A car of mass m traveling at speed v crashes into the rear of a truck of mass 2

Question

A car of mass m traveling at speed v crashes into the rear of a truck of mass 2m that is at rest and in neutral at an intersection. If the collision is perfectly inelastic, what is the speed of the combined car and truck after the collision? Kinetic energy of the car + truck system is not conserved in the collision

a) Calculate the percentage of kinetic energy lost in the collison

b) Total energy should still be conserved. Where is the "missing" energy if it's not kinetic energy? Be specific, don't just say "potential energy"

Explanation / Answer

v = velocity of car

V = velocity of combined car and truck

using conservation of momentum

mv + 2m (0) = (m + 2m) V

V = v/3

b)

percentage of KE lost = loss x 100 / initial KE = (initial KE - final KE) x 100 /initial KE

percentage of KE lost = 100 [(0.5) mv2 - (0.5) (m + 2m) V2 ] /((0.5) mv2 )

percentage of KE lost = 100 [(0.5) mv2 - (0.5) (3m) (v/3)2 ] /((0.5) mv2 )

percentage of KE lost = 100 (0.67) (0.5) mv2 / (0.5) mv2 = 67%

c)

the lost kinetic energy is used in heat energy and sound energy due to collision

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