A massless string, passing over the frictionless pulley, connects the two masses as shown. Block m1 hangs vertically without touching the wall, but m2 slides along the wall with friction (μs = 0.61, and μk = 0.14). If θ = 53°, how many times heavier than block 1 must block 2 be to start the system moving?
1. ƩFx = max and ƩFy = may
2. fs = μsN
3. fk = μkN
The Attempt at a Solution
I set up a free body diagram for m2, 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): m2gsinθ in the -x-direction and m2gcosθ in the -y-direction
N (normal): +y direction
fs (static friction): +x-direction (when m2 is NOT moving)
fk (static friction): -x-direction (when m2 IS moving)
So I figured the static friction would be this:
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 m2, I'm having trouble figuring out another equation so a ratio can be set up.
Any help appreciated, thanks in advance!