Solving 2 Spring Questions: Max Compression and Work Done

[Sasor]

Question 1:

Homework Statement

You have a spring at height d where it is relaxed.
You drop a ball (mass m) from a height (h) so that it lands on the spring with spring constant k.
What is the max compression of the spring in terms of given variables?
Given-

m
g
k
d
h

Homework Equations

Find
dmax=max compression distance

The Attempt at a Solution

i did-

deltaUgrav+deltaUspring=0

(mg(d-dmax)-mg(d+h))+(.5k(dmax)^2-.5k(d-d))=0

mgd-mgdmax-mgd-mgh+.5k(dmax)^2=0

-mg(dmax)-mg(h)+.5k(dmax)^2=0

.5k(dmax)^2=mg(dmax+h)

Can you solve for dmax or do u have to do quadratic equation?Question 2:

Homework Statement

If you have a spring and an object with mass m
and you put the object on the spring and let go, without giving it any initial velocity, what is the work done by the spring on the object? Answer is symbolic
Given variables-

Fspring with respect to s
m
g
k
s0(= initial length, relaxed length)
sf

Homework Equations

Symbollically, what is the work done?

The Attempt at a Solution

I did it like this-

Work= Integral(Fspring) evaluated from initial s to final s

so

Integral of ks ds= .5ks^2] sf-s0

=.5k(sf)^2-.5k(s0)^2
=.5k(sf-s0)

Is this the right amount of work?

 

[HallsofIvy]

It is almost impossible to read what you have written. Calculate the kinetic energy and potential energy the weight has when it hits the spring (take the floor as 0 potential energy so I think you mean the natural length of the spring). Find the work done to compress the spring a distance x and the potential energy at height d- x. Set the total energy at each height equal and solve for x.

 

[Sasor]

Ok let me change things to be more readable