4. A man walks from one end of a flat car to the other end on a horizontal railr
ID: 2213382 • Letter: 4
Question
4. A man walks from one end of a flat car to the other end on a horizontal railroad track, then stops. His mass is 80 kg, the mass of the flat car is 200 kg, the flat car is 15 m long. The flat car is initially at rest. Neglect friction and neglect the mass of the wheels. You are standing on the side of the railroad track. a) How far and in which direction does the main move with respect to you? b) How far and in which direction does the flat car move with respect to you? c) What is the final speed of the man and the flat car?Explanation / Answer
It may strike you that intuitively these first two answers are pretty low compared to the 69 you were getting. A big problem with teddyboy's answer, aside from not seeing the worker's walking slows the car down, is that he thinks the car's velocity ADDS to the worker's speed in traversing the car. So t=2.88sec is totally bizarre and wrong. Aristide's answer is wrong b/c t*v_car(initial) = 11.5 * 6 = 69, much higher than what he caculated. Here's a little simpler approach than aristide's, without resorting to a transformation which is just the conervation of momentum equation in disguise: solve for time spent walking, use cons. of momentum to solve for the car's velocity during worker's walking, then multiple the two. Presumably the the initial momentum of the car and worker before the worker starts walking is 395 * 6 = 2370, that is, the worker's presence doesn't slow the car down from 6m/s. (They don't actually say this. They say this is how fast the car alone is going. In any case, it's a reasonable assumption that this is what they meant.) Time spent walking = 11.5sec (obvious) Momentum while worker is walking: 300kg * v + 95kg * (v+2) Setting the momentums before and after the walking is started gives you the velocity, v, of the car while the man is walking: 5.52m/s Now just multiple the velocity and time to get 63.5m, which is what aristede's answer would have been if he had just punched in 6 instead of 4 for v_car, the speed of the car before the worker starts walking, to get the COM speed.
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