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Center of Mass/Linear Momentum

  1. Mar 21, 2009 #1
    1. The problem statement, all variables and given/known data
    In the "before" part of Fig. 9-60, car A (mass 1100 kg) is stopped at a traffic light when it is rear-ended by car B (mass 1500 kg). Both cars then slide with locked wheels until the frictional force from the slick road (with a low μk of 0.21) stops them, at distances dA = 5.3 m and dB = 3.4 m. What are the speeds of (a) car A and (b) car B at the start of the sliding, just after the collision? (c) Assuming that linear momentum is conserved during the collision, find the speed of car B just before the collision.

    (see attachment for image)

    2. Relevant equations

    (A = CarA, B = CarB)

    PAi + PBi = PAf + PBf
    (mA)vAi + (mB)vBi = (mA)vAf + (mB)vBf

    3. The attempt at a solution

    I've been sitting here looking blankly at this problem for about an hour now. I really have no idea where to start with this, i've tried a few things, but it always ends up giving me two unknown variables. Looking at another thread that was posted on this question, I realize that all the kinetic energy is transferred to thermal in the end, how does that help?


    Attached Files:

  2. jcsd
  3. Mar 21, 2009 #2


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    Homework Helper

    Hi Nikolan, welcome to PF

    For a) & b) think about one car at a time. After the collision, the work done by friction slowing the car will equal the decrease in kinetic energy of the car.
  4. Mar 21, 2009 #3
    Thank you very much!

    I ended up taking what you said and applying it like this:

    (Using this solution for both cars A and B)

    Fk = (uk)FN to find force of friction.

    W of Friction = (Fk)(D) = Kf - Ki = 1/2mvf^2 - 1/2mvi^2

    to get:

    W = - 1/2mvi^2 => sqrt(((-2)(W))/M) for initial speeds of both cars directly after impact.
    I then used Momentum of Cars before = Momentum afterwards
    Pai + Pbi = Paf + Pbf
    mavai + mbmbi = mavaf + mbvbf

    and plugging in relevant values to end up with initial speed of car B before collision.

    Again, thanks for your help! :approve:
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