At the scene of an automobile accident a physics pathologist studies the wreckag
ID: 1631637 • Letter: A
Question
At the scene of an automobile accident a physics pathologist studies the wreckage. She determined that the first car (mass = 2000 kg) was traveling east, and a sport car (mass = 1200 kg) was traveling north. There were no skid marks before the collision, and the masses of the two were stuck together afterwards. Analyzing further, it was determined that the combined mass after the collision was proceeding at 30 km/hr at 50 degree North of East. a. How fast were the two cars going before impact in km/hr? [v_e = 30.85 km/hr, v_ = 61.28 km/hr] b. How much energy was lost due to impact? [1.362 times 10^5 J]Explanation / Answer
(a) Applying momentum conservation for the collsion,
(2000 v1)i + (1200 v2)j = (2000 + 1200)(30) (cos50i + sin50j)
Along i direction,
2000 v1 = 3200 x 30 x cos50
v1 = 30.85 km/hr ........Ans(velocity of first car)
1200 v2 = 3200 x 30 x sin50
v2 = 61.28 km/hr .....Ans
(b) v1 = 30.85 x 1000 m / 3600 s = 8.57 m/s
v2 = 61.28 x 1000 / 3600 = 17.02 m/s
v = 30 km/h = 8.33 m/s
Ki = (2000 x 8.57^2 / 2) + (1200 x 17.02^2 / 2) = 2.473 x 10^5 J
Kf = (2000 + 1200)(8.33^2) / 2 = 1.11 x 10^5 J
energy lost = Ki - Kf= 1.362 x 10^5 J ....Ans
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