Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Conservation of Momentum question

  1. Oct 20, 2011 #1
    1. The problem statement, all variables and given/known data

    Three identical train cars, coupled together, are rolling east at 3.71 m/s. A fourth car travelling east at 6.74 m/s catches up with the three and couples to make a four-car train. A moment later, the train cars hit a fifth car that was at rest on the tracks, and it couples to make a five-car train. All 5 cars are identical. What is the speed of the five-car train?

    2. Relevant equations
    m1v1+m2v2+... = m1v1'+m2v2'+...
  2. jcsd
  3. Oct 20, 2011 #2


    User Avatar
    Homework Helper

    Welcome to PF, Janfor.
    I can't help much until you attempt the problem yourself (bad for your education and boring for me).

    You have two collisions in this problem. You can deal with them one at a time. For a collision, you write
    Put in "mv" for each moving object, before and after.
    Then put in the numbers for each m and v.
    Hopefully there will only be one unknown so you can solve for it!
    Bon chance.
  4. Oct 20, 2011 #3
    you have the right equation, so just plug in the variables:
    the momentum of the train initially is the total of all three cars plus the total of the fourth cart:
    (3m)*(3.71)+(6.74m) = (4m)(V)
    the reason that this is the equation is because momentum before the collision equals the momentum after the collision. Since the cars are identical, mass can be identified as a constant m. also, when the fourth train impacts the three trains, the velocity will change because the momentum is moving faster, meaning we need a new variabe, V
    When solving algebraically for v, you'll find that the m's cancel and you get v=4.47
    now given the new velocity of the train, do the same thing:
    (4m)*(4.47) = (5m)(v)
    there is no addition because there is only one thing moving before and after the collision, since car 5 is initially at rest and the cars combine afterwards
    solve for v again and get v = 3.57m/s
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook