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Homework Help: Ramp Problem, Friction, Find Theta

  1. Sep 16, 2012 #1
    Challenging Ramp and Pulley Problem

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

    Two blocks of masses 2m and m are connected by a weightless string over a frictionless, massless pulley, as shown in the figure. The coefficient of kinetic friction between the block and the incline is [itex]\mu[/itex]. The system is in a uniform gravitational field directed downward of strength [itex]g[/itex]. Find the incline angle [itex]\theta[/itex] such that the blocks move at a constant speed. Distinguish between the cases of upward and downward motion. Rationalize your solutions using a simple physical picture.

    2. Relevant equations
    [tex]\mathbf{F} = m\mathbf{a} [/tex]
    3. The attempt at a solution

    So we start by looking at the forces acting on each block. In this case, we will be looking at downward motion. For the [itex]2m[/itex] mass:
    [tex] 2mg\sin\theta - \mu mg\cos\theta - T = 0 [/tex]
    And for the second block:
    [tex] T - mg = 0 \implies T = mg [/tex]
    Using the second equation and plugging into the first equation, we find:
    [tex] 2\sin\theta - 2\mu\cos\theta = 1 [/tex]
    I can't figure out how to solve for [itex]\theta[/itex]. Wolfram's answer is pretty ugly.

    Attached Files:

    Last edited: Sep 16, 2012
  2. jcsd
  3. Sep 16, 2012 #2

    Simon Bridge

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    Science Advisor
    Homework Helper

    You need trig identities and a bit of manipulation:

    Divide through by ##\cos(\theta)##

    Square both sides and expand the RHS

    Change variables: ##x=\tan(\theta)##
    Look familiar?

    Note - you have misplaced a minus sign in the first equation.
    gravity and friction both point in the opposite direction to tension.
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