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Inclined plane with pulley

  1. Apr 4, 2015 #1
    1. The problem statement, all variables and given/known data
    A 10 kg mass is on a frictionless inclined plane 30 degrees to the horizontal. At the top of the plane is a pulley that has a rope attached to mass with tension T = 75 N. If the mass starts from rest, what is its velocity after 2 seconds?

    2. Relevant equations
    F = ma
    Vf=Vi + at

    3. The attempt at a solution
    So my book lists the formula as T = mgsinθ + ma. I set the problem up pretty much the same as:
    ∑Fx = max
    75 N - 10 N = (10 kg) a
    My acceleration is 6.5 m/s2. Plugging this value in to vf=vi + at, I get 13.0 m/s but my book says it's supposed to be 5 m/s. What am I doing wrong? Thanks in advance!
     
  2. jcsd
  3. Apr 4, 2015 #2

    ehild

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    Where did you get that 10 N from?
     
  4. Apr 4, 2015 #3
    The x component of the weight: -mgsinθ
     
  5. Apr 4, 2015 #4

    ehild

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    m=10 kg, g=10 m/s2, θ=30° . How would it give 10 N ?????
     
  6. Apr 5, 2015 #5
    I see. Well, I redid this problem and I did a force table. My T is 75 N, my x component of the force is -50 N. If I set up the problem I get:
    T - mgsinθ = ma
    75-50 = 10 a
    a = 2.5 m/s^2

    The answer is 5 m/s^2.
     
  7. Apr 5, 2015 #6
    I totally misread this problem and it serves me right for not paying close attention. This is a two part problem. I solved for the acceleration using F=ma, which is 2.5 m/s^2. Then with the known time (2 s), I plugged it in to the equation Vf=Vi + at. Vf = 5 m/s.
     
  8. Apr 5, 2015 #7

    ehild

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    Well done at the end!
     
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