From Kaplan Physics Review book- collision problem

[jillzhou]

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pg. 99 # 8:
A 2500kg car traveling at 20 m/s crashes into a 6000kg truck that is originally at rest. What is the speed of the truck after the collision, if the car comes to rest at the point of impact? (neglect the effects of friction)

I assumed that since this was an inelastic collision, I could use the formula
m1v1a (initial) +m2v2b (initial) = (m1+m2)vf
but Kaplans explanation states with an inelastic collision the following formula has to be used (final velocities are treated separately):

mv(car.initial)+mv(truck.initial)=mv(car.final)+mv(truck.final) and obtained the final velocity of the truck as 8 m/s, I thought all inelastic collisions followed the formula I had written above, since they end up "sticking together"..I'm getting confused with this and would appreciate any help! 😕

 

[caereax]

Why do you assume it's an inelastic collision? If that car "comes to rest at the point of impact," that sounds like a perfectly elastic collision where all momentum transfered to the truck. And by the way, the first formula you wrote is for inelastic collisions. The second is for elastic collisions.

 

[Temperature101]

pg. 99 # 8:
A 2500kg car traveling at 20 m/s crashes into a 6000kg truck that is originally at rest. What is the speed of the truck after the collision, if the car comes to rest at the point of impact? (neglect the effects of friction)

I assumed that since this was an inelastic collision, I could use the formula
m1v1a (initial) +m2v2b (initial) = (m1+m2)vf
but Kaplans explanation states with an inelastic collision the following formula has to be used (final velocities are treated separately):

mv(car.initial)+mv(truck.initial) = mv(car.final) + mv(truck.final) and obtained the final velocity of the truck as 8 m/s, I thought all inelastic collisions followed the formula I had written above, since they end up "sticking together"..I'm getting confused with this and would appreciate any help! 😕

This should equal to zero. If the car come to rest after the collision that means car and truck do not stick together (elastic collision) . Momentum is still conserved anyway.

 

[milski]

This should equal to zero. If the car come to rest after the collision that means car and truck do not stick together (elastic collision) . Momentum is still conserved anyway.

You are right about the formula but that is not an elastic collision. For elastic collisions, total kinetic energy is preserved. It should be fairly easy to see that this is not the case here. The cars sticking together is just one example of inelastic collision but any collision which results in a change of KE is inelastic, by definition.