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Frictionless Incline Problem

  1. Oct 3, 2013 #1
    1. The problem statement, all variables and given/known data

    M1 and M2 are two masses connected as shown. The pulley and the incline are frictionless. Find the mass M1, given that M2 (4.00 kg) accelerates downwards at 3.53 m/s2, and that θ = 32.0°.

    dYVQnGg.gif

    2. Relevant equations

    F = m*a
    Fk = u*N

    3. The attempt at a solution

    Forces on m1

    Fy = T - N - m1*g*sin(theta) = m1*a
    Fx = N - m1*g*cos(theta) = 0

    Forces on m2

    Fy = m2*g*T = m2*a


    Using equations above,

    T = m2(g-a)
    N = m1*g*cos(theta)

    m2*(g-a) - m1*g*cos(theta)-m1*g*sin(theta) = m1*a

    rearranging for m1

    m1 =[m2*(g-a)]/[a+g(sin(theta) + cos(theta))]


    Plugging in the correct values, I get 1.47kg for my answer which is... wrong :(


    Thank you,
    Noobe
     
  2. jcsd
  3. Oct 3, 2013 #2

    Mentz114

    User Avatar
    Gold Member

    I get

    T - sin(θ)m1 g = m1 a
    T - m2 g = -m2 a

    Two equation with 2 unknowns. Does that help ?
     
    Last edited: Oct 3, 2013
  4. Oct 3, 2013 #3
    Thank you Mentz that is very helpful! I get the right answer when I use your equations. Thank you again. =]


    Question:

    T - m2 g = -m2 a

    Why is it -m2 a and not just m2 a?
     
  5. Oct 3, 2013 #4
    Think about newton's second law: F=ma
    What is the acceleration of m1? What is the acceleration of m2?
    consider gravity and the coordinate system Mentz114 has chosen when drawing free body diagrams for both blocks. That should answer your question.
     
  6. Oct 10, 2013 #5
    Thank you very much guys, I understand it now! :), Physics is fun
     
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