A box weighing 69 N rests on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end.

Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs one of the following:
a)29N
b)56N
c)96N

1 answer

If the table is smooth, it should be N=69N normal to the table in all cases.
If the table is rough, with a coefficient of kinetic or static friction of μ, then it falls into two cases:
There is no motion, T<μN, T=tension in rope.
Then the force exerted on the box by the table is the normal reaction + static friction, equal to T.
If there is motion, the forces would be the normal reaction N, added (vectorially) to the kinetic friction force μN.