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Combining Newton's Laws and Kinematic

  1. Dec 3, 2016 #1
    1. The problem statement, all variables and given/known data

    Max (65 kg) pushes Toni (50 kg) with a force of 360 N. The force of friction is 0 on Toni and 80 on Max.
    (a) Find each girls acceleration
    (b) If Max pushes Toni for 0.1 s, how far will Toni travel in 0.5 s?
    2. Relevant equations
    Fnet=ma
    v2=v1+at
    d=v1(t)+1/2a(t)^2

    3. The attempt at a solution
    For (a), I got the correct answers by using Fnet=ma
    Max's acceleration:4.3m/s^2 (left)
    Toni's acceleration: 7.2m/s^2 (right)
    For (b), Toni's acceleration is only 7.2 during the 0.1 seconds so...
    d=v1(t)+1/2a(t)^2
    d=(0)(0.1)+1/2(7.2)(0.1)^2
    d=0.036
    To find the distance for the remaining 0.4 seconds, I need to find v1 which is v2 of the 0.1 seconds
    v2=v1+at
    v2=7.2(0.1)
    v2=0.72 m/s
    So v1 for the 0.4 s is 0.72. I assumed acceleration is 0 during this time and that she is now moving at a constant velocity
    d=0.72(0.4)+1/2(0)(0.4)^2
    d=0.288
    d1+d2=0.324
    It's very close to the answer my teacher gave which is 0.33 m..but I'm just curious as to why it's a little off because it might be considered wrong on a test.
     
  2. jcsd
  3. Dec 3, 2016 #2

    kuruman

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    Science Advisor
    Homework Helper
    Gold Member

    It's off probably because of round off errors. Carry the intermediate calculations to more decimal places and see what happens. Better yet, derive a symbolic answer and substitute the given quantities at the very end.

    On edit: I ran the numbers and got 0.324 m. If you are concerned about this, you may consider asking your teacher.
     
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