# Conservation of moentum and a spring.

1. Jan 19, 2014

### JohnGG

1. The problem statement, all variables and given/known data
We got a ball moving at speed 2/√3 m/s, and it hits another ball that is attached to the string. Ball 2 has 3 times the mass of ball 1. After the crash, ball one stucks in ball 2 and the spring gets .02m shorter at its minimum length. There are frictions with n=1/12 and g=10m/s^2. Find the constant k of the spring.
2. Relevant equations
ΔP=0=>mu=4mu', u'=u/4, you cant use hooke's law as it isnt in the textbook.
Fy=0<=>N=mg
M=3m, M'=4m
3. The attempt at a solution
I used conservation of energy principle to get 1/2Mu'^2=1/2kx^2-nM'g=>Mu'^2+2nM'g=kx^2=>(Mu'^2+2nM'g)/x^2=k and thn just plug in numbers, but the problem is I ended up with a k as a function of m.

2. Jan 19, 2014

### voko

Your equation for the conservation of energy cannot be correct. It has nM'g as an addend, and its dimension is that of force.

Another issue is when one ball gets stuck in another ball in a collision, there is a loss of energy, while you assume it is fully conserved.

3. Jan 19, 2014

### JohnGG

What would be the correct equation?

I found that 1/3 of kinetic energy turned into heat in a question I skipped here. How could I use that to find k?

4. Jan 19, 2014

### voko

The correct equation would have the kinetic energy of the two balls immediately after the collision, and the work of the spring and friction over the distance of maximum compression.

5. Jan 19, 2014

### JohnGG

1/2M'u'^2=-Tx+?
What is the work of the spring?

6. Jan 19, 2014

### voko

How is work related with potential energy?

7. Jan 19, 2014

### JohnGG

W=-ΔU. But where is the k I search for?

8. Jan 19, 2014

### voko

In you very first message, you had ${1 \over 2} kx^2$. Where did that come from?