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Incline plane

  1. Mar 10, 2005 #1

    tony873004

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    Can someone tell me if I did this right?

    An object of mass m is hung from a rope that passes over a pulley at the top of a ramp and is attached to a block of mass M.

    (a) Assume m is large enough that the block accelerates up the ramp. Find an expression for the block’s acceleration.

    (b) From your result for part (a), determine the minimum ratio m/M such that the block, once moving, accelerates up the ramp.


    (the diagram is simple, M is on the incline plane and m is hanging straight down)

    [tex]a = \frac{Force}{mass}[/tex]

    [tex]a=\frac{Mg sin\theta + \mu Mg cos \theta -mg}{M}[/tex] (answer for part A)

    Set the force equal to 0
    [tex]Mg sin \theta + \mu Mg cos \theta - mg = 0[/tex]
    [tex]Mg sin \theta + \mu Mg cos \theta = mg [/tex]

    factor out Mg
    [tex]Mg(sin \theta + \mu cos \theta) = mg[/tex]

    the g's cancel

    [tex]m = M(sin \theta + \mu cos \theta)[/tex]

    [tex]m/M = sin \theta + \mu cos \theta[/tex]
     
  2. jcsd
  3. Mar 10, 2005 #2

    dextercioby

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    AWKWARDLY,the answer to poin b) is correct (the minimum value is the one u found),but the acceleration you find is incorrect,assuming the rope is inextensible (the same tension in it in every point)...

    How about correcting your mistake?

    Daniel.
     
  4. Mar 10, 2005 #3

    tony873004

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    Thanks, Dex.
    I'm guessing that I should have M+m in the denominator of my first answer instead of simply M. They must accelerate at the same rate so should be treated as a single mass.

    By awkardly, did you mean because I had to get the first part to get the second part?
     
  5. Mar 10, 2005 #4

    dextercioby

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    Yes,exactly,you got the point perfectly.Well done!

    Daniel.
     
  6. Mar 10, 2005 #5

    tony873004

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    Thanks, Dextercioby. I'd have turned it in as is if you didn't make me go back and look!
     
  7. Mar 10, 2005 #6

    dextercioby

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    Good thing that u decided to check by posting it here.

    Daniel.
     
  8. Mar 11, 2005 #7

    tony873004

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    You couldn't be more right. We had a mid term today, and this exact problem, but with specific numbers, was on the exam. I'd have missed it had we not gone through it last night!!
     
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