Inelastic collision: where did my kinetic energy calculation go wrong?

[dj_killer_lamb]

A 2000kg car traveling to the right at 30 m/s is chasing a second car of the same mass that is traveling to the right at 10 m/s

1) if the two cars collide and stick together, what is their speed after the collision?
2) What fraction of the initial kinetic energy of the cars is lost during this collision?

Ok so I'm pretty sure I've got the first question answered using the formula for calculating momentum (Momentum = Mass * Velocity) but I'm having a bit of trouble answering question 2. The collision should result in a loss of kinetic energy but I've come up with an answer that says it has gained kinetic energy :S.

Here is the work I have done thus far:

1) Momentum Before = (2000kg * 30m/s) + (2000kg * 10m/s)
= 80, 000 kg m/s

therefore V after = (Momentum1 + Momentum2)/(Mass1 + Mass2)
= 80,000kg m/s / 4000kg
= 20m/s

2) KE1 = 1/2 MV^2
= 1/2 2000 * 30^2
= 900,000 J

KE2 = 1/2 MV^2
= 1/2 2000 * 10^2
= 100,000 J

Therefore total initial KE = 1,000,000 J

Therefore KE after = 1/2 (m1 + m2) * (total velocity)
= 1/2 8000 * 20
= 1,600,000 J

Any help would be greatly appreciated!

 

[cristo]

Therefore KE after = 1/2 (m1 + m2) * (total velocity)
= 1/2 8000[/color] * 20
= 1,600,000 J

Any help would be greatly appreciated!

This doesn't look correct for the sum of the masses of the two vehicles.

 

[denverdoc]

yea perfect til the last few lines, the square of velocity was dropped as well. plus the math went awry, even if the terms were wrong.

 

[dj_killer_lamb]

LOL! arrrg of course! I don't know where that 8000 came from! Thanks heaps :)

 

[dj_killer_lamb]

Thanks a lot guys, i nailed my spoken today...would have taken me forever to pick up on those errors!