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Inclined Blocks Connected By a String

  1. Sep 30, 2009 #1
    1. The problem statement, all variables and given/known data
    The mass of block a or Ma is equal to 3.00 kg and the mass of block b or Mb is equal to 1.50 kg. The two blocks are connected by a string and are sitting on an incline of 38[tex]\circ[/tex] with block b being the higher on the incline than block a. The string between them is taut. I need to find the acceleration of the system of the two blocks and the tension in the connecting string.

    2. Relevant equations
    [tex]F_{net}=m\cdot a[/tex]
    [tex]F_{w}=m\cdot g[/tex]
    [tex]F_{N}=-F_{w}[/tex]
    [tex]F_{x}=m\cdot g\cos\theta[/tex]
    [tex]F_{y}=m\cdot g\sin\theta[/tex]

    3. The attempt at a solution
    Ok so I am thinking that because the x compoent of force on Block b is less than Block a the acceleration of the system would just be the x component of the vector for Block a over the mass of Block a minus the mass of Block b:
    [tex]a=\frac{m_{a}\cdot g\cos\theta}{m_{a}-m_{b}}[/tex]
    I think subtracting the masses is correct because Block b is preventing Block a from achieving its full potential acceleration because they are connected via the string. I also think that this is the formula for the acceleration of the system because if the x component of the force for Block b were higher than that of Block a then the string would slacken because Block b would be accelerating faster than Block a.

    If there is any flaws to my logic please point them out.

    Also for the tension of the string I am not sure what to start with to solve the problem. I think something like:
    [tex]T_{s}=m_{a}\cdot g\cos\theta - m_{b}[/tex]
    would be it but I dont know.

    Please help. Thanks.
     

    Attached Files:

    Last edited: Sep 30, 2009
  2. jcsd
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