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Very simple tension problem

  1. May 6, 2009 #1
    1. The problem statement, all variables and given/known data
    Two masses are suspended by a frictionless string on a frictionless pulley, one with mass 75 kg and the other 100 kg.
    What is the tension of the string and the acceleration of the masses

    3. The attempt at a solution
    My attempt was to say since mass A, 75 kg, was 75 percent of mass B, then the acceleration of mass B would be 25 percent of the acceleration of gravity 9.8 m/s^2.
    so it would be roughly 2.5 m/s^2. Since the acceleration was 2.5 m/s^2, I thought the tension would be equivelant to the force of the mass of both A and B times the acceleration 2.5 m/s^2 ie. F=ma. Clearly there is something wrong with this approach. What is it that I'm missing? is there a generalized formula for tension of a string?
     
  2. jcsd
  3. May 6, 2009 #2

    tiny-tim

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    Hi physicsnewb7! :smile:

    Call the tension T, and then apply good ol' Newton's second law twice (to each mass separately) …

    since the acceleration, a, of each mass is the same (in opposite directions), you can solve for T and a :wink:
     
  4. May 6, 2009 #3
    so if a I say a100kg=100g-T and a75=T-75g, where a is the acceleration, g is gravitational acceleration and T is tension, then add the two equations together to get a=25/175g=1/7g and then solve for T by plugging a in the equations. Is that right? would the acceleration be 1/7g? any help would be greatly appreciated!
     
  5. May 6, 2009 #4

    tiny-tim

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    Hi physicsnewb7! :smile:

    Yes, that's right! :approve:

    Another way of doing it is to imagine that the string is straight …

    there's 100g of force pulling it left, and 75g pulling it right, making a total of 25g … since the total mass is 175, that makes a = 175g/25 = g/7. :wink:

    (or, if you're not interested in the tension, you could even use conservation of energy and a = dv/dt = v dv/dh = 1/2 d(v2)/dh)
     
  6. May 6, 2009 #5
    Thank you so much TinyTim for responding and helping.:smile:
     
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