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String with mass pulling block up frictionless ramp

  1. Sep 23, 2014 #1
    1. The problem statement, all variables and given/known data
    A block of mass M has a string of mass m attached to it. A force F is applied to the string and it pulls the block up a frictionless plane that is inclined at an angle theta. Find the force that the string exerts on the block


    2. Relevant equations
    F=ma


    3. The attempt at a solution
    Force of the string on the block = Force of the block on the string = N
    Force applied to string = F
    acceleration of block = acceleration of string = a


    My first equation was the net-force equation for the string:
    ma = -mg*sin(theta) - N + F


    My second equation was the net-force equation for the block:
    Ma = -Mg*sin(theta) + N


    solving for the acceleration in the top equation and plugging it into the second equation gives the following (after a small amount of algebra)

    N = (F/m)*(1+M/m)^-1

    Which is not the answer I am supposed to be getting. I am guessing the problem is with my net-force equations but I can't located a specific problem. Anyone want to explain what I'm doing wrong here?
     
  2. jcsd
  3. Sep 23, 2014 #2
    first try and write the net-force equation for the whole system (meaning substitute a block M and a string m, with a new object with mass M+m) Now we can forget about internal forces between mass and string. so we just have two force, the force f we apply and the one due to gravity. This way you can find a (acceleration) of the objects.
     
  4. Sep 24, 2014 #3

    haruspex

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    Your initial equations are ok but you must have gone wrong in the subsequent algebra. Your final equation is not dimensionally consistent.
     
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