Solving Collision Problem: Find Speed, Spring Constant & Inelastic Energy

[PhilCam]

Homework Statement

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.

Homework Equations

F=kx

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.

 

[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.

 

[PhilCam]

displacement of the block is .20 m.

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

 

[rl.bhat]

Yes. Here V final is zero.

 

[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.

 

[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

 

[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.

 

[rl.bhat]

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

 

[PhilCam]

I solved it.

Thanks a lot.