1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple Momentum Problem Help

  1. Nov 14, 2013 #1
    1. A railroad car loaded with rocks coasts on a level track without friction. A worker on board starts throwing the rocks horizontally backward from the car. Then what happens?
    (a) car slows down
    (b) car speeds up
    (c) first the car speeds up and then slows down
    (d) car's speed remains constant

    2. Which answer would you choose if the rocks were to fall out through a hole in the floor of the car one at a time?

    So the answer to number 1 is (b) speeds up and the answer to number two is (d) car's speed remains constant. I understand number one but I can't understand why number two would be (d) using the following equation for momentum:




    Pi=Pf
    Here's what I was thinking please tell me where I'm going wrong:
    (c=car and r=rock)

    McVc + MrVr = McV'c + MrV'r

    Initially Vc=Vr=Vi
    and since rocks are being dropped directly downward, final momentum of the rocks (being dropped one at a time) should be zero because their falling down, out of the railroad car.
    So:

    Vi( Mc+Mr) = McV'c

    V'c = [Vi(Mr+Mc)] / Mc


    But wouldn't that increase the velocity? I know logically thinking it wouldn't but I can't seem to get this equation to show that.

    Someone please help explain this to me!!
     
  2. jcsd
  3. Nov 14, 2013 #2
    You have to remember, momentum is a vector quantity, so having rocks fall down in the vertical direction doesn't change the car's velocity in the horizontal direction.
     
  4. Nov 14, 2013 #3

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    They're dropping straight down relative to the car. To an observer on the ground, they have the same forward speed as the car (until they hit the ground, of course, but that doesn't affect the car's motion).
     
  5. Nov 14, 2013 #4
    Your second equation must include the final momentum of the rocks and of the Earth/objects the rocks hit. Remember, momentum is always conserved in a CLOSED system, meaning there are no external forces. So, if your system only includes the train and the rocks, it is not a closed system (gravity is acting on the rocks as they fall, speeding them up and momentum "disappears" once they hit the ground). But if the Earth is included, the system is closed and the momentum lost by the train as the rocks fall is preserved by a miniscule gain in velocity by the Earth. So the train loses mass (rocks) and thus momentum, the Earth and rocks attract each other equally but in opposite directions, and the fallen rocks transfer momentum to the Earth itself or objects on the ground once they hit.
     
    Last edited: Nov 14, 2013
  6. Nov 14, 2013 #5
    The car itself doesn't change velocity in the second situation because no force is applied to it.
     
  7. Nov 14, 2013 #6
    McVc+MrVr=McV'c+MrV'r+P'

    Where P' equals any momentum gained by the objects hit by the rocks. So, there is no need for the car to speed up: the momentum lost by the car/rocks is gained elsewhere.
     
  8. Nov 14, 2013 #7
    This is enough to answer question 2. Why is there a need to use momentum formula at all? No force no acceleration, no change in velocity.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Simple Momentum Problem Help
Loading...