Question

7. [1pt]
A boxcar of length 8.00 m and height
2.40 m is at rest on frictionless rails. The empty boxcar has a mass of 2800 kg. Inside the boxcar, located at the
left end, is a tank containing 2550 kg of water. The tank is 1.90 m long and 2.40 m tall. The tank starts to leak, and the water fills the floor of the boxcar uniformly. Assume that all the water stays in the box car. After all the water has leaked out of the tank,

a) what will be the final velocity of the boxcar? (Take movement to the right as positive.)

b) What is the displacement of the boxcar 7 s after the water has settled in the bottom? (Take positive displacement as being to the right.)

Answer 1

(a) Intiial momentum of the system = 0 (because system is at rest)
Therefore by conservation of momentum
Final momentum = Initial momentum
Final momnetum = 0
Hence the final velocity = 0
(b) Initial cente of mass of the system
X_Cm = (m₁X₁ + m₂X₂ )/(m₁ +m₂)
X_cm = (2800*4 + 2550*0.95)/(2800+2550) = 2.546 m
Now after water settle down then the new center of mass will be x_cm = 8/2 = 4 m
Now the displacement will be = X_cm - x_cm = 2.546 - 4 = - 1.454 m
-ve sign means displacement should be toward left.