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Friction/spring/inclined plane problem

  1. Jul 17, 2015 #1
    1. The problem statement, all variables and given/known data
    There is a block of 1kg (m1) resting frictionless on another block of 5kg (m2). m1 is connected by a horizontal spring to m2. m2 is resting on an inclined plane of 45°. Between m2 and the plane there is friction.
    A force of 200N is applied on m2, pushing it upwards.

    F=200N, m1=1kg, m2=5kg, f=0.2, k=100N/m, initial spring length= 0.20m, g=10m/s²

    What is the spring length at equilibrium?

    2. Relevant equations
    F=m*a
    F=k*spring length
    Friction W= (reaction force R)*f

    3. The attempt at a solution
    Increase in spring length = l
    I start with 4 equations:
    F - w*cos45 - R*cos45 - k*l = (m1+m2)*a
    m1*g + m2*g - w*sin45 - R*sin45 = 0
    w=0.2*R
    k*l=m1*a

    Solving this i get a=20m/s² which can't be right.
     

    Attached Files:

  2. jcsd
  3. Jul 17, 2015 #2
    Why do you add k*l in 1st equation ??

    You should be writing 1st equation considering both blocks together as one system . You will then not get k*l in the equation .

    The rest seems fine .
     
  4. Jul 17, 2015 #3

    haruspex

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    As qwertywerty notes, that kl term should not be there. That is internal to the two-mass system.
    But the second equation looks wrong too. Check the signs, and consider what the vertical acceleration is.
     
  5. Jul 17, 2015 #4
    You're right - my bad . So you would have to consider some net acceleration and write horizontal and vertical accelarations in it's terms .
     
  6. Jul 20, 2015 #5
    Thanks for the quick reply.
    New equations:
    F - w*cos45 - R*cos45 = (m1+m2)*ah
    (m1+m2)*g + w*sin45 - R*sin45 = (m1+m2) *av
    w=0.2*R

    Now to solve this i'm still missing a relationship between ah and av.
    I've taken av = ah ( angle is 45°, if the block has moved 1m to the right, it will have moved the same distance vertically, xv = xh -> av = ah)
    Now i end up with R=495N and a=36.7m/s²

    Not possible imo.
    Do you guys see where i go wrong?

    thanks!

    regards,
     
  7. Jul 20, 2015 #6
    Would you check your calculations ?
     
  8. Jul 20, 2015 #7
    In your second equation, you have the wrong sign on the ma term. The blocks are accelerating vertically upward. The way you have it, av = - ah

    Chet
     
  9. Jul 20, 2015 #8
    Ah yes of course. Well, i've got it now. 7cm spring elongation :)
    Thx a lot!
     
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