# Normal Force in Elevator

I've recently been studying Newton's laws of motion and came across this example of apparent weight in an accelerating elevator. Taking the upwards direction as positive, when the elevator is accelerating upwards with acceleration $$a$$ , the total acceleration of the person must be $$a-g$$.

I have two doubts.

1. Here as the total acceleration of the person will become smaller, shouldn't the normal force acting on the person become smaller as well?

2. If the normal force is the force caused due to the Pauli Exclusion Principle, how and why does it increase?

The acceleration here is caused due to the elevator moving upwards. How does it have any connection to the normal force present between the person and the weight machine

Sorry if this sounds very silly, or in the worst case wrong. • No, not a-g. Opposite directions yes, but also opposite sides of the equation in free-body diagrams. In $\sum F=ma$ the a is the actual acceleration of the body as a result of the net force. The g in the mg is a force exerted by gravity and so appears on the $\sum F$ side of the equation physics.stackexchange.com/questions/632735/… Jul 14 at 3:25
• Okay, but the thing I am most doubtful about is why should the Normal force (N), the force caused due to the Pauli Exclusion Principle, increase to cause the said acceleration to the body..... Shouldn't it always be the same value ( mg in opposite direction ) ? Jul 14 at 3:31
• To accelerate, there must be net external force and that is provided by the normal reaction. If $N=mg$, the man will remain still or move with constant velocity. To have an upward acceleration $N$ should be greater than $mg$.
– ACB
Jul 14 at 3:36

Taking the upwards direction as positive, when the elevator is accelerating upwards with acceleration a , the total acceleration of the person must be a−g

When the elevator accelerates upward, the net force will be $$ma = N - mg$$ where $$N$$ is the normal force. This means that $$N = ma + mg$$

Here as the total acceleration of the person will become smaller, shouldn't the normal force acting on the person become smaller as well?

No. Inside the elevator, the downward force due to your weight and the inertial force, which acts downward due to the upward acceleration of the elevator, point in the same direction.

In other words, inside the elevator $$F=mg+ma=\text{normal force}$$ where $$a$$ is the upward acceleration of the elevator, and $$F$$ will also be equal to the normal force exerted by the ground on you.

If the normal force is the force caused due to the Pauli Exclusion Principle, how and why does it increase?

The degeneracy pressure is due to the normal force, and so if an additional acceleration is added in the direction to the original normal force, as explained above, then your new apparent weight must be greater. Your weight is always opposite to the normal force. If the elevator were to accelerate downwards, your apparent weight would decrease.