# Homework Help: Collision problem

1. Nov 1, 2009

### PhilCam

1. The problem statement, all variables and given/known data
A bullet of mass .060 kg hits a 5.000 kg block with an initial speed of 225 m/s. The block is connected to a spring. The friction between the block and the table is negligible. Upon impact the bullet bounces back from the box with a speed of 75 m/s.

Calculate the speed of the block right after the collision.

As a result of the collision the spring compresses to a maximum of .20 m. Find the spring constant.

Find the inelastic energy lost during the collision.

2. Relevant equations
F=kx

3. The attempt at a solution

I solved part A by using mv = MV - mv(final) and ended with an answer of 3.6 m/s.

Part b uses the equation F=kx, where x is the compression, f is force, and k is the spring constant.
F=k(.20m)
I also have the formula PE = 1/2Kx^2, but because PE=mgh and I have no h, I am unsure of how to solve this problem.

I have no idea how to start part 3, we have not gone over inelastic collisions in class, only elastic.

Any help would be greatly appreciated.

2. Nov 1, 2009

### rl.bhat

You have found the initial velocity of the block. What is the final velocity?
Displacement of the block is given. Find the acceleration and force. From that find k.

3. Nov 1, 2009

### PhilCam

displacement of the block is .20 m.

Do I use the formula V^2 = Vinitial^2 +2ax to find the acceleration?

4. Nov 1, 2009

### rl.bhat

Yes. Here V final is zero.

5. Nov 1, 2009

### PhilCam

Thank you.

Okay, I used the formula:

0=3.6^2 + 2(a)(.2)
-12.96 = .4a
a=-32.4

F=-kx
-162=-k(.2)
K=810

It says the answer is 1620, which is twice of what I ended up with so I assume I am close.

6. Nov 1, 2009

### rl.bhat

Since force is not acting during compression, you have to use conservation of energy.
1/2*M*v^2 = 1/2*k*x^2

7. Nov 1, 2009

### PhilCam

Thanks! I got the correct answer.

Do you know how I can start on part C) of the problem, finding inelastic energy lost?

Thanks again.

8. Nov 1, 2009

### rl.bhat

Find the initial KE of bullet and final energies of bullet and block. Find the difference.

9. Nov 2, 2009

### PhilCam

I solved it.

Thanks a lot.