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6.2 Friction  (Page 2/12)

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The figure shows a crate on a flat surface. A black arrow points toward the right, away from the crate, and 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 and is labeled as f. A magnified view of a bottom corner of the crate and the supporting surface shows that the roughness in the two surfaces leads to small gaps between them. There is direct contact only at a few points.
Frictional forces, such as 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. For the object to move, it must rise to where the peaks of the top surface 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. (In fact, perfectly smooth, clean surfaces of similar materials would adhere, forming a bond called a “cold weld.”)

The magnitude of the frictional force has two forms: one for static situations (static friction), the other for situations involving motion (kinetic friction). What follows is an approximate empirical (experimentally determined) model only. These equations for static and kinetic friction are not vector equations.

Magnitude of static friction

The magnitude of static friction f s is

f s ≤ μ s N ,

where μ s is the coefficient of static friction and N is the magnitude of the normal force.

The symbol ≤ means less than or equal to , implying that static friction can have a maximum value of μ 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), the object moves. Thus,

f s ( max ) = μ s N .

Magnitude of kinetic friction

The magnitude of kinetic friction f k is given by

f k = μ k N ,

where μ k is the coefficient of kinetic friction .

A system in which f k = μ k N is described as a system in which friction behaves simply . The transition from static friction to kinetic friction is illustrated in [link] .

(a) The figure shows a block on a horizontal surface. The situation is that of impending motion. The following forces are shown: N vertically up, w vertically down, F to the right, f sub s to the left. Vectors N and w are the same size. Vectors F and f sub s are the same size. (b) The figure shows a block on a horizontal surface. The motion is to the right. The situation is that of friction behaving simply. The following forces are shown: N vertically up, w vertically down, F to the right, f sub k to the left. Vectors N and w are the same size. Vectors F is larger than f sub s. (c) A graph of the magnitude of the friction force f as a function of the applied force F is shown. In the interval from 0 to when the magnitude of f equals f sub s max, the graph is a straight line described by f sub s equals F. This is the static region, and f sub s max equals mu sub s times N. For values of F larger than this maximum value of f, the graph drops a bit then flattens out to a somewhat noisy but constant on average value. This is the kinetic region in which the magnitude of f is f sub k which is also equal to mu sub k times N.
(a) The force of friction f → between the block and the rough surface opposes the direction of the applied force F → . The magnitude of the static friction balances that of the applied force. This is shown in the left side of the graph in (c). (b) At some point, the magnitude of the applied force is greater than the force of kinetic friction, and the block moves to the right. This is shown in the right side of the graph. (c) The graph of the frictional force versus the applied force; note that f s ( max ) > f k . This means that μ s > μ k .

As you can see in [link] , the coefficients of kinetic friction are less than their static counterparts. The approximate values of μ are stated to only one or two digits to indicate the approximate description of friction given by the preceding two equations.

Approximate coefficients of static and kinetic friction
System Static Friction μ s Kinetic Friction μ k
Rubber on dry concrete 1.0 0.7
Rubber on wet concrete 0.5-0.7 0.3-0.5
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
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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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