A boxcar of length 9.5 m and height 2.4 m is at rest on frictionless rails. Insi
ID: 1371635 • Letter: A
Question
A boxcar of length 9.5 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 1700 kg of water is located at the left end. The tank is 1.0 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.)
What is the displacement of the boxcar 8 s after the water has settled in the bottom. (Take positive displacement as being to the right.)
Explanation / Answer
Solution:
Given
Mas of box car = m =2800 kg
L = 9.5 m
Height = 2.4 kg
Initial velocity = vi = 0
mass of water = 1700 kg
length of tank L1= 1m
Height of tank = h1= 2.4 m
After all the water entered into the box car from the tank, the mass of water = m = 2800 kg
After all the water got leaked into the box car, some water still remains in the tank. The bottom of the box car and the water tank are at the same level.
There will be a shift in the center of gravity of the box and that is the height thru which the water falls.
Shift in center of mass = 9.5 - (1/2 + 9.5/2 ) = 4.25 m
From the conservation of energy , kinetic energy of moving water = potential energy of falling water
1/2mv^2 = mgh
=> v = sqrt (2gh) = sqrt ( 2 * 9.8 * 4.25) = 9.126 m/s
Displacement = velocity x time = 9.126 X 8 = 73 m
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