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Two Blocks on an Incline

  1. Feb 7, 2008 #1
    SOLVED :)

    1. The problem statement, all variables and given/known data

    The figure shows two identical blocks tied together with a string which passes over a pulley at the crest of the inclined planes, one of which makes an angle q1 = 30° to the horizontal, the other makes the complementary angle q2 = 60°.

    a) If there is no friction anywhere, with what acceleration do the blocks move?
    b) If each block has a mass m = 1 kg, what is the tension in the string while they are both moving?
    c) Now suppose the coefficient of sliding friction between the blocks and planes is µ = 0.02. With what acceleration do the blocks move in this case?

    2. Relevant equations

    F = ma
    Hint for a): Draw a free-body diagram for each block. Using your free-body diagram and F = ma for each block, find two equations and two unknowns, the unknowns being the acceleration (part (a)) and the tension (part (b)).

    3. The attempt at a solution

    My freebody diagrams for the box on the left (which I labeled box 1) included a perpendicular normal force, gravity straight down, and tension up the box.
    My freebody diagram for the box on the right (box 2) included gravity down, normal force perpendicular to the plane, and tension toward the incline of the plane.

    So the equation I came up with:
    F=ma --->
    F(box1) = Ftension - mg(sin30)
    F(box2) = mg(sin60) - Ftension

    and that is all I've been able to come up with for the past hour of racking my brain :( . I was hoping someone could point me in the right direction. Much appreciated!
    Last edited: Feb 7, 2008
  2. jcsd
  3. Feb 7, 2008 #2
    the hint is making it complicated imo, i was taught to do it like this:
    a) consider the blocks as one system and ignore tension, draw one FBD for them
    b) since you know that the acceleration of both of them will be the same, draw an FBD for one of them and solve for Tension.
    c) same as a) except you consider the force of friction
  4. Feb 7, 2008 #3
    Solved :P Thanks afg34 , I ended up basically doing what you said!
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