An uncovered hopper car from a freight train rolls without friction or air resis

Question

An uncovered hopper car from a freight train rolls without friction or air resistance along a level track at a constant speed of 6.57 m/s in the positive x-direction. The mass of the car is 1.21·105 kg.

a) As the car rolls, a monsoon rainstorm begins, and the car begins to collect water in its hopper (see the figure). What is the speed of the car after 1.67·104 kg of water collects in the car's hopper? Assume that the rain is falling vertically in the negative y-direction.

b) The rain stops, and a valve at the bottom of the hopper is opened to release the water. The speed of the car when the valve is opened is again 6.57 m/s in the positive x-direction (see the figure). The water drains out vertically in the negative y-direction. What is the speed of the car after all the water has drained out?

Explanation / Answer

a)apply the law of conservation of linear momentum conservation

mu = MV

1.21e5*6.57 = (1.21 e 5+1.67 e4) V

V = 5.77 m/s

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b) again using linear momentum conservation

MV0 = m v1

(1.21 e 5 + 1.67 e 4) *6.57 =1.21 e 5*v1

v1 = 7.47 m/s

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