Question

9. A boxcar of length 8.3 and height 2.4 is at rest on frictionless rails. Inside the boxcar (whose mass when empty is 3100 ) a tank containing 2000 of water is located at the left end. The tank is 0.9 long and 2.4 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. After all the water has leaked out what will be the final velocity of the boxcar? (Take movement to the right as positive. Assume that the mass of the boxcar is evenly distributed.)

What is the displacement of the boxcar 8 after the water has settled in the bottom. (Take positive displacement as being to the right.)

Answer 1

The CM of the filled water tank is located (8.3 - 0.5m) = 7.8 metres from the right end.
The water has a mass of 2000kg., and when it has all leaked out of the tank, its CM is (8.3/2) = 4.15 metres from the right end.
Note that some water will still be in the tank in the end, as the floor of the tank and the floor of the boxcar are at the same level.
The shift in centre of mass = (7.8 - 4.15) = 3.75 metres to the right end.
The mass of water which has actually NOT shifted is (0.9m/8.3m) x 2000 = 216.86kg. still in the tank when the water finds its own level.
Mass shifted = (2000 - 216.86) = 1783.14kg.
(3100 + 2000)/(1783.14*3.75m) = 0.762 metres left (negative).