Bullet speed and thermal equilibrium

[Vanessa23]

[SOLVED] bullet speed and thermal equilibrium

Homework Statement

A 11.7 g lead bullet is tested by firing it into a fixed block of wood with a mass of 1.15 kg. If the block and imbedded bullet together absorb all the heat energy generated and, after thermal equilibrium has been reached, the system has a temperature rise measured as 0.0230C°. Estimate the entering speed of the bullet.

Homework Equations

specific heat capacity of lead is .130 (I think)
specific heat of wood is 1700 J/kgK
KE=1/2mv^2
Q=mc*deltaT

The Attempt at a Solution

1.15kg --> 1150g
1700 J/kgK --> 1.7 J/gC

1/2*11.7*v^2=1150*1.7*.023 + .130*11.7*.023

I get that v=2.77, but it is the wrong answer. Please let me know what I am doing wrong. Thank you!

 

[Doc Al]

1/2*11.7*v^2=1150*1.7*.023 + .130*11.7*.023

Note that all the terms on the right hand side are in Joules, which is fine. But on the left you use the mass of the bullet in grams, which is not fine. The standard units are kg and Joules.

The reason why it's OK to use grams in calculating the thermal energy is because you used the specific heats in units of Joules/gram to get the energy in Joules. I would advise using standard units throughout your calculations.