A man stands in a lift that is accelerating vertically downwards, as shown. Which statement describes the force exerted by the man on the floor?

Question 6

A man stands in a lift that is accelerating vertically downwards, as shown.

Which statement describes the force exerted by the man on the floor?

A It is equal to the weight of the man.

B It is greater than the force exerted by the floor on the man.

C It is less than the force exerted by the floor on the man.

D It is less than the weight of the man.

Reference: Past Exam Paper – November 2017 Paper 13 Q8

Solution:

Answer: D.

The force of gravity acts on both the man and the lift.

Since the man is standing in the lift, there is a contact (upward) force by the lift on the man.

So, there are 2 forces on the man: his weight (downward) and the contact force (upward).

Since the lift (and the man) is accelerating downwards, the resultant force on the man is downwards. This resultant force is the force exerted by the man on the floor.

Resultant force = Weight – Contact force

So, the resultant force is less than the weight.

Choice A: The resultant force is equal to the weight when there is no contact force. This can occur when the man is not touching the floor.

Choice B and C: From Newton’s third law, these 2 forces are equal and opposite. If choice C was correct, the man would lose contact with the floor.