A boxcar of length 10.1 m and height 2.4 m is at rest on frictionless rails. Ins

Question

A boxcar of length 10.1 m and height 2.4 m is at rest on frictionless rails. Inside the boxcar (whose mass when empty is 2800 kg) a tank containing 1600 kg of water is located at the left end. The tank is 0.8 m long and 2.4 m tall. 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 9 s after the water has settled in the bottom. (Take positive displacement as being to the right.)

Explanation / Answer

Solution:

Taking the left end of the car to be x = 0, the CM of the combined loads is located at:

Xcm = (m1x1 + m2x2) / (m1 + m2)

where,

m1 = 2800 kg

m2 = 1600 kg

x1 = 5.05m (It's half of the length 10.1 cm)

x2 = 0.4 m (Half of 0.8m)

Xcmi = (2800*5.05 + 1600*0.4) / (2800 + 1600)

Xcmi = 3.359 m

When the water runs out, Xcmf = 5.05 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 (5.05 - 3.359) = 1.69 m to the left of its initial position.

Here , Time is irrelevent.

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