# Normal Force Changes: Explained

• Tokspor
In the elevator, you are pushed up by the floor, which is supported by the normal force. The floor pushes you with a force equal to the normal force, but in the opposite direction. So you end up being more "pinned" to the floor (or feeling heavier). It's the same idea as if you were standing on a bathroom scale, except the scale would show you your "apparent weight."

#### Tokspor

Hi guys, I am confused about how the normal force exerted on an object changes depending on the situation.

Let's say an object weighs 10 N at rest. The normal force here is 10 N as well since that is by how much the object is pushing down on the surface.

When someone tries to pull it upward with a 6 N force, it "relieves" some of the normal force. Since the object is now only pushing down on the surface with 4 N, the normal force is 4 N.

So the proper set-up for an equation here is F(normal) = F(gravity) - F(upward)

But in an elevator, let's say the elevator is accelerating upward at 2 m/s^2. If a person were inside the elevator, why doesn't this "relieve" some of their normal force as well? Instead, I have been told that the proper equation for this situation is F(upward) = F(normal) - F(gravity). Rearranging that equation, F(normal) = F(upward) + F(gravity). So now the normal force is actually much greater as a result of an upward force.

Why is this so?

action- reaction , if the elevator is accelerating upward this adds to the force , like you would feel heavier going up. And in relativity there is no difference between being accelerated by a rocket or being in a gravitational field .

Welcome to PF!

Hi Tokspor! Welcome to PF! (try using the X2 tag just above the Reply box )
Tokspor said:
… So the proper set-up for an equation here is F(normal) = F(gravity) - F(upward)

But in an elevator, let's say the elevator is accelerating upward at 2 m/s^2. If a person were inside the elevator, why doesn't this "relieve" some of their normal force as well? Instead, I have been told that the proper equation for this situation is F(upward) = F(normal) - F(gravity). Rearranging that equation, F(normal) = F(upward) + F(gravity). So now the normal force is actually much greater as a result of an upward force.

Why is this so?

Because you're using "F(upward)" to mean two different things

in the first case, it's a separate (third) applied force, but in the second case it's the total of the (two) forces. Let's apply good ol' Newton's second law …

in the first case, a = 0, and so all the forces must add to 0 …

F(normal) + F(gravity) + F(applied) = 0,

ie F(normal) = mg - F(applied),​

('cos gravity is downward )

but in the second case, a = 2,

F(normal) + F(gravity) = 2,

ie F(normal) = mg + 2,​

… see? no applied force! Tokspor said:
So the proper set-up for an equation here is F(normal) = F(gravity) - F(upward)

But in an elevator, let's say the elevator is accelerating upward at 2 m/s^2. If a person were inside the elevator, why doesn't this "relieve" some of their normal force as well? Instead, I have been told that the proper equation for this situation is F(upward) = F(normal) - F(gravity). Rearranging that equation, F(normal) = F(upward) + F(gravity). So now the normal force is actually much greater as a result of an upward force.
The proper set-up in both cases is to use Newton's 2nd law:

ΣF = ma

F(normal) - F(gravity) = ma

When the acceleration is zero, the normal force equals your weight. If the elevator is accelerating upward (thus a > 0), the normal force is greater than your weight--you feel heavier. (The normal force must not only support your weight but accelerate you.)

Edit: While I was goofing off, tiny-tim beat me to it! But in an elevator, let's say the elevator is accelerating upward at 2 m/s^2. If a person were inside the elevator, why doesn't this "relieve" some of their normal force as well?

This is because in this elevator scenario, the normal force is the source of this "upward force" too. If suppose a huge guy infront holds you by your neck and lifts you, the "upward force" is provided by *his* hands. In that case, the normal force gets some help and is relieved as you hoped. (Also hope he releases you soon.)

## 1. What is normal force?

Normal force is the force that a surface exerts on an object that is in contact with it. It is always perpendicular to the surface and acts to prevent the object from falling through the surface.

## 2. How does normal force change?

Normal force can change in response to external forces acting on an object. For example, if an object is placed on an inclined plane, the normal force will decrease as the angle of the incline increases.

## 3. What factors affect normal force?

The magnitude of normal force is affected by the weight of the object, the angle of the surface, and the coefficient of friction between the object and the surface. It also depends on the strength of the surface itself.

## 4. Can normal force be greater than weight?

Yes, it is possible for normal force to be greater than weight. This can happen when an object is accelerating upwards, such as in an elevator, or when an object is on an incline and the angle of the surface is less than the angle of repose.

## 5. Why is understanding normal force important?

Understanding normal force is important in many areas of science and engineering, such as mechanics and structural analysis. It helps us predict how objects will behave in different situations and design structures that can withstand external forces without collapsing.