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General Forces on Slope Problem

  1. Mar 22, 2008 #1
    a) Find a general expression for mass m2 so that m1 will move at a constant speed up the ramp. Your answer will be based on (mu) and (theta).
    b) Give a numerical value for (mu) and (theta) so that m2/m1 > 1
    c) Give a numerical value for (mu) and (theta) so that m2/m1 < 1


    Fg2 = m2g
    Fg1x = m1gsin(theta)
    Ff = (mu)Fn
    Fn = Fg2y
    a = 0m/s2
    Fnet = ma
    g = 9.8 m/s2

    Fnet = Fg2 - Fg1x - Ff
    0 = m2g - m1gsin(theta) - (mu)cos(theta)
    m2g = m1gsin(theta) + (mu)cos(theta)
    m2 = [m1gsin(theta) + (mu)cos(theta)] / g

    My problem is that I don't understand how to give a numerical value for (mu) and (theta) so that m2/m1 > or < 1 without also determining the mass of either m1 or m2 since they are both a part of the general equation. Is it even possible without also giving a numerical value to one of the masses?? Any clarification is greatly appreciated.
     

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  3. Mar 22, 2008 #2

    Doc Al

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    Staff: Mentor

    That last term--the friction force--is missing a few factors. Redo it and the solution may be clearer.
     
  4. Mar 23, 2008 #3
    0 = m2g - m1gsin(theta) - (mu)m1gcos(theta)
    m2g = m1gsin(theta) + (mu)m1gcos(theta)
    m2 = [m1gsin(theta) + (mu)m1gcos(theta)] / g

    Although the equation makes a bit more sense, I'm still confused about how to give a numerical value for (mu) and (theta) so that m2/m1 > or < 1 without also determining the mass of either m1 or m2 since they are both a part of the equation.
     
  5. Mar 23, 2008 #4

    Doc Al

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    Staff: Mentor

    Good. Now further simplify that last expression: Start by factoring out the m1 and the g.
     
  6. Mar 24, 2008 #5
    m2 = [m1gsin(theta) + (mu)m1gcos(theta)] / g
    m2 = [m1g[sin(theta) + (mu)cos(theta)]]/g
    m2 = m1[sin(theta) + (mu)cos(theta)]

    So factoring has eliminated g but m1 and m2 are sill part of the equation, leaving me just as confused as before.
     
  7. Mar 24, 2008 #6

    Doc Al

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    Staff: Mentor

    You're almost there. Write it as m2/m1 = ?

    Now you get to play around with theta and mu. Hint: Compare a small angle (~ 5 degrees) with a bigger angle (~ 85 degrees).

    Remember: All you need to do is make up a few values that satisfy the requirements.
     
  8. Mar 24, 2008 #7
    Thank you for your help Doc Al. It all makes sense now.
     
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