a) A single 30000 kg railroad hopper car is freely rolling on a level track with

Question

a) A single 30000 kg railroad hopper car is freely rolling on a level track with an initial speed of 5 m/s. As it rolls under a loading platform, 90000 kg of coal is dumped into the top of the hopper car. What is the speed of the hopper car afterward? We neglect friction.

b) Now suppose that a locomotive is pulling a string of hopper cars on a level railroad track at a constant speed of 5 m/s while coal is being loaded onto the cars at a continuous rate of 3000 kg/s. What average force needs to be supplied by the locomotive to keep the hopper cars moving at this constant speed? Again we neglect friction.

Explanation / Answer

step;1

given that

initial mass M1=30000 kg

finial mass M2=90000 kg

initial speed v1=5 m/s

step;2

now we find the speed of the hopper car afterwards

according law of conservation of momentum

M1v1+M2v2'=(m1+m2) V

the speed of the hopper car afterwards V=v1{m1/m1+m2}

=5*30000/30000+90000

=1.25 m/s

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(b) ans

Given that

=>dm/dt=3000 kg/s

=>speed v=5 m/s

step;2

now we find the average force

the average force Favg=v(dm/dt)

=3000*5=15000 N

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