1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    You need trig identities and a bit of manipulation:

    Divide through by ##\cos(\theta)##
    ##1/\cos(\theta)=\sec(\theta)##

    Square both sides and expand the RHS
    ##\sec^2(\theta)=1+\tan^2(\theta)##

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook