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Troutkibe
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Homework Statement
When an applied force elevated at angle θ is used to drag mass m along a surface with μ as the coefficient of friction, the mass accelerates horizontally with some value, a. Derive the cleanest and most simplified formula for the applied force, Fapplied, that will give the required acceleration.
Since the Fapplied is elevated at angle θ one could break it down into components FaCosθ
[Horizontal]and FaSinθ[Vertical]. Additionally, FN will be mg-FaSinθ because FaSinθ is alleviating some of the force that FN normally has to counteract Fg, meaning that Ff will be μ(mg-FaSinθ).
I'm just so sure my derivation is correct but when I used sample numbers it didn't work at all, I'd really appreciate any advice or help, thanks!
Homework Equations
a=Fnet/m
Fg=mg
Ff=μFn
The Attempt at a Solution
a=Fnet/m
a=FaCosθ- μ(mg-FaSinθ/m
a=FaCosθ-μmg-μFaSinθ/m
am+μmg=Fa(cosθ-μsinθ)
am+μmg/cosθ-μsinθ=Fa
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