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Classical mechanics: Force versus time graph

  1. Dec 5, 2015 #1
    1. The problem statement, all variables and given/known data
    force_vs_time_graph.png
    A particle of mass m=4.0 kg is moving along the x-axis. The particle is being acted upon by a variable single force F⃗ , directed along the x-axis. At t=0 s, the particle is moving at v_0=−3 m/s.

    What is the first time t>0 when the particle comes to a stop momentarily?

    3. The attempt at a solution
    because I know the initial velocity ,I know the initial momentum and I know the final momentum too(as the particle stops temporarily) but the force is variable otherwise I would have equated change in momentum to the impulse imparted.and found the time t.

    what should I do?
     
  2. jcsd
  3. Dec 5, 2015 #2

    gneill

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    Staff: Mentor

    What does area under a Force vs Time curve represent?
     
  4. Dec 6, 2015 #3
    it represents impulse.

    ##mv_f-mv_i=J##
    ##0-m(-3)=∫F. dt##
     
  5. Dec 6, 2015 #4

    cnh1995

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    So you'll have to calculate the value of t at which the area of the curve becomes 12.
     
    Last edited: Dec 6, 2015
  6. Dec 6, 2015 #5
    how will I do it? I don't have the force as a fn of time.
     
  7. Dec 6, 2015 #6

    cnh1995

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    You do.
    ses.edx.org%2Fasset-v1%3AMITx%2B8.MechCx_2%2B2T2015%2Btype%40asset%2Bblock%2Fforce_vs_time_graph.png
    First you need to formulate F as a function of time between various intervals.
     
  8. Dec 6, 2015 #7
    you mean from 0 to 1 sec its 2.5
    from 1 to 4 its 12

    but the answer is 3.375
     
  9. Dec 6, 2015 #8

    cnh1995

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    Indeed it is. That's the final answer.
    No. From t=0 to t=1, what is F(t) and so on..
     
  10. Dec 6, 2015 #9

    cnh1995

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    Ok right, if you are talking in terms of areas directly..
     
  11. Dec 6, 2015 #10
    area under the f/t curve is all I know what else are you saying.also I am fairly new to calculus
     
  12. Dec 6, 2015 #11

    cnh1995

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    Ok. So, from 0 to 4, the area is 14.5. So, t must be between 1 to 4. Agree? Because total area is 12 and out of that, 2.5 is already in between 0 to 1.
     
  13. Dec 6, 2015 #12
    yes totally because of the areas.
     
  14. Dec 6, 2015 #13

    cnh1995

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    So, from t=1 to t=4, you need to find at what value of t will the area be 9.5(i.e. 12-2.5). Can you do it?
     
  15. Dec 6, 2015 #14

    cnh1995

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    You know its a rectangle from t=1 to t=4. You know the height. I believe the answer is in plain sight. Good luck..
     
  16. Dec 6, 2015 #15
    ##∫F.dt+F_c(t-1)=-mv_i##
    (the integral is form t=0 to t=1) (c means const)
    ## 2.5+4(t-1)=-4*(-3)##
    ##t=3.375##

    @cnh1995
    thank you
     
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