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!

2 masses, a massive pulley and an inclined surface

  1. Sep 7, 2016 #1
    1. The problem statement, all variables and given/known data
    Snap1.jpg
    A mass m lies on an inclined surface with equal coefficients of friction μ=μsk. the pulley has also mass m and the weight is 2m. what is the velocity after it has descended distance h and during how much time.

    2. Relevant equations
    Moment of inertia of a massive disk: ##I_{cen}=\frac{1}{2}mr^2##
    Torque and angular acceleration: ##M=I\alpha##

    3. The attempt at a solution
    $$\Sigma F=ma:~~\left\{\begin{array}{l} 2mg-T_1=2ma \\ T_2-mg\sin\theta-mg\mu\cos\theta=ma \end{array}\right.$$
    $$\rightarrow~T_1=\frac{2}{3}(1+\sin\theta+\mu\cos\theta)mg$$
    $$T_2=\frac{mg}{9}(4+7\sin\theta+7\mu\cos\theta)$$
    $$M=I\alpha:~~a=\frac{2}{m}(T_1-T_2)=...=\frac{2g}{3}\left( \frac{2}{3}-\frac{1}{3}\sin\theta-\frac{\mu}{3}\cos\theta \right)$$
     
  2. jcsd
  3. Sep 7, 2016 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Well done - I have not checked the algebra but that looks like a good approach to take.
    Is there a question in all that?
     
  4. Sep 7, 2016 #3
    Thank you Simon, i am not sure about my answer, that is why i posted. thank you
     
  5. Sep 8, 2016 #4

    ehild

    User Avatar
    Homework Helper
    Gold Member

    I got different result. T1 and T2 are not needed. Eliminate them by adding the force equations and substituting T1-T2 from the torque equation.
     
  6. Sep 8, 2016 #5

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Looks like you divided by 3 twice over.
     
  7. Sep 8, 2016 #6
    $$\left\{\begin{array}{l} (\rm 1)~2mg-T_1=2ma \\ (\rm 2)~T_2-mg\sin\theta-mg\mu\cos\theta=ma \end{array}\right.$$
    $$(\rm 1)+(\rm 2),~T_2-T_1=-\frac{1}{2}ma:~~a=\frac{2}{7}(2-\sin\theta-\mu\cos\theta)g$$
     
  8. Sep 8, 2016 #7

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Correct!
     
  9. Sep 8, 2016 #8
    Thanks Ehild, Simon and Haruspex
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: 2 masses, a massive pulley and an inclined surface
Loading...