A 1 235.0 kg car traveling initially with a speed of 25.000 m/s in an easterly d

Question

A 1 235.0 kg car traveling initially with a speed of 25.000 m/s in an easterly direction crashes into the back of a 9 200.0 kg truck moving in the same direction at 20.000 m/s. The velocity of the car right after the collision is 18.000 m/s to the east. VTf Before After (a) What is the velocity of the truck right after the collision? (Give your answer to five significant figures.) Your response differs from the correct answer by more than 10%. Double check your calculations, m/s east (b) What is the change in mechanical energy of the car-truck system in the collision? Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. J (c) Account for this change in mechanical energy

Explanation / Answer

(a) Apply conservation of momentum -

Means, momentum of the system before collision = momentum of the system after the collision

=> M1 * U1 + M2 * U2 = M1 * V1 + M2 * V2.

Here, 1 stands for car, 2 for truck. M is mass, U is initial velocity (before collision) and V is final velocity (after collision).

=> M2 * V2 = 1235 * 25 + 9200* 20 - 1235 * 18 = 192645

=> V2 = 192645 / 9200 = 20.94 m/s

(b) Kinetic energy before collision KEi = (1/2)(M1*U1^2 + M2*U2^2)

= 0.5*(1235*25^2 + 9200*20^2)

= 0.5* 4451875 = 2225937.50 J

Kinetic energy after collision KEf = (1/2)(M1*V1^2 + M2*V2^2)

= 0.5*(1235*18^2 + 9200*20.94^2)

= 0.5*( 400140 + 4034049.12) = 2217094.56 J

So, change in the mechanical energy of the system = KEi - KEf

= 2225937.50 - 2217094.56 = 8842.94 J

(c) The change in the mechanical energy is that some part of the energy is converted into the heat and sound during the collision and therefore, the collision is an in-elastic collision.

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