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# Normal Force in Sliding Friction

by Ron Kurtus (revised 17 November 2016)

The * normal force in sliding friction* is the perpendicular force pushing the object to the surface on which it is sliding. It is an essential part of the standard sliding friction equation.

That force can be due to the weight of an object or that caused by an external push.

When the weight is on an incline, the normal force is reduced by the cosine of the incline angle.

Questions you may have include:

- What is the standard friction equation?
- When it weight the normal force?
- What are examples of external normal force?

This lesson will answer those questions. Useful tool: Units Conversion

## Standard sliding friction equation

The normal force is seen in the standard sliding friction equation:

F_{s}= μ_{s}N

or

N = F_{s}/μ_{s}

where:

**N**is the normal or perpendicular force pushing the two objects together**F**is the sliding force of friction_{s}**μ**is the sliding coefficient of friction for the two surfaces (Greek letter "mu")_{s}

(

See Standard Friction Equation for details.)

### Static and kinetic coefficients

The sliding coefficient of friction can be static when the object is stationary or kinetic when the object is sliding over the other surface.

The coefficient of sliding friction in the static mode of motion (**μ _{ss}**) is greater that the coefficient in the kinetic or moving mode (

**μ**).

_{ks}

μ_{ss}> μ_{ks}_{}

(See Coefficient of Sliding Friction for more information.)

## Weight as normal force

The normal force **N** can be the weight of an object as caused by gravity. This would apply in situations where you slide a heavy object across the floor or some horizontal surface.

Since weight is the force pushing the objects together, the friction equation becomes:

F_{s}= μ_{s}W

where **W** is the weight of the object.

For example:

Thus if a box weighs 100 pounds and the coefficient of friction between it and the ground is 0.7, then the force required to push the box along the floor is 70 pounds.

Likewise if a box weighs 500 newtons is placed on ice with a coefficient of friction of only 0.001, then it would only take 0.5 newtons to move the box.

### Weight on incline

If the weight is on an incline, the normal force will be reduced by the cosine of the incline angle. The equation is

N = W*cos(β)

where:

**N**is the normal force on the incline**W**is the weight**β**is the incline angle (Greek letter beta)**cos(β)**is the cosine of the angle**β****W*cos(β)**is**W**times**cos(β)**

Thus, the friction equation is:

F_{s}= μW*cos(β)

An illustration of the friction on a box on an incline is:

Normal force is weight times cosine of angle

(

See Sliding Friction on an Inclined Surface for more information)

## External normal force

Examples of external normal forces include pushing a sanding block on an object and a pair of pliers.

### Pushing object sideways

If you push a sanding block against a wooden desk you were sanding, the normal force would be the amount of force you pushed on the block. You would move the sanding block in one direction and the force of friction would be in the opposite direction.

Applying normal force on sanding block and wooden desk

### Two normal forces

Sometimes, two normal forces are used to cause the friction.

One example is a pair of pliers that applies a normal force on both sides of a piece of wood that the pair of pliers is holding. Another example are the calipers on automobile disc brakes that apply a force on both sides of the metal disc to slow down the car.

## Summary

The normal force in the standard friction equation is the force pushing the two objects together, perpendicular to their surfaces. That force can be due to the weight of an object or that caused by an external push. When the weight is on an incline, the normal force is reduced by the cosine of the incline angle.

It all makes sense

## Resources and references

### Websites

**Friction Resources** - Extensive list

**Friction Concepts** - HyperPhysics

### Books

**Top-rated books on Friction Science**

**Top-rated books on Friction Experiments**

**Friction Science and Technology** (Mechanical Engineering Series) by Peter J. Blau; Marcel Dekker Pub. (1995) $89.95

**Control of Machines with Friction** (The International Series in Engineering and Computer Science) by Brian Armstrong-Hélouvry; Springer Pub. (1991) $179.00

## Questions and comments

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## Normal Force in Sliding Friction