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

Question

A railroad hopper car has a mass of 2 Times 10^4 kg when empty and contains 10^4 kgof coal. As it coasts along the track at 6 m/s the bottom of the hopper opens and steadily releases all the coal onto a platform below the rails over a period of 5 s. How fast is the hopper car traveling after all the coal is dumped? What is the horizontal impulse delivered to coal by the platform? If the coal comes to rest 1 second after the dumping is finished, what was the average horizontal force on the platform? If the coal fell 3 m, what is the total energy converted into heat in the process of the coal coming to rest? Now 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 is the car traveling after all the coal is thrown instead of dumped?

Explanation / Answer

a)

let car's final speed is v m/s.

using conservation of momentum principle:

initial momentum=final momentum

==>(2*10^4+10^4)*6=2*10^4*v

==>v=9 m/s

b)impulse=change in momentum=mass*change in speed

=10^4*(0-6)=-6*10^4 kg.m/s

c)impulse=average force*time period

==>6*10^4=force*6

==>force=10^4 N

d)

initial energy of coal=potential energy+kinetic energy

=10^4*9.8*3+0.5*10^4*6^2

=474000 J

as coal falls onto ground and speed becomes zero

both potential and kinetic energy become 0

hence heat energy geenrated is 474000 J

e)it will travel with the same speed as obtained in part a i.e, 9 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.