Change in internal energy of an inelastic collision.

[flyboy9]

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.

Homework Equations

P_f=P_i+F*time
E_f=E_i+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.

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

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

I then found the change in energy by E_f,sys-E_i,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.

 

[Doc Al]

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

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

 

[flyboy9]

so would I calculate the magnitudes of the velocities first?

 

[Doc Al]

so would I calculate the magnitudes of the velocities first?

Yes.