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Pushing a crate

  1. Apr 7, 2009 #1
    1. The problem statement, all variables and given/known data

    The force F, acting in a constant direction on the 20 kg block has a magnitude which varies with position s of the block. Determine the speed of the block after it slides 3 m. When s=0 the block is moving to the right at 2 m/s. The coefficient of kinetic friction is .3
    F = 50s^2 and pushes on the crate from the hypot of a 3,4,5 triangle.


    3. The attempt at a solution

    I found the x,y components of force to be Fx = 40s^2, Fy = 30s^2
    I found the Normal to be 30s^2 + 196.2 which i multiplied by u=.3 to get a frictional force in the oposite direction of 9s^2+58.86

    I do not understand how to incorporate the initial velocity of 2 m/s, nore do i kow what equations to use. My book seems to hint at .5mv^2+Ps-uNs=.5mv^2 but i do not know what P is. Please help
     
  2. jcsd
  3. Apr 7, 2009 #2

    rl.bhat

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    Find net Fx.
    You can write f = dv/dt = dv/ds*ds/dt = v*dv/ds
    So along x-axis v*dv = [40s^2 - ( 9s^2+58.86)]ds
    Find the integration. To find the constant of integration c, use the condition , when s = 0 v= 2 m/s. Then to get the required answer put s = 3 m.
     
  4. Apr 8, 2009 #3
    Hey thanks a lot. Im pretty sure i got it but could u double check.

    ok so i integrated and c=2, i pluged it in and solved for v

    v=((80/3)s^3-6s^3-117.72s+2)^1/2 @ s=3, v=14.38 m/s

    let me know how i did
     
  5. Apr 8, 2009 #4

    rl.bhat

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    Your answer is correct.
     
  6. Jun 18, 2011 #5
    Forgive me if I'm incorrect, but as I understand it that is the incorrect approach.

    I believe the hint you described suggests that this problem should be solved using the work-energy relationship.

    the first .5mv^2 refers to initial kinetic energy or ΣT(1) [this is where you use the initial velocity]
    Ps-UNs refers to the change in work; P being the applied force (Fx), U being coefficient of friction, and s being displacement, or [ΣU(1-2)]
    the last .5mv^2 refers to final kinetic energy, or ΣT(2)

    I found a different final velocity using this method.
    good luck!
     
  7. Jun 18, 2011 #6

    rl.bhat

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    Hi INTJ BSME, welcome to PF.
    Show your calculations.
     
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