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Resistive Forces on Objects on an Incline

  1. Aug 17, 2015 #1
    1. The problem statement, all variables and given/known data
    A boy on a board B slides down a slope. The angle of the slope to the horizontal is 30°. The total resistive force F acting on B is constant.
    The boy on the board B moves with velocity v down the slope. The variation with time t of v is shown in Fig. 3.2.
    upload_2015-8-17_19-41-17.png
    Calculate the resistive force.



    2. Relevant equations
    wsinA----?

    3. The attempt at a solution
    Resistive force= WsinA
    = 75 x 9.81 x 0.5
    = 367.5 N
    My answer does not match with the correct answer. How do you solve this?
    Thanks!
     
  2. jcsd
  3. Aug 17, 2015 #2

    SammyS

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    Use the graph to determine the acceleration.

    You didn't include the weight or mass of the boy and board in the problem statement .

    What component of the weight is parallel to the incline ?
     
  4. Aug 17, 2015 #3
    Oh, I am so sorry! The mass of the boy is 75kg.
    The question doesn't say which component of weight is parallel to the incline, but I think it is WsinA.
     
  5. Aug 17, 2015 #4

    SammyS

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    Find the acceleration.
     
  6. Aug 17, 2015 #5
    a=(v-u)/t
    a= 7.4/ 2.5 (the question asks us to calculate all the answers till 2.5s)
    = 2.96 m/s^2
    But then what? Do I use F=ma? With this formula the answer comes to 222N, but the answer is 147N.
     
  7. Aug 17, 2015 #6

    SammyS

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    What are you using for the net force?

    Show your work.
     
  8. Aug 17, 2015 #7
    I multiplied the acceleration I found with the mass of the boy:
    F=75 x 2.96
    = 222 N
    Is this the net force or the force that opposes the boy?
     
  9. Aug 17, 2015 #8

    SammyS

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    That's the net force required for the boy and board to have an acceleration of 2.96m/s2.

    What two forces combine to make that net force?
     
  10. Aug 17, 2015 #9
    The resistive force opposing the horizontal component of weight and the contact force?
     
  11. Aug 17, 2015 #10

    SammyS

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    Yes for the resistive force. No for the contact force.

    What does W⋅sin(A) result from? You seem to have abandoned it .
     
  12. Aug 17, 2015 #11
    W sin A results from the weight of the boy, which is a force.
    So the weight of the boy + the resistive force= the net force?
    Then,
    The resistive force= 222-367.5
    =-145.5
    On rounding off to 2 sf, it gives 150N, just like in the answer!
    Thanks!
     
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