More Examples on Newton's Third Law

Tammy travels from the ground floor to the fifth floor of a hotel in a lift moving at constant velocity. Which ONE of the following statements is TRUE about the magnitude of the force exerted by the floor of the lift on Tammy's feet? Use Newton's third law to justify your answer.

1. It is greater than the magnitude of Tammy's weight.

2. It is equal in magnitude to the force Tammy's feet exert on the floor of the lift.

3. It is equal to what it would be in a stationary lift.

4. It is greater than what it would be in a stationary lift.

Step 1: Analyse the situation

This is a Newton's third law question and not Newton's second law. We need to focus on the action-reaction pairs of forces and not the motion of the lift. The following diagram will show the action-reaction pairs that are present when a person is standing on a scale in a lift.

Newton's action-reaction pairs in a lift.

In this question statements are made about the force of the floor (lift) on Tammy's feet. This force corresponds to \({F}_{2}\) in our diagram. The reaction force that pairs up with this one is \({F}_{1}\), which is the force that Tammy's feet exerts on the floor of the lift. The magnitude of these two forces are the same, but they act in opposite directions.

Step 2: Choose the correct answer

It is important to analyse the question first, before looking at the answers. The answers might confuse you if you look at them first. Make sure that you understand the situation and know what is asked before you look at the options.

The correct answer is number \(\text{2}\).

Bridget presses a book against a vertical wall as shown in the photograph.

1. Draw a labelled force diagram indicating all the forces acting on the book.

2. State, in words, Newton's third law of Motion.

3. Name the action-reaction pairs of forces acting in the horizontal plane.

Step 1: Draw a force diagram

A force diagram will look like this:

Note that we had to draw all the forces acting on the book and not the action-reaction pairs. None of the forces drawn are action-reaction pairs, because they all act on the same object (the book). When you label forces, be as specific as possible, including the direction of the force and both objects involved, for example, do not say gravity (which is an incomplete answer) but rather say 'Downward (direction) gravitational force of the Earth (object) on the book (object)'.

Step 2: State Newton's third law

If body A exerts a force onto body B, then body B will exert a force equal in magnitude, but opposite in direction, onto body A.

Step 3: Name the action-reaction pairs

The question only asks for action-reaction forces in the horizontal plane. Therefore:

Pair 1: Action: Applied force of Bridget on the book; Reaction: The force of the book on the girl.

Pair 2: Action: Force of the book on the wall; Reaction: Force of the wall on the book.

Note that a Newton's third law pair will always involve the same combination of words, like 'book on wall' and 'wall on book'. The objects are 'swapped around' in naming the pairs.