A 1 100.0 kg car traveling initially with a speed of 25.000 m/s in an easterly d
ID: 1458377 • Letter: A
Question
A 1 100.0 kg car traveling initially with a speed of 25.000 m/s in an easterly direction crashes into the back of a 9 700.0 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. (a) What is the velocity of the truck right after the collision? (Give your answer to five significant figures.) (b) What is the change in mechanical energy of the car-truck system in the collision? (c) Account for this change in mechanical energy.Explanation / Answer
(a) As the car has not deviated from the earlier direction, we assume that the collision is one-dimensional. It also makes calculations simple.
As losses are present, we can take only conservation of momentum for our calculations.
M1 * U1 + M2 * U2 = M1 * V1 + M2 * V2.
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 = 1100 * 25 + 9700 * 20 - 1100 * 18 = 201700
This gives V2 = 201700 / 9700 = 20.79381 m/s
B,C)To calculate losses, we will find the kinetic energies before & after collision. Any difference would give us the losses (in energy form).
(KE)1 = (KE)2 + Losses.
(KE)1 = 0.5 * (M1 * U1^2 + M2 * U2^2) =>0.5(1100 * 252 + 9700 * 202) => 2283750 J
(KE)2 = 0.5 * (M1 * V1^2 + M2 * V2^2) => 0.5(1100 * 182 + 9700*20.7932) = 2275091.9 J
Losses = (KE)1 - (KE)2 = 8658.08 Joules
Hope this helped!
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.