How Does Releasing Coal Affect the Speed and Dynamics of a Railroad Car?

[pleasehelpme6]

Homework Statement

A railroad hopper car has a mass of 20000 kg when empty and contains 30000 kg of coal. As it coasts along the track at 7 m/s the hopper opens and steadily releases all the coal onto a platform below the rails over a period of 5 s.

a) How fast does the car travel after all the coal is dumped?

b) What is the horizontal impulse delivered to coal by the platform?

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

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

e) Let's say that instead of the coal falling out of the bottom of the coal car, some very strong physics student threw it backwards from the car, so that the velocity of each piece of coal was zero just after it left her shovel. How fast does the car travel after all the coal is thrown instead of dumped?

Homework Equations

p = mv
pi =pf

The Attempt at a Solution

The answer for part a was 7 m/s, so apparently the platform was attached to the hopper, but I have no idea where to begin with solving any of the others. Please help.

 

[bharath423]

impulse is the change in momentum of a body,so if u calculate the velocity with which coal goes out and hit platform you know initial momentum of the coal before hitting platform after hitting its zero as it rests there... so you get impulse...
finding average force is change of momentum /time taken to change,
actually time derivative of momentum is force.. the average force came from there...

 

[pleasehelpme6]

impulse is not zero, which is why its so difficult.

7 m/s is the velocity, so there should be NO impulse, but that's not the right answer.

 

[pleasehelpme6]

well i solved for impulse, it was 210000, but I am still not getting part c

 

[pleasehelpme6]

solved for part c...

i was only using 1 s as the interval, but i had to add that to the time over which the coal was dumped.

so average force = mass * average acceleration.
average acceleration = change in velocity / time

time =6, change in velocity = 210000
average force = 35000

 

[bharath423]

finding average force is change of momentum /time taken to change,

so if coal comes to rest in 1 sec then averge force would be the change in momentum itself...

 

[bharath423]

7 m/s is n't the velocity of car after dumping coal it should definitely increase

 

[pleasehelpme6]

7 is correct, since it is not propelled off the back, there is no external force acting on the cart.

its an online assignment, trust me, that's the right answer.

im still unsure how to find the energies for part d though.

 

[bharath423]

for d its the potential energy mgh that may convert to heat..for e apply conservation of momentum you'll get it

 

[pleasehelpme6]

yup, just got it.

i had to use potential energy + kinetic energy, since it also had a vi = 7.
so mgh + 1/2mv^2 = 1912200.