# Normal force

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Normal force is a force that manifests the tendency of two surfaces not to move into each other. In other words, it is a force that opposes the inward motion of two surfaces in contact. It acts in the normal direction (the direction perpendicular to the plane of contact) and always acts outward.

## Important points about normal force

• Direction: Normal force always acts in a direction normal to the plane of contact, and it acts outward.
• Magnitude: The magnitude of normal force is precisely enough to be equal and opposite to the external applied force that is creating a tendency for the bodies to move into each other. For instance, for a block on a table, the block experiences a normal force in the upward direction, to counter the gravitational force it experiences in the downward direction.
• For two bodies ${\displaystyle A}$ and ${\displaystyle B}$ whose surfaces are in contact, the normal force exerted by ${\displaystyle B}$ on ${\displaystyle A}$ at the contact surface, and the normal force exerted by ${\displaystyle A}$ on ${\displaystyle B}$ at the contact surface are equal in magnitude and opposite in direction. For instance, for a block sitting on a table, the normal force on the block is upward, while the normal force on the table is downward. This is the principle of action and reaction.
• The way normal force acts between two surfaces is independent of whether the surfaces are slipping against each other

## Significance of normal force

### Weighing machines measure normal force

When an object is placed on a weighing machine, the machine does not directly measure the object's mass, or the gravitational force acting on it. Rather, the gravitational force creates a tendency for the object to move downwards. To balance this, the machine exerts an upward normal force on the object. By the principle of action and reaction, the object exerts a downward force on the weighing machine, and it is this force that is measured by the weighing machine.

Weighing machines placed in elevators measure different weights. If the elevator is accelerating upwards, the measured weight is greater than the actual weight, while if the machine is accelerating downward, the measured weight is less than the actual weight. An extreme case of this is free fall, where an object is falling freely, and its weight is measured as zero.

### Relation between normal force and friction

The harder two surfaces are pressed against each other, the greater the possibility of friction between them:

• The static friction between two bodies is limited from above by the normal force between them, multiplied by a constant ${\displaystyle \mu _{s}}$ called the coefficient of limiting static friction. This coefficient depends on the nature of the surfaces in contact.
• The kinetic friction between two bodies in contact, that are slipping against each other, is the normal force between them, multiplied by a constant ${\displaystyle \mu _{k}}$ called the coefficient of kinetic friction. Like the coefficient of limiting static friction, this coefficient depends on the nature of the surfaces in contact.
• In introductory physics courses, the normal and friction forces are typically treated as two distinct and separate forces. Alternatively, they can be viewed simply as two components of a single contact force that is exerted between two objects, namely the components perpendicular to (normal force) and parallel to (friction force) the contact surface.