(a) An empty box car of mass M and initial velocity V rolls under a coal hopper, which
dumps coal of mass 2M vertically into the box car. What is the velocity of the box
car after receiving the coal?
(b) Suppose now that the coal is fed continuously into the box car, falling vertically from
above at the rate dM/dt. Using momentum arguments, find V as a function of M.

Question

(a) An empty box car of mass M and initial velocity V rolls under a coal hopper, which
dumps coal of mass 2M vertically into the box car. What is the velocity of the box
car after receiving the coal? 
(b) Suppose now that the coal is fed continuously into the box car, falling vertically from
above at the rate dM/dt. Using momentum arguments, find V as a function of M.

anonymous · Answer

@ganeshie8

ganeshie8 · Answer

for part a, consider the system consisting of car and coal.
use the conservation of lienar momentum : 

momentum before receving coal = momentum after receiving coal

$MV+2M*0 = (M+2M)V'$

you can solve $V'$

ganeshie8 · Answer

part b is slightly tricky

anonymous · Answer

Wont it be solved in the same way as part (a)?

ganeshie8 · Answer

@IrishBoy123

irishboy123 · Answer

thanks ganesh

hi em, did you answer the other ones yet?  i saw you posted some similar stuff but i am under the kosh right and didn't get round to trying to help :-(

as background, Newton's second law is really $F = \dfrac{d}{dt}(mv) $and not just $F = ma$. so here no external force, momentum would be conserved, exactly as per ganeshie's approach, just a little bit extra.

you start with $m(t) \, v(t) = constant = MV$

then $v = \dfrac{MV}{m(t)} = \dfrac{MV}{\dfrac{dm}{dt} \times t}$

that should be along the right lines.....and shows that the thing will slow down :p