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Work done by a varying force

  1. Apr 27, 2010 #1
    1. The problem statement, all variables and given/known data
    A cord is attached to a cart that can slide along a frictionless horizontal rail aligned along an x-axis. The left end of the cord is pulled over a pulley, located at height h = 1.2m. There is negligible frictional force. The cart slides from x1=3.00m to x2=1.00m. During the move, the tension in the cord is a constant 25.0N. What is the change in kinetic energy of the cart during the move


    2. Relevant equations



    3. The attempt at a solution
    My approach to the question is as follow:
    Since tension is constant, the horizontal component of T will decrease as the angle T makes with the horizontal increases. So I need to form an expression for horizontal component of T in term of h and x. But I don't know how to form this equation.

    tan
     
  2. jcsd
  3. Apr 27, 2010 #2

    Hootenanny

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    HINT: Draw a force diagram and use the properties of a right-angled triangle. :wink:
     
  4. Apr 27, 2010 #3
    why draw force diagram? There is only one force involved
     
  5. Apr 27, 2010 #4

    Hootenanny

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    Yes, but there is two components and you want the angle between the force and one of its components (in the x-direction). You should then be able to write the angle in terms of the displacement and the pulley height.
     
  6. Apr 27, 2010 #5
    tanθ = 1.2/x
    θ = tan-11.2/x
    Tcosθ = Tcos(tan-11.2/x)
    Is it like this?
     
  7. Apr 27, 2010 #6

    Hootenanny

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    It would perhaps be easier to use the fact that
    cosθ = x/sqrt(x^2+h^2). Can you see why?
     
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