Ballistic Pendulum initial velocity of bullet

[MathHelpa]

Homework Statement

A ballistic pendulum is used to measure the speed of a bullet fired from a gun. The pendulum consists of a 20.0g block hanging from a string. A bullet, with mass 0.50gg, imbeds itself in the block causing the block to swing up to a height of 5.00cm. Find the speed of the bullet as it leave the gun.

Homework Equations

W_nc = ΔK + ΔU
K = 1/2 mv^2
U = mgh
W = Fdcos∅
p = mv

The Attempt at a Solution

I wanted someone to double check my work, and if I used correct units or not.

pendulum
U = mgh
U = (20.0g)(9.8)(0.05cm)
U = 9.8 Joules (this is not gravity it is what mgh came out to)

bullet
K = 1/2 mv^2
9.8(U of pendulum) = 1/2(0.005)v^2
v^2 = 9.8/0.0025
v^2 = 3930
v = 62.6099
v = 62.6 m/s

 

[voko]

The bullet EMBEDS itself in the block.

 

[haruspex]

In case you don't understand the significance of voko's comment, you have assumed work is conserved. That is unjustified (and quite wrong here).