on the trampoline?  
Well, you would be increasing their total weight, and so, to start, the 
trampoline would stretch more,  a little more if “k” is big, a lot more 
if “k” is small.

How high would they go?  Now that depends on how hard the person starts 
jumping.  When someone first climbs on a trampoline, the trampoline 
stretches and the person stands without moving on the somewhat stretched 
trampoline.  To get them flying in the air, the person needs to start 
pushing with their legs to get the trampoline to stretch more.  As the 
person starts squatting down and pushing up, they are pushing more on the 
trampoline, and increasing the displacement.  This makes the trampoline 
push back on them more, that is, with more force.  If the person keeps 
doing this, the force from the trampoline can get so large that it tosses 
them right into the air.

How will their weight affect this?  The heavier the person is (it doesn’t 
matter if it’s their own weight or added weights) the harder they would 
need to push to get them moving.  It’s just like jumping into the air; it 
would be harder for you to jump off the ground if you’re wearing a heavy 
backpack, than if you aren’t.  The trampoline would have to push a heavier 
person harder to get them to the same height as a lighter person, and the 
heavier person would have to do more work to get the trampoline to stretch 
enough to do it.

The end result of all this is that a person with extra weights wouldn’t 
necessarily go higher than when they didn’t have the weights.  As a matter 
of fact, they would have to worker harder to go as high as they could 
without the weights!

Well, Anne, I hope I’ve answered your question.  Again, let me emphasize, 
please be careful on your trampoline, I certainly wouldn’t want you to get 
hurt!

Good luck and have fun thinking of more physics experiments!

Please let us know if you have any more questions.

Sincerely,

Jim Guinn
Georgia Perimeter College