# Change in internal energy of an inelastic collision.

## Homework Statement

A car of mass 2200 kg collides with a truck of mass 4500 kg, and just after the collision the car and truck slide along, stuck together, with no rotation. The car's velocity just before the collision was < 35, 0, 0 > m/s, and the truck's velocity just before the collision was < -18, 0, 27 > m/s.

Pf=Pi+F*time
Ef=Ei+Q+W

## The Attempt at a Solution

I attempted to use the change in kinetic energy of the system to solve of the change in internal energy.

Ef=.5*m*v2
Ef=.5*6700*<-.597,0,18.134>2 <-- final velocity of the system was calculated in an earlier step and found to be correct
Ef,sys=<1194,0,1101620>

Ei,car=.5*2200*<35,0,0>2
=<1347500,0,0>
Ei,truck=.5*4500*<-18,0,27>2
=<72900,0,1640250
EI,sys=Ei,car+Ei,truck
= <1420400,0,1640250>

I then found the change in energy by Ef,sys-Ei,sys and then getting the magnitude to solve get change in internal energy. This however did not get me the correct answer. I am stuck and not sure what to try.

## Answers and Replies

Doc Al
Mentor
Ef=.5*m*v2
Ef=.5*6700*<-.597,0,18.134>2 <-- final velocity of the system was calculated in an earlier step and found to be correct
Ef,sys=<1194,0,1101620>

Ei,car=.5*2200*<35,0,0>2
=<1347500,0,0>
Ei,truck=.5*4500*<-18,0,27>2
=<72900,0,1640250
EI,sys=Ei,car+Ei,truck
= <1420400,0,1640250>
Looks like you're using vector notation to express the energy. KE is a scalar, not a vector--it has no components. Use the full speed when calculating KE.

so would I calculate the magnitudes of the velocities first?

Doc Al
Mentor
so would I calculate the magnitudes of the velocities first?
Yes.