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}{composition-setup} {table:border=1|frame=void|rules=cols|cellspacing=0|cellpadding=8} {tr:valign=top} {td:width=290|bgcolor=#F2F2F2} {live-template:Left Column} {td} {td} h1. Kinetic Friction {excerpt}Whenever sliding motion is occuring, friction will apply a force that is directly opposed to the sliding motion. This force will have essentially constant size independent of the speed of the object for a given object sliding on a given surface. The size of the [kinetic friction] force _will_ depend, however, on the contact force existing between the object and the surface and also on the material characteristics of the surface and the object.{excerpt} h3. Kinetic Friction as a Force h4. Magnitude For an object that is already sliding along a surface or is accelerating from rest on a surface, the size of the friction force will be given by: {latex}
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Excerpt

The specific manifestation of friction that is directly opposed to an object's sliding motion along a surface. The force of kinetic friction has a size independent of the speed of the object, and proportional to the normal force exerted on the object by the surface.

Kinetic Friction as a Force

Magnitude

For an object that is already sliding along a surface or is accelerating from rest on a surface, the size of the friction force will be proportional to the normal force exerted by the surface on the object. This mathematical relationship is usually stated:

Latex
\begin{large}\[ F_{k} = \mu_{k} N\]\end{large}
{latex} {note}Note that the size of the kinetic friction is fixed by the normal force and the coefficient. In contrast to the case of [static friction], there is no upper limit in the expression. Thus, it is not necessary to consider the complete net force to find the friction force for the kinetic case.{note} where &mu;~k~ is the *coefficient of kinetic friction*. The coefficient of kinetic friction is a dimensionless number, usually less than 1.0 (but _not_ required to be less than 1.0). Rough or sticky surfaces will yield larger coefficients of friction than smooth surfaces. _N_ is the [normal force] exerted on the object _by the surface which is creating the friction_, which is a measure of the strength of the contact between the object and the surface. The coefficient of kinetic friction for a given object on a given surface will usually be *different* than the corresponding coefficient of static friction. It is usually the case that &mu;~k~ < &mu;~s~. {info}The fact that &mu;~k~ is generally less than &mu;~s~ has important consequences for cars. Antilock brakes are specifically designed to prevent skids, which change the tire-road friction from static to kinetic. Changing braking friction to kinetic by skidding reduces the force of friction and so the effectiveness of the braking.{info} h4. Direction There are two possibilities to consider when determining the direction of kinetic friction: # For a sliding object, the direction of the kinetic friction must be opposite to the direction of the velocity. # For an object just beginning to slide (the object still has zero velocity) then the friction must oppose the acceleration. h3. Kinetic Friction as Non-Conservative Work When an object is sliding on a surface that can be considered to be at rest in an [inertial frame of reference], kinetic friction is the prototypical [non-conservative force]. When the motion of an object sliding on a surface is viewed from a frame at rest with respect to the surface, the force of friction always opposes the object's motion, and so always does negative [work]. For the case of a constant friction force, the definition of [work] can be integrated to give: {panel:title=Work done by a Constant Friction Force}{latex}\begin{large}\[W_{f} = -F_{k}d\]\end{large}{latex}{panel} where _d_ is the *distance* traveled by the object along the surface. {info}Contrast this with a conservative force like [gravity (near-earth)], which does negative [work] on an object that is rising, and then returns energy by doing positive [work] on the object as it falls.{info} {warning}The [work] done by [friction] becomes very confusing when a reference frame is chosen in which the surface is _moving_. See the discussion of [static friction] for more details.{warning} h3. {toggle-cloak:id=examples}Example Problems involving Kinetic Friction {cloak:id=examples} {contentbylabel:kinetic_friction,example_problem|operator=AND|maxResults=50|showSpace=false|excerpt=true} {cloak:examples} {td} {tr} {table} {live-template:RELATE license}

where μk is a constant of proportionalty called the coefficient of kinetic friction. The coefficient of kinetic friction is a dimensionless number, usually less than 1.0 (but not required to be less than 1.0). Rough or sticky surfaces will yield larger coefficients of friction than smooth surfaces. N is the normal force exerted on the object by the surface which is creating the friction.

The coefficient of kinetic friction for a given object on a given surface will usually be different than the corresponding coefficient of static friction. It is usually the case that μk < μs.

Direction

Kinetic friction is always directed opposite to the direction of the velocity.

Kinetic Friction as Non-Conservative Work

When the Surface is at Rest

When an object is sliding on a surface that can be considered to be at rest in an inertial frame of reference, kinetic friction is the prototypical non-conservative force. When the motion of an object sliding on a surface is viewed from a frame at rest with respect to the surface, the force of friction always opposes the object's motion, and so always does negative work. For the special case of a friction force with constant magnitude , the definition of work can be integrated to give Wf = – Fkd where d is the distance traveled by the object along the surface.

When the Surface is Moving

Finding the work done by friction can be confusing when a reference frame is chosen in which the surface is moving. See the discussion of static friction for more details.

Example Problems involving Kinetic Friction

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Examples from Dynamics involving Kinetic Friction

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Examples from Energy and Work involving Kinetic Friction

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Examples from Rotation and Torque inolving Kinetic Friction

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All Example Problems inolving Kinetic Friction

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