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h1a8
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Homework Statement
Block A weighs 60N and rests on top of block B which weighs 80N and rests on an incline plane with angle of elevation 30 degrees. Block A is restrained by a mass-less rope as shown. What force F will cause block B to start moving down the plane? Assume all surfaces have a coefficient of friction of 1/3.
The answer is printed as F = 40.3N
http://imagizer.imageshack.us/v2/640x480q90/802/an0g.jpg
According to what's printed, the answer is supposed to be F = 40.3 N
But that's not what I'm getting.
Homework Equations
Free body diagrams for both blocks with y-axis perpendicular to incline plane.
Newton's 2nd Law after free body diagrams to form equations.
Newton's 3rd Law for normal forces and friction forces between blocks.
fs=μNB and fAB=fBA=μNA
Block B
1. μNB+μNA-F-WBcosθ=0 x-direction
2. NB-NA-WBcosθ=0 y-direction
Block A
3. NA-WAcosθ=0 y-direction
4. T-μNA-WAsinθ=0 x-direction
The Attempt at a Solution
I created free body diagrams and set up equations based off Newtons 2nd law. fAB is the force block B is pulling block A with (maximum static friction) and fBA is the maximum force block A is restraining block B with.3. → NA=WAcosθ
2. → NB=(WA+WB)cosθ
1. → F=μ(WA+WB)cosθ+μWAcosθ-WBsinθ
or F= μ(2WA+WB)cosθ-WBsinθ = 17.7N
I solved the systems and finally got F = 17.7N. I'm thinking the answer F = 40.3N is wrong (the professor made a mistake). Or did I make a mistake somewhere? Are my free body diagrams and forces correct? I appreciate any help thanks.P.S. I collect physics problems and try to solve them for fun (like this one). Does anyone know of another good block incline problem?
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