- #1

lillybeans

- 68

- 1

## Homework Statement

A 8g bullet hits a block of wood with mass of 450g which is at rest. The impact compresses the spring by 0.15m. The spring constant is 80N/m.

a) Find the velocity of the block and bullet when they first begin to move together.

b) Find the initial kinetic energy of the bullet.

**HERE IS THE PROBLEM. I did this question before (it's from a physics test), I got it right, but now I no longer understand the reasoning behind my solution. It makes absolutely no sense.**

## The Attempt at a Solution

Here is what I did, and apparently, it's right. I just don't understand why.

a)Ee=1/2kx

^{2}=(1/2)(80)(0.15)

^{2}=0.9J

Ek=1/2mv

^{2}

0.9=1/2(0.458kg)v

^{2}

v=1.982m/s

b)m1v1+m2v2=m(1+2)*Vmin <--minimum separation

0.008v + 0 = 0.458*1.982

v1=113.47

Ek=1/2(0.008)(113.47)

^{2}

=51.5J

-------------------------------------

Here is why I no longer think my solution makes sense.

Total energy before collision = kinetic energy in the bullet

Total energy during collision (minimum separation)= all converted to stored energy in the spring

Total energy after collision = kinetic energy again

**Problem 1**: notice, during minimum separation, Et=Est, which means there IS NO kinetic energy! Which means, it's not possible to find the velocity at minimum separation since it's all stored energy and no kinetic energy. Thus, shouldn't the minimum separation velocity be zero, and not 1.982m/s?

**Problem 2**: If all the system's energy has been converted to stored energy in the spring during minimum separation, doesn't that mean Et=Est=0.9J? Since Et before and after collision does not change, doesn't it imply that the initial kinetic energy of the bullet is also 0.9J, and not 51.5J? Since Et=Ek initial?