Question

# A box weighing 70 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 a) 30 N b) 60 N and c) 90 N

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A box weighing 70 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 a) 30 N b) 60 N and c) 90 N

2021-03-28
According to the Newton’s third law of motion, the force exerted by the table on the box
is equal to the net force exerted by the box on the table in the opposite direction.
(a)
The force exerted by the table on the box is equal to,
$$\displaystyle{F}_{{{a}}}={W}_{{{1}}}-{W}_{{{2}}}$$
=70N-30N
=40N
(b)
The force exerted by the table on the box is equal to,
$$\displaystyle{F}_{{{b}}}={W}_{{{1}}}-{W}_{{{2}}}$$
=70N-60N
=10N
(c)
The weight of the hanging mass, that is, $$\displaystyle{W}_{{{2}}}$$ is greater than the weight of the box, that is, $$\displaystyle{W}_{{{1}}}$$. Therefore, the box rises and the box loses the contact with the table.
Hence, the force exerted by the table on the box is equal ti zero, that is,
$$\displaystyle{F}_{{{c}}}={0.00}{N}$$