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Modelling the height of a block up a slope with time

  1. Nov 26, 2015 #1
    sMQV3XL.png
    1. The problem statement, all variables and given/known data


    A block, of mass M1, on the rough slope shown is attached to another mass M2 by a light, inextensible string which passes over a frictionless pulley as shown in the diagram (the coefficient of friction between the block and the slope is u ). The block is released from rest. Find an expression for the height of the block above the bottom of the slope as a function of time. (You should consider the full range of behaviour that may happen for different values of the parameters).

    2. Relevant equations

    F(gravity down slope) = mgsin(theta)
    F(friction down slope) = umgcos(theta)
    f=ma
    s = ut +1/2at^2

    3. The attempt at a solution

    Force of gravity on block is m1gsin(theta)
    Force of friction on block is um1gcos(theta)
    Force needed to push block up slope at constant speed = m1gsin(theta) + um1gcos(theta)
    If M2g > Force needed then block will accelerate up slope with a=(M2g-(m1gsin(theta) + um1gcos(theta)))/m1
    vertical component of that acceleration = asin(theta)
    height = ut + 1/2at^2
    height = 0.5*(m2g-(m1gsing(theta) + um1gcos(theta)))/m1)sin(theta)*t^2
    I'm pretty sure this answer is wrong as it is so complex, but would just like either confirmation that it is right/wrong and where to go
     
  2. jcsd
  3. Nov 26, 2015 #2

    haruspex

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    The problem statement does not discriminate static and kinetic coefficients, but it does ask you to consider all possibilities. What would be a more circumspect statement than the above?
    True. What if it isn't, though?
    Don't forget M2 will accelerate too. Consider the tension and analyse the forces on each mass separately.
     
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