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consider an plane inclined at an angle theta with a block on it. the problem asks me to find a horizontal acceleration such that the block will not slide down the plane.

in part (a), friction is neglected, in part(b), friction is considered.

here is what i have done. i fixed the coordinate system so that the force of the push applied to the inclined plane is in the x-direction.

(a): Fnetx = Fnx (normal force in x direction) + Fp (force of push) = 0

Fnety = Fny + Fg = 0

solving for Fp, i get Fp = Fn(cos(theta)). this seems reasonable, but too easy. have i left something out?

(b): considering friction, i have fixed the coordinate system as in part a.

Fnetx = Fp + Fnx -Ffx (force of friction in x direction) = 0

Fnety = Fg + Ffy +Fny = 0

solving for Fp, i get Fp = -Fn(sin(theta))*(1-μs) (μs = coefficient of static friction) however, there should be a minimum and a maximum force.. the minimum force is with maximum friction, and the maximum force is the force that force that is on the verge of accelerating the block in the negative x direction. or am i wrong? have i left something out? i am pretty sure i have.

any help is greatly appreciated. (i have attached a picture of the problem)

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# Homework Help: Accelerating an inclined plane

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