This is a solved equation so no need for preface, my question is in the solving process. I numbered the steps below. Why and how does the second "F" get dropped on steps 5 to 6 (the F by the sin. So Fsin0 on step 5) Why does it disappear on step 6? I get all the other math besides that. Thank you!!!

F = (μs mg)/(cosθ + μs sinθ)

Explanation:

Hi!

In order to find F in terms of m, g, θ and μs we need to find N in terms of the same variables.

This can be accomplished by solving the second equation (vertical components) for N:

1.) Fsinθ+N−mg=0

2.) N = mg - Fsinθ

Now we can replace the value of N in the first equation (horizontal components):

3.) Fcosθ − μsN=0

4.) Fcosθ − μs(mg - Fsinθ) = 0

5.) Fcosθ − μs mg + μs Fsinθ = 0

6.) F (cosθ + μs sinθ) = μs mg

Therefore:

F = (μs mg)/(cosθ + μs sinθ)

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