Free body diagram for a non-fixed (movable) ramp, with a box at rest on top of it

Question

I'm having trouble figuring out how this free body diagram would look. The question involves a block at rest on a ramp, which is in turn at rest on a table. All objects are made of the same material, with the same coefficients of friction. Below is what I've got so far, but it doesn't seem correct.

I fail to intuitively get how the friction on the ramp due to the box would affect its movement. Additionally, I'm also not sure if it's correct to introduce the friction due to the table; after all, if I draw yet another free body diagram of the system including both box and ramp, then the friction due to the table still exists - what cancels this force out?

Answer 1

No, there is no friction between table and ramp. Even on a smooth frictionless table, the system of block-stuck-on-ramp wouldn't be moving. If they are stuck to each other due to high friction between them, then when considering the system as a whole, they can be considered as one single object lying on the table. Why would an object lying on the table try to slide sideways, so that the table must apply a friction?

Answer 2

What you are not considering is accelerations. I feel you should follow a 5-step process which will never leave any confusion about motions of objects.

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 1.Mark all forces.
 2.Mark all accelerations.
 3.Choose a suitable pair of axes.
 4.Calculate the components of forces and accelerations along these axes.
 5.Apply F=Ma along each axes.

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Now, back to question. Suppose if the friction is high enough such that there is no motion between the block and ramp, then the horizontal components of the friction due to block on ramp and the normal reaction on the ramp due to block cancels out and no horizontal force is present. There will be no friction between table and ramp. Refer to answer by Steven. Now if there are accelerations, consider the given Force Diagram. Choose the axes as X-Y pair. If the coefficient of friction is same for all pair of surfaces, then replace uN appropriately everywhere.

If you are skeptical why there is no friction acting on table when no motion is present between the block and ramp, suppose the friction acts. Now calculate that friction substituting acc=0 everywhere.