Calculating Spring Force with a Man's Jump and Platform Compression

[southernbelle]

Homework Statement

An 80 kg man jumps from a height of 2m onto platform mounted on springs. As the springs compress the platform is pushed down a maximum distance of 0.2m below its initial position, and it rebounds.
a) What is the man's speed at the instant the platform depressed 0.1m?
b) If the man had just stepped gently onto the platform how much would it have been pushed down?

Homework Equations

The Attempt at a Solution

A) I am stuck. I think maybe Ua + Ka = Ub + Kb
and mgh = 1/2kmv2
but then I don't know how to get k and v.

B) ΣFy = 0
ΣFy = Fs - mg
Fs = kd
0 = kd - mg
kd = mg
Now what?

 

[Rake-MC]

potential + kinetic = potential + kinetic
This is right.

So initially he has all gravitational potential (when he's 2m from the spring) no kinetic and no spring potential.

The moment he hits the board, he has some gravitational potential, some kinetic and is just about to receive some spring potential.

When he is 0.1 m into it he has some gravitational potential, some kinetic and some spring potential.

I'll give you this sum:

$$mg\delta h = \frac{1}{2} kx^2 + mg\delta h + \frac{1}{2} mv^2$$

Solving for v of course.

You can get k, by the information given. Maximum compression = 0.2m and you have his mass (80kg) and you have the acceleration of gravity (-9.81ms^-2).

Does F=-kx ring a bell?

Let me know how you go.

 

[Rake-MC]

potential + kinetic = potential + kinetic
This is right.

So initially he has all gravitational potential (when he's 2m from the spring) no kinetic and no spring potential.

The moment he hits the board, he has some gravitational potential, some kinetic and is just about to receive some spring potential.

When he is 0.1 m into it he has some gravitational potential, some kinetic and some spring potential.

I'll give you this sum:

$$mg\Delta h = \frac{1}{2} kx^2 + mg\Delta h + \frac{1}{2} mv^2$$

Solving for v of course.

You can get k, by the information given. Maximum compression = 0.2m and you have his mass (80kg) and you have the acceleration of gravity (-9.81ms^-2).

Does F=-kx ring a bell?

Let me know how you go.