Acceleration of a sliding mass with a sliding mass on top of it?

[Blkmage]

Say we have a rectangular object A accelerating with some acceleration a across a rough horizontal surface. Object B starts with velocity v on the top left corner and slides across the top of A subject to a friction force.

Now if we consider object A by itself, it is subject to a friction force between itself and the surface opposing the direction of motion (call it f1), and a friction force between itself and object B in the direction of motion (call it f2), correct?

So since we are considering object A by itself, is the force equation in the horizontal direction

Fx = f2 - f1 = (mass of A only)*a

or

Fx = f2 - f1 = (mass of A+B)*a

My intuition tells me it should be the second one since the object B is exerting a downward force on A, which contributes to the weight and therefore the mass. Is this right?

 

[eczeno]

hello,

when applying Fnet = ma to object A, you must use only the mass of object A. the increase in the friction force (and the introduction of a second friction force) accounts for the presence of object B.

hope this helps