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Object with mass ##m## is sliding down a sloped (incline = ##\alpha##) object of mass ##M##. The coefficient of kinetic friction acting between ##m## and ##M## is ##\mu##. There isno frictionbetween object ##M## and the ground.

In the drawing above, the red vectors above are the forces acting on the big object ##M##. I realize I should have drawn the vectors extending out from object ##M##, but I did it this way to make the angles clearer. So what I have is that there are two forces acting on the sloped object ##M## in thehorizontaldirection:

1) ##\mu F_g cos^2\alpha## to the left - the horizontal component of the opposite friction force exerted by ##m## onto ##M##

2 ##F_gcos\alpha sin\alpha## to the right - due to the weight of mass ##m##.

Two questions:

2) Do the above two forces correctly (and comprehensively) describe the forces acting on object ##M## in the horizontal direction?

2) Does this mean that it is possible, given a small enough angle ##\alpha##, for the inclined object ##M## to accelerateto the left(ie. assuming ##\mu F_g cos^2\alpha > F_gcos\alpha sin\alpha##)?

Thank you

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# B Direction of acceleration of an incline

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