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## Homework Statement

A massless string, passing over the frictionless pulley, connects the two masses as shown. Block m

_{1}hangs vertically without touching the wall, but m

_{2}slides along the wall with friction (μ

_{s}= 0.61, and μ

_{k}= 0.14). If θ = 53°, how many times heavier than block 1 must block 2 be to start the system moving?

## Homework Equations

1. ƩF

_{x}= ma

_{x}and ƩF

_{y}= ma

_{y}

2.

*f*

_{s}= μ

_{s}N

3.

*f*

_{k}= μ

_{k}N

## The Attempt at a Solution

I set up a free body diagram for m

_{2}, oriented as it is in space, such that the positive x-direction points up the slope and the positive y-direction points perpendicularly out of the slope. Then the forces are as follows:

T (tension): + x-direction

W (weight): m

_{2}gsinθ in the -x-direction and m

_{2}gcosθ in the -y-direction

N (normal): +y direction

*f*

_{s}(static friction): +x-direction (when m

_{2}is NOT moving)

*f*

_{k}(static friction): -x-direction (when m

_{2}IS moving)

So I figured the static friction would be this:

*f*

_{s}= μ

_{s}(m

_{2})(g)(sinθ)

as per equation 2.

But this is about as far as I got. I'm trying to find how many times heavier than block 1 must block 2 be to start the system moving-- I inferred from this that block 2 would move UP the ramp if block 1 was heavier, which makes sense, and while I have an equation containing m

_{2}, I'm having trouble figuring out another equation so a ratio can be set up.

Any help appreciated, thanks in advance!

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