Analyzing the Motion of a Jumping Spring: Tips and Techniques

[luckis11]

A spring is pushed against the ground (or against the wall) and then left free to move. So, besides its motion as a traveling object, it also contracts and expands. Where can I find this motion analysis?

 

[tiny-tim]

hi luckis11!

… Where can I find this motion analysis?

you'll find plenty of threads on it here …

use conservation of energy (kinetic energy + spring potential energy) ​

 

[luckis11]

What do you mean "on it"? I'll find there the case of my question?

 

[tiny-tim]

What do you mean "on it"? I'll find there the case of my question?

similar cases

try conservation of energy … what do you get? ​

 

[luckis11]

At what expansion will it lose contact with the wall?

 

[tiny-tim]

show us how far you've got, and where you're stuck, and then we'll know how to help!

 

[luckis11]

I am stuck here:

The speed of the spring (the spring=? I guess the centre of the mass of the spring) that will have just after losing contact with the wall is the last speed of the centre of the mass of the spring that it had just before it lost contact with the wall?

 

[AlephZero]

This is actually a hard problem to solve, if you are talking about a "real" spring where the mass is distributed along the length of the spring.

I suggest you start with two easier problems:

1. A massless spring, with one end pushed against the ground and a mass on the other end.

2. The same as #1, but with equal masses on each end of the spring.

 

[luckis11]

You tell me to change my problem? That's a joke I guess.

Ι BET that it's not hard, but impossible.

 

[AlephZero]

You tell me to change my problem? That's a joke I guess.

No, it's not a joke. If you don't know how to solve those easier problems, you don't know enough to understand a solution of your problem even if we told you how to do it.

If you can solve the second one correctly for a vertical spring and including gravity, then you will know WHY your problem is hard.

Ι BET that it's not hard, but impossible.

No, it's not impossible.

 

[luckis11]

A hand pushes it against the wall and then let it free. No mass attached.

At what expansion will it lose contact with the wall?

 

[AlephZero]

A hand pushes it against the wall and then let it free. No mass attached.

At what expansion will it lose contact with the wall?

If the spring is horizontal it will lose contact with the wall when it is at its unstretched length, at time L/c, where L is the length and c is the axial wave velocity in the spring. c^2 = E/\rho where E is the elastic modulus and \rho is the density (assuming the spring is "smeared out" into a uniform material)

If it is vertical the situation is more complicated because of the weight of the spring. When it leaves the ground it will not be uniformly stretched. If it is only compressed a small amount it may not leave the ground at all.

You haven't given us any clues about how much math and physics you know already, so I'm not going to try to explain why that is the answer.

 

[luckis11]

Where's that solution?

Should't there be a solution with the usual mdu/dt=kx? I think it should.

 

[luckis11]

"it will lose contact with the wall when it is at its unstretched length"

http://www.youtube.com/watch?v=00I2uXDxbaE&NR=1

Where can I see a spring losing contact with the wall before (or just when) it reaches its normal length?