A boxcar of length 8.0 m and height 2.3 m is at rest on frictionless rails. Insi
ID: 1417844 • Letter: A
Question
A boxcar of length 8.0 m and height 2.3 m is at rest on frictionless rails. Inside the boxcar (whose mass when empty is 3300 kg) a tank containing 1600 kg of water is located at the left end. The tank is 1 m long and 2.3 m tall. At some point the walls of the tank start to leak, and the water fills the floor of the boxcar uniformly. Assume that all the water stays in the boxcar. What is the displacement of the boxcar 5 s after the water has settled in the bottom of the car (take positive displacement as being to the right)?
Explanation / Answer
Taking the left end of the car to be x = 0, the CM of the combined loads is located at:
Xcmi = (3300*4 + 1600*.5)/(3300+1600) = 2.857 m
When the water runs out, Xcmf = 4.0 m (by symmetry)
However, due to conservation of momentum, the CM must stay in its original position relative to the outside observer, so the car must move (4 - 2.857) = 1.143 m to the left of its initial position.
The 5 sec is irrelevant......
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