### Video Transcript

A box with a weight of 15 newtons is placed on a table. What force does the table exert on the box?

In this question, we are asked to think about the force exerted on a box by a
table. We know that the weight of the box is 15 newtons. Recall that weight is a force that acts vertically downwards. So, we know that the box exerts a force of 15 newtons, vertically downwards, on the
table. We’ll show this on our diagram by drawing an arrow labeled 𝐹 sub B for box. This is the force exerted on the table by the box. The table also exerts a force on the box, called a normal reaction force. We’ll draw this on our diagram and label it with an 𝑁.

To work out the reaction force, the force exerted on the box by the table, we need to
remember Newton’s third Law. Newton’s third law tells us that for a pair of interacting objects, the force exerted
by the first object on the second is equal in magnitude and opposite in direction to
the force exerted by the second object on the first. In other words, the force exerted on the box by the table is equal in magnitude but
opposite in direction to the force exerted on the table by the box.

We know that the weight of the box has a magnitude of 15 newtons. This force is equal and opposite to the force of the table on the box. So, the force exerted on the box by the table must also have a magnitude of 15
newtons. We also know that the box’s weight acts vertically downwards. So, the force exerted on the box by the table must act in the opposite direction to
this; it must act vertically upwards.

We have to be careful when expressing forces that act in different directions. In this question, we’re told that the weight of the box, which acts downwards,
corresponds to a positive value of force: plus 15 newtons. This tells us that we’re working in a coordinate system in which downward forces are
positive. This means that upward forces, like the force exerted on the box by the table, must
be negative.

So, we have worked out that the normal reaction force from the table has a magnitude
of 15 newtons and is negative. So, this gives us our final answer. The table exerts a force of negative 15 newtons on the box.