(The question below will refer to the following information: An SUV with mass 1.

Question

(The question below will refer to the following information: An SUV with mass 1.83 103 kg is traveling eastbound at +15.8 m/s, while a compact car with mass 9.15 102 kg is traveling westbound at -15.8 m/s. (See figure.) The cars collide head-on, becoming entangled.)

Use the values from above to help you work this exercise. Suppose the same two vehicles are both traveling eastward, the compact car leading the SUV. The driver of the compact car slams on the brakes suddenly, slowing the vehicle to 6.36 m/s. If the SUV traveling at 17.6 m/s crashes into the compact car, find the following:

(a) the speed of the system right after the collision, assuming the two vehicles become entangled

(b) the change in velocity for both vehicles

(c) the change in kinetic energy of the system, from the instant before impact (when the compact car is traveling at 6.36 m/s) to the instant right after the collision

Try as I might, I am stuck! Please provide step-by-step explanation along with final answers, so I can figure out where I am wrong. Thank you!!!

Explanation / Answer

The mass of SUV is M = 1.83*103 kg The mass of the car is m = 9.15*102 kg The speed of the SUV is U = 17.6 m/s The speed of the car is u = 6.36 m/s As both are entangled after the colision, the situation resembles the inelastic collision and both move with same common velocity v a) Applying the law of conservation of linear momentum, MU + mu = (M+m)v v = (MU + mu)/(M+m) v = 13.85 m/s b) The change in velocity of SUV is v = 3.75 m/s The change in velocity of car is v' = 7.49 m/s c) The initial kinetic energy of the system just before the collision is Ki = 0.5MU2 + 0.5mu2 Ki = 301936.092 J The final kinetic energy of the system just after the collision is kf = 0.5(M+m)v2 kf = 263276.38125 J The change in kinetic energy is K = 38659.71 J ˜ 3.86*104 J kf = 263276.38125 J The change in kinetic energy is K = 38659.71 J ˜ 3.86*104 J

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