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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]

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# Homework Help: Incline plane

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