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What is the Coefficient of Kinetic Friction?

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  • Written By: James Doehring
  • Edited By: Lauren Fritsky
  • Last Modified Date: 06 December 2016
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The coefficient of kinetic friction is a unitless variable based on material properties used to calculate the force of sliding friction. It is applicable to the classical mechanics of rigid objects. Multiplying the coefficient of kinetic friction by the normal force on an object will give the force of kinetic friction. Kinetic friction, therefore, depends only on material properties and the normal force on an object.

It is important to note that the coefficient of kinetic friction is a concept of classical mechanics and part of a theory produced from experimental observations. Classical mechanics was largely developed by British physicist Isaac Newton and his contemporaries in the 17th century. The subject deals with the interaction of large objects moving at relatively low speeds. In particular, the classical mechanics of rigid solids applies to this coefficient. This sub-discipline of classical mechanics can describe the friction resulting from two solids sliding against each other, and it ignores forces produced by any fluids.

Within this domain, the coefficient of kinetic friction can provide very accurate predictions. If fluids are to be considered, the field of fluid mechanics must be introduced. If the scales involved are extremely small, quantum mechanics can address the associated complications.

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The force produced by kinetic friction is equal to the product of two variables. The first is the coefficient of kinetic friction, and the second is the normal force. A normal force is the force provided by an object’s surface to keep another object from moving through it. In the case of gravity, it is the vertical force from the ground that keeps objects from falling further down. The force is always equal to the gravitational weight of an object in contact with the ground; therefore, an object can remain at rest because the gravitational force is exactly canceled by the normal force.

The formula for kinetic friction does not include an object’s velocity or size. This means that the force of friction on a sliding object is independent of how fast it’s moving. The frictional force on a box will be the same whether it’s sliding at one mile or kilometer per hour or two. Similarly, the force does not depend on an object’s area in contact with the ground. It will be the same whether a box is flat and wide or tall and thin.

The coefficient of kinetic friction itself is an empirical property of the materials involved. This means that it is only a matter of which materials make up the two contacting surfaces. Furthermore, such coefficients are derived from experiment rather than theory. The coefficient of kinetic friction is typically denoted by the Greek letter mu with subscript k.

Given identical materials, the force from kinetic friction only depends on the normal force applied to an object. In the case of gravity on Earth’s surface, the force will only depend on an object’s mass. Heavier objects have proportionally more sliding friction than lighter objects.

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