How much mechanical energy is lost in a car-truck collision?

[AdnamaLeigh]

A 991kg car traveling initially with a speed of 32.2m/s in an easterly direction crashes into the rear end of an 8650kg truck moving in the same direction at 17.8m/s. The velocity of the car right after the collision is 10.4m/s to the east. How much mechanical energy is lost in the collision? Answer in J.

I already solved for the velocity of the truck after the collision: 20.298m/s.

I did Mech Energy = Initial kinetic energy - final kinetic energy

Initial
Ke= .5(991)(32.3)^2 + .5(8650)(17.8)^2 = 1887283.195J

Final
Ke= .5(991)(10.4)^2 + .5(8650)(20.298)^2 = 1835531.357J

The difference between the two is 51751.838J and it's incorrect. I've checked my math too many times and I still get the same answer. Or is the answer supposed to be -51751.838J? I figured that since they said "energy is lost," they only wanted the magnitude of energy lost. I'm stumped.

 

[Andrew Mason]

A 991kg car traveling initially with a speed of 32.2m/s in an easterly direction crashes into the rear end of an 8650kg truck moving in the same direction at 17.8m/s. The velocity of the car right after the collision is 10.4m/s to the east. How much mechanical energy is lost in the collision? Answer in J.
I already solved for the velocity of the truck after the collision: 20.298m/s.
I did Mech Energy = Initial kinetic energy - final kinetic energy
Initial
Ke= .5(991)(32.3)^2 + .5(8650)(17.8)^2 = 1887283.195J
Final
Ke= .5(991)(10.4)^2 + .5(8650)(20.298)^2 = 1835531.357J
The difference between the two is 51751.838J and it's incorrect. I've checked my math too many times and I still get the same answer. Or is the answer supposed to be -51751.838J? I figured that since they said "energy is lost," they only wanted the magnitude of energy lost. I'm stumped.

There is an underlying assumption that the road is frictionless so that momentum is conserved.

It may be just a significant figure problem. KEi = 1887 KJ. KEf = 1836 KJ. The difference is 51 KJ.

AM

 

[AdnamaLeigh]

The online homework service allows for a +/- 1% error. We don't have to worry about sig figs. I agree that the underlying assumption is that the road is frictionless. I was able to use the conservation of momentum in order to figure out the velocity of the truck and i understand that kinetic energy is lost due to sound, heat, deformation, etc.

I still don't know...

 

[Andrew Mason]

The online homework service allows for a +/- 1% error. We don't have to worry about sig figs. I agree that the underlying assumption is that the road is frictionless. I was able to use the conservation of momentum in order to figure out the velocity of the truck and i understand that kinetic energy is lost due to sound, heat, deformation, etc.
I still don't know...

I get: Initial KE = 1887283 J. Final KE = 1835452 J.
The difference is 51813 J. So your answer is correct. Don't worry. Sometimes the given answers are wrong.

AM