# Action reaction forces in an accelerating elevator [duplicate]

If an elevator with one man in it, is accelerating as it moves upwards, the reaction force the floor exerts on the man will be more than the weight of the man. Why is that though? Shouldn't the weight and the reaction force be the same, as action reaction forces are always equal?

• Weight and reaction force cancel out
– Kosm
Nov 21 '18 at 11:52

The Weight of the man and the normal reaction of the floor are not action reaction pairs!
The action reaction pairs will be:

1. The force with which earth pulls on the man, and the force with which the man pulls the earth. This is the gravitational force (which you call weight). This pair exists even if you aren't in contact with the ground.

2. The floor pushing up on you, and you pushing down on the floor. This is the reaction force. This pair won't exist if you break contact with ground.

You can read this What identifies an action-reaction pair of forces?.

When the elevator goes upwards, from the Newton's Third Law, the person will feel the same acceleration in the opposite direction.

Now, in this case, the acceleration in the upwards direction so the person will feel an acceleration in a downward direction. And also there's gravity. Hence, the total acceleration will be $$g+a$$ in a downward direction.

Again from Newton's third law the floor applies the same force to the man in the opposite direction.

Here, critical point is to see that the third law between the man and the elevator.

Let's think the same case for the elevator that accelerates downwards. In this case, the man will an acceleration in an upward direction so the net acceleration will be $$g-a$$.

Assume that the lift is moving up with an acceleration a

Frame of reference: on the ground

Upward force:

• Normal reaction(N)

Downward force:

• Gravity(mg)

Net movement: Upwards

so,

N-mg=ma

Conclusion:

N=mg+ma

So whatever acceleration you are moving up with,when multiplied with mass and added to the actual weight of the body will give you the reaction force!

Extra point:

If you were measuring your weight: it would be greater than what your actual weight is