Bullet-Block Collision: Solving for Initial Speed and Energy Dissipation

[bfusco]

Homework Statement

A bullet of mass 1.4×10−3 {\rm kg} embeds itself in a wooden block with mass 0.999 {\rm kg}, which then compresses a spring (k = 110 {\rm N/m}) by a distance 5.5×10−2 {\rm m} before coming to rest. The coefficient of kinetic friction between the block and table is 0.46.
a)what is the initial speed of the bullet?
b)What fraction of the bullet's initial kinetic energy is dissipated (in damage to the wooden block, rising temperature, etc.) in the collision between the bullet and the block? (answer: ΔK/K

 

[tal444]

You must attempt to at a solution first before we can help you.

 

[bfusco]

You must attempt to at a solution first before we can help you.

i did i didn't feel like typing it, but here you go.

i started by drawing a diagram labeling part A to be where the spring is compressed, part B to be where the block started pushing the spring, part C to be where the bullet impacts the block, and part D the firing of the bullet.
I then used energy conservation, stating that the E@A=E@B. 1/2kx^2=1/2mv^2, solving for v and getting sq.rt of (kx^2/m). plugging in the numbers i get v=.5767 m/s. Then i attempt to use energy conservation from B to C, 1/2mv^2=1/2mv^2-(work by friction+work by spring) but i kind of just put that equation together myself because i know energy is lost by work done) and i don't really know what to do.