Calculate velocity and acceleration during collisions.

Question

A small car of mass 500kg is travelling at 120km/h when it hits stationary truck (of 1.5 tonne mass) head on. The small car rebounds and travels in the opposite direction at 40km/h. The collision takes 1.2 seconds.

a) Calculate the final velocity of the once stationery truck.

b) Calculate the average acceleration on the small car, during the collision.

c) Is the kinetic energy conserved? If yes, show using calculations. If not, explain what is happening.

Answer 1

In any collision total momentum is conserved as long as there are no external forces acting.

 

a) 500*120 + 1500*0 = 500 *(-40) +1500*V

      V = 53 kph

 

b) a = (v-u)/t;    converting; 1kph = 1000/3600 mps

     a = 1000/3600*(-40-120)/1.2 = 37 m/s²

 

c) Because the collision was not perfectly elastic, kinetic energy was not conserved. Some of this 'lost' energy could have been transfered to sound and/or heat (internal) energy

proof; initial KE = 1/2 mv²  = 1/2* 500*(120/3.6)²                                           = 277,777 Joules

     final KE = 1/2* 500* (-40/3.6)² + 1/2*1500*(53/3.6)²

                     ^{=30,864 + 162,558 =193,422 Joules, which is only 69% of the initial KE, hence kinetic energy was not conserved.}