How Hot Does a Bullet Get When Fired Into Wood?

[ldbaseball16]

Homework Statement

Ricky Plaxico Bobby grabs his .22 pistol and fires a 5.00g lead bullet into a block of wood. The muzzle Velocity 301 m/s. Assume that 50 % of the bullet turns to heat
A.What is the temperature rise of the bullet?
B. Will the bullet become hot enough to melt?
C.If so, what percent of the bullet melts?

Homework Equations

L=alphaL(subzero)T

The Attempt at a Solution

I converted the equation to get the temperature
L/alphaL(subzero)=T? i get a weird answer can i get some help? please

 

[mgb_phys]

First work out the kinetic energy of the bullet
then you need the specific heat capacity of lead to work out what temperature rise this energy corresponds to.
And finally the melting point of lead.

(Be careful of units, the bullet is given in grams )

 

[ldbaseball16]

i found the the kinetic energy its 752.5 and the melting point of the lead is 327 celsius and the specific heat is 130 kg c... i don't know how the kinetic energy plugs into this equation? I am using Q=mcT and to find Q i used this equation Q=mL, and then i pluged it into this one but i know its wrong because the answer i got was cold and its suppose to be hot?

(.005kg)(25kg= the heat fusion)=Q
.125kg

.125kg=(.005)(130)T
T=.1923076923 C?

 

[mgb_phys]

All the kinetic energy becomes heat.
So Q = 1/2 m v² and Q = m c T
Where T is the change in temperature - you just need to find if the temperature change is enough to reach lead's melting point