A boxcar of length 9.1 $m$ and height 2.4 $m$ is at rest on frictionless rails.

Question

A boxcar of length 9.1 $m$ and height 2.4 $m$ is at rest on frictionless rails. Inside the boxcar (whose mass when empty is 3500 $kg$) a tank containing 1600 $kg$ of water is located at the left end. The tank is 1.1 $m$ long and 2.4 $m$ 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. 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.)

Explanation / Answer

Shift is potential energy of the water is the cause for the velocity to the boxcar.

so

intially center of mass of water in the tank is at 1.1/2 = 0.55 m

Volume of water is same 1.1 * 2.4 * b = 9.1* b * H

H = 0.29 m

Center of mass will be now at = 0.29/2 = 0.145 m

Change in height = 1.1/2 - 0.145 = 0.405

Decrease in potential energy = increase in kinetic energy

m g h = 0.5 * ( m +M) V^2

1600 * 9.8 * 0.405 = 0.5 * (3500+1600) * V^2

V =1.57 m/s

-----------------------------------

Displacemnt X = Vt

V = 1.57* 7 = 11 m

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