MCAT Passage: Inelastic Collision

[mrlucky0]

[SOLVED] MCAT Passage: Inelastic Collision

Homework Statement

A car (1000 kg) and a truck (2000kg) start from rest on a long, straight track. At time t=0, the truck is at position x=0 and the car is at position x=100m. Both vehicles then accelerate toward each other and collide.

Both the truck and the car accelerate uniformly - and at the same rate - until the speed of the each vehicle is 21 m/s, just as they collide. The resulting collision is perfectly inelastic, and the vehicles skid for 7 m before coming to rest. The coefficient of kinetic friction between the track and the vehicle's tires is 0.35.

What was the total kinetic energy of the vehicles just after the collision?

A. 73.5 kJ
B. 147 kJ
C. 330.8 kJ
D. 661.5 kJ

Homework Equations

KE = 1/2mv^2

The Attempt at a Solution

Can I apply the conservation of momentum here? I'm also not sure how to use the coefficient of kinetic friction although I'm sure the solution involves it.

I've determined that the initial total KE of the system is 661.5 kJ and was tempted to choose that as the answer but it's not right.

I'm also confused about the wording of the problem (if someone can clarify): does "just after the collision" imply after the cars have crashed but before the combined mass starts to skid? If this is the case, why bother with kinetic friction?

 

[alphysicist]

Hi mrlucky0,

Yes, I believe "just after the collision" means after the crash and before any appreciable skidding has occurred. I think the reason they give the coefficient of friction is so you can solve the problem in two ways: either use momentum conservation during the collision, or use an energy approach after the collision.

 

[mrlucky0]

Hi mrlucky0,

Yes, I believe "just after the collision" means after the crash and before any appreciable skidding has occurred. I think the reason they give the coefficient of friction is so you can solve the problem in two ways: either use momentum conservation during the collision, or use an energy approach after the collision.

Thanks. Your tip helped me solve the problem!