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Help! Problem on INCLINED planes.

  1. Mar 25, 2006 #1
    Hello, here is the question.

    Two masses, 4.0 kg and 6.0 kg, are connected by a “massless” rope over a “frictionless” pulley as pictured in the diagram. The ramp is inclined at 30.0º and the coefficient of kinetic friction on the ramp is 0.18.

    [​IMG]


    (b) Determine the acceleration of the system once it begins to slide.



    i only need help on b.. finding the acceleration. if i can get the right acceleration i can get all the other parts.

    Now i solved it by doing this. making 2 equations.

    4 kg = m1 6kg = m2 motion to the right is positive. uk = 0.18

    m1a = T - [Ff + Fg||]
    m1a = T - (uk)(m1g)cos30 - sin30m1g
    m1a = T - 6.1 - 19.6 equation 1

    m2a = m2g - T
    m2a = 58.8 - T equation 2

    add the two equations together you get. (T cancel out)

    a (m1 + m2) = 58.8- 25.7
    a = 33.1 / 10
    a = 3.3 m/s ^2

    i have been lookin over my calculation over and over and the acceleration is different from the answers.

    here is the SOLUTION:
    (b)

    For the 4.0-kg mass:
    [​IMG]


    4.0 kg(a) = T – uKmg(cosX) – mg(sin X)

    4.0 kg(a) = T – 13.5 N



    For the 6.0-kg mass:

    [​IMG]

    6.0 kg(a) = 58.8 N – T



    Solving the system of equations:

    a = 4.5 m/s2




    according to the solution... for equation 1.. it is + 6.1 - 19.6 = -13.5

    but it doesnt make sence because it should be -6.1 - 19.6 = -25.7

    is there a trick im missing or do you think the solution is wrong? this question is vital for a test on monday.



    thank you

    byron
     
  2. jcsd
  3. Mar 25, 2006 #2

    Curious3141

    User Avatar
    Homework Helper

    You are correct, friction always opposes motion. The signs used in the accepted solution are wrong.
     
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