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The figure shows a crate on a flat surface, and a magnified view of a bottom corner of the crate and the supporting surface. The magnified view shows that there is roughness in the two surfaces in contact with each other. A black arrow points toward the right, away from the crate, and it is labeled as the direction of motion or attempted motion. A red arrow pointing toward the left is located near the bottom left corner of the crate, at the interface between that corner and the supporting surface. The red arrow is labeled as f, representing friction between the two surfaces in contact with each other.
Frictional forces, such as f size 12{f} {} , always oppose motion or attempted motion between objects in contact. Friction arises in part because of the roughness of the surfaces in contact, as seen in the expanded view. In order for the object to move, it must rise to where the peaks can skip along the bottom surface. Thus a force is required just to set the object in motion. Some of the peaks will be broken off, also requiring a force to maintain motion. Much of the friction is actually due to attractive forces between molecules making up the two objects, so that even perfectly smooth surfaces are not friction-free. Such adhesive forces also depend on the substances the surfaces are made of, explaining, for example, why rubber-soled shoes slip less than those with leather soles.

The magnitude of the frictional force has two forms: one for static situations (static friction), the other for when there is motion (kinetic friction).

When there is no motion between the objects, the magnitude of static friction f s size 12{f rSub { size 8{s} } } {} is

f s μ s N , size 12{f rSub { size 8{s} }<= μ rSub { size 8{s} } N} {}

where μ s size 12{μ rSub { size 8{s} } } {} is the coefficient of static friction and N is the magnitude of the normal force (the force perpendicular to the surface).

Magnitude of static friction

Magnitude of static friction f s size 12{f rSub { size 8{s} } } {} is

f s μ s N , size 12{f rSub { size 8{s} }<= μ rSub { size 8{s} } N} {}

where μ s size 12{μ rSub { size 8{s} } } {} is the coefficient of static friction and N is the magnitude of the normal force.

The symbol size 12{<= {}} {} means less than or equal to , implying that static friction can have a minimum and a maximum value of μ s N size 12{μ rSub { size 8{s} } N} {} . Static friction is a responsive force that increases to be equal and opposite to whatever force is exerted, up to its maximum limit. Once the applied force exceeds f s ( max ) size 12{f rSub { size 8{s \( "max" \) } } } {} , the object will move. Thus

f s ( max ) = μ s N . size 12{f rSub { size 8{s \( "max" \) } } =μ rSub { size 8{s} } N} {}

Once an object is moving, the magnitude of kinetic friction f k size 12{f rSub { size 8{k} } } {} is given by

f k = μ k N , size 12{f rSub { size 8{k} } =μ rSub { size 8{k} } N} {}

where μ k size 12{μ rSub { size 8{K} } } {} is the coefficient of kinetic friction. A system in which f k = μ k N size 12{f rSub { size 8{k} } =μ rSub { size 8{k} } N} {} is described as a system in which friction behaves simply .

Magnitude of kinetic friction

The magnitude of kinetic friction f k size 12{f rSub { size 8{K} } } {} is given by

f k = μ k N , size 12{f rSub { size 8{k} } =μ rSub { size 8{k} } N} {}

where μ k size 12{μ rSub { size 8{K} } } {} is the coefficient of kinetic friction.

As seen in [link] , the coefficients of kinetic friction are less than their static counterparts. That values of μ size 12{μ} {} in [link] are stated to only one or, at most, two digits is an indication of the approximate description of friction given by the above two equations.

Coefficients of static and kinetic friction
System Static friction μ s size 12{μ rSub { size 8{s} } } {} Kinetic friction μ k size 12{μ rSub { size 8{K} } } {}
Rubber on dry concrete 1.0 0.7
Rubber on wet concrete 0.7 0.5
Wood on wood 0.5 0.3
Waxed wood on wet snow 0.14 0.1
Metal on wood 0.5 0.3
Steel on steel (dry) 0.6 0.3
Steel on steel (oiled) 0.05 0.03
Teflon on steel 0.04 0.04
Bone lubricated by synovial fluid 0.016 0.015
Shoes on wood 0.9 0.7
Shoes on ice 0.1 0.05
Ice on ice 0.1 0.03
Steel on ice 0.4 0.02

The equations given earlier include the dependence of friction on materials and the normal force. The direction of friction is always opposite that of motion, parallel to the surface between objects, and perpendicular to the normal force. For example, if the crate you try to push (with a force parallel to the floor) has a mass of 100 kg, then the normal force would be equal to its weight, W = mg = ( 100 kg ) ( 9 . 80 m/s 2 ) = 980 N size 12{W="mg"= \( "100""kg" \) \( 9 "." "80"`"m/s" rSup { size 8{2} } \) ="980"N} {} , perpendicular to the floor. If the coefficient of static friction is 0.45, you would have to exert a force parallel to the floor greater than f s ( max ) = μ s N = 0.45 ( 980 N ) = 440 N size 12{f rSub { size 8{S \( "max" \) } } =μ rSub { size 8{S} } N=0 "." "45" times "980"N="440"N} {} to move the crate. Once there is motion, friction is less and the coefficient of kinetic friction might be 0.30, so that a force of only 290 N ( f k = μ k N = 0 . 30 980 N = 290 N size 12{f rSub { size 8{k} } =μ rSub { size 8{k} } N= left (0 "." "30" right ) left ("980"" N" right )="290"" N"} {} ) would keep it moving at a constant speed. If the floor is lubricated, both coefficients are considerably less than they would be without lubrication. Coefficient of friction is a unit less quantity with a magnitude usually between 0 and 1.0. The coefficient of the friction depends on the two surfaces that are in contact.

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Source:  OpenStax, Concepts of physics. OpenStax CNX. Aug 25, 2015 Download for free at https://legacy.cnx.org/content/col11738/1.5
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