(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The included image shows the problem in its entirety. The problem is from a physics review book that I have which also includes the answer, but the explanation is beyond me. I was hoping someone could walk me through the solution.

T, the rope tension (constant throughout the rope)

m_{b}- the mass of the block = 20 kg

m_{p}- the mass of the lower pulley = unknown

F as the net force acting on the pulley (shown in image) = 100 N

[tex]\vartheta[/tex], the angle of incline = 30 degrees

http://img705.imageshack.us/img705/7307/pullyramp.png [Broken]

2. Relevant equations

3. The attempt at a solution

Here's how I tackled this:

(1) a_{b}= 2 a_{p}The acceleration of the block is twice that of the pulley, since moving the pulley a distance d results in the block moving a distance 2d

A free-body diagram for the block shows that the forces pushing the block up or down the ramp are T, the rope tension pushing up, and gravity acting to move the block down the ramp.

So, taking the direction up the block to be positive we have:

(2) T - mgsin[tex]\theta[/tex] = m_{b}a_{b}

Similarly for the bottom pulley we have (taking down to be positive)

(3) 2T - F = m_{p}a_{p}

That's as far as I get. I have 4 unknowns: T, m_{p}, a_{p}, a_{b}

but only 3 equations.

Any insight or help will be appreciated.

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# Homework Help: Inclined Plane with Pulley

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