A boxcar of length 9.9 M and height 2.4 M is at rest on frictionless rails. Insi
ID: 2036848 • Letter: A
Question
A boxcar of length 9.9 M and height 2.4 M is at rest on frictionless rails. Inside the boxcar (whose mass when empty is 2800 g) a tank containing 2000 Kg of water is located at the left end. The tank is 1.1 M long and 2.4 mn 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.) Selini AaeTries Oist the boxcar 10 S after the water What is the displacement of the boxcar 10 S after the water has settled in the bottom. (Take positive displacement as being to the right.)Explanation / Answer
As there is no external force acting on the system of car + tank +water, in horizontal direction, momentum of system in horizontal direction will remain constant , that is equal to zero.
After all the water leaks out, it remains in the car only and there is no relative velocity between the water and car, that is both have same velocity, Velocity of car + plus water must be zero. ( with no relative velocity between 2 masses of the system, only way to have zero omentum is that both masse are at rest.
Once water has settled, there is horizontal shift in the center of mass of water to right. In absence of any external force in horizontal direction, center of mass of the system remains unchanged.
Initial Center of mass of water, wrt left end of car = 1.1/2 = 0.55m
Final center of mass of water wrt left end = 1.1 + ( 8.8/2) = 5.5
Shift in COM of water wrt car = 5.5 - 0.55 = 4.95 m
Dispacement of car = mass of water * displacement of water wrt car / total mass of system
= 2000*4.95 / 4800
= 2.06 m
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