A railroad hopper car has a mass of 10 4 kg when empty and contains 2 × 10 4 kgo

Question

A railroad hopper car has a mass of 104 kg when empty and contains 2 × 104 kgof coal. As it coasts along the track at 4 m/s the bottom of the hopper opens and steadily releases all the coal onto a platform below the rails over a period of 4 s.

1. How fast is the hopper car traveling after all the coal is dumped? ______ m/sec

2. What is the horizontal impulse delivered to coal by the platform? kg m/sec

3. If the coal comes to rest 1 second after the dumping is finished, what was the average horizontal force on the platform?

4. If the coal fell 2 m, what is the total energy converted into heat in the process of the coal coming to rest? ____J

5. Now let's say that instead of the coal falling out of the bottom of the coal car, some very strong physics studentthrew it backwards from the car, so that the velocity of each piece of coal was zero just after it left her shovel. How fast is the car traveling after all the coal is thrown instead of dumped? ____ m/sec

Explanation / Answer

here,

mass of cart, m = 104 kg
mass of coal, mc = 2*10^4 kg

Velocity of coasting, v = 4m/s

Time, t = 4 s

Part A:
Dumping the coal does not affect the car's velocity, as they both continue along (horizontally) at 4 m/s.

Part B:
Impulse = mass* change in velocity
I = 2*10^4 * -4
Impulse = -8*10^4 Kg.m/s

Part C:
Average force = Impulse /time
Favg = -8*10^4 /(4)
Favg = -2*10^4 N

Part D:
Energy = potential Energy + Kinetic Energy
E = mgh + 0.5 * m * v^2
E = m(gh+0.5*v^2)
E = (2*10^4)*(9.81*2+0.5*4^2)
E = 552400 J

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