# Sliding (motion)

Sliding is a type of frictional motion between two surfaces in contact. This can be contrasted to rolling motion. Both types of motion may occur in bearings.

The relative motion or tendency toward such motion between two surfaces is resisted by friction. Friction may damage or 'wear' the surfaces in contact. However, wear can be reduced by lubrication. The science and technology of friction, lubrication, and wear is known as tribology

Sliding may occur between two objects of arbitrary shape, whereas rolling friction is the frictional force associated with the rotational movement of a somewhat disclike or other circular object along a surface. Generally the frictional force of rolling friction is less than that associated with sliding kinetic friction.[1] Typical values for the coefficient of rolling friction are less than that of sliding friction.[2] Correspondingly sliding friction typically produces greater sound and thermal bi-products. One of the most common examples of sliding friction is the movement of braking motor vehicle tires on a roadway, a process which generates considerable heat and sound, and is typically taken into account in assessing the magnitude of roadway noise pollution.[3]

## Sliding Friction

Static friction (also called kinetic friction) is a contact force that resists the sliding motion of two objects or an object and a surface. Sliding friction is almost always less than that of static friction; this is why it is easier to move an object once it starts moving rather than to get the object to begin moving from a rest position.

${\displaystyle F_{kF}=\mu _{k}\cdot N}$

Where Fk, is the force of kinetic friction. μk is the coefficient of kinetic friction, and N is the normal force.

## Examples of Sliding Friction

Slippery when wet signs alert drivers that they need to slow down because the kinetic friction between the tires and a wet surface is much less than that of a dry surface.
• Sledding
• Pushing an object across a surface
• Rubbing one's hands together (The friction generated by rubbing's one hands is what generates heat.)
• A car sliding on ice
• Opening and closing a sliding door
• A car turning a corner
• Rope and a pulley system
• Almost any motion where there is contact between an object an a surface

## Motion of Sliding Friction

The motion of sliding friction can be modeled (in simple systems of motion) by Newton's Second Law

${\displaystyle \sum F=ma}$

${\displaystyle F_{E}-F_{k}=ma}$

Where ${\displaystyle F_{E}}$ is the external force.

• Acceleration occurs when the external force is greater than the force of kinetic friction
• Slowing Down (or Stopping) occurs when the force of kinetic friction is greater than that of the external force
• This is also follows Newton's first law of motion as there exists a net force on the object
• Constant Velocity occurs when there is no net force on the object, that is the external force is equal to force of kinetic friction.

### Motion on an Incline Plane

Free body diagram for a block subject to friction as it slides on an incline plane

One of the most common physics problems in introductory physics classes is a block subject to friction as it slides up or down an incline plane.

In this case the force of gravity is accounted for and is given by:[4]

${\displaystyle F_{g}=mg\sin {\theta }}$

The force of friction opposes the motion of the block and the normal force (perpendicular to the surface is given by:

${\displaystyle N=mg\cos {\theta }}$

Therefore:

${\displaystyle F_{k}=\mu _{k}\cdot mg\cos {\theta }}$

To find the coefficient of kinetic friction on an incline plane, one must find the moment where the force parallel to the plane is equal to the force perpendicular; this occurs when the block is moving at a constant velocity at some angle ${\displaystyle \theta }$

${\displaystyle \sum F=ma=0}$

${\displaystyle F_{k}=F_{g}}$ or ${\displaystyle mg\cos {\theta }=\mu _{k}mg\sin {\theta }}$

Here it is found that:

${\displaystyle \mu _{k}={\frac {mg\sin {\theta }}{mg\cos {\theta }}}=\tan {\theta }}$ where ${\displaystyle \theta }$ is the angle at which the block begins moving at a constant velocity[5]

## References

1. ^ Benjamin Silliman, Principles of Physics, Or Natural Philosophy, Ivison, Blakeman, Taylor & company publishers, 710 pages {1871)
2. ^ Hans-Jürgen Butt, Karlheinz Graf, Michael Kappl, Physics and Chemistry of Interfaces, Wiley Publishers, 373 pages, ISBN 3-527-40413-9 (2006)
3. ^ [1] C. Michael Hogan, Analysis of Highway Noise, Journal of Soil, Air and Water Pollution, Springer Verlag Publishers, Netherlands, Volume 2, Number 3 / September, 1973
4. ^ "New Page 1". www.pstcc.edu. Retrieved 2017-04-10.
5. ^ "Friction". hyperphysics.phy-astr.gsu.edu. Retrieved 2017-04-10.