Fundamental Engineering Concepts - Mathematics and Statistics for the Environment - page 243

11.5.1 F riCtion
Earlier, in discussing the principle of the inclined plane, we ignored the effect of friction. In actual
use, friction cannot be ignored and you must have some understanding of its characteristics and
applications. Friction results when an object on the verge of sliding, rotating, rolling, or spinning,
or in the process of any of these, is in contact with another body. Friction allows us to walk, ski,
drive vehicles, and power machines, among other things. Whenever one object slides over another,
frictional forces opposing the motion are developed between them. Friction force is the force tan-
gent to the contact surface that resists motion. If motion occurs, the resistance is due to kinetic
friction, which is normally lower than the value for static friction. Contrary to common perception,
the degree of smoothness of a surface area is not responsible for these frictional forces; instead, the
molecular structure of the materials is responsible. The coefficient of friction ( M ) (which differs
among different materials) is the ratio of the frictional force ( F ) to the normal force ( N ) between
two bodies.

F
N

M = (11.5)

For dry surfaces, the coefficient of friction remains constant, even if the weight of an object (i.e.,
force N ) is changed. The force of friction ( F ) required to move the block changes proportionally.
Note that the coefficient of friction is independent of the area of contact, which means that pushing
a brick across the floor requires the same amount of force whether it is on end, on edge, or flat. The
coefficient of friction is useful in determining the force necessary to do a certain amount of work.
Temperature changes only slightly affect friction. Friction causes wear. To overcome this wear
problem, lubricants are used to reduce friction.

■ EXAMPLE 11.7
Problem: How much force is required to more a 300-lb box if the static coefficient of friction
between it and the horizontal surface upon which it is resting is 0.66?

Solution:

F = (0.66)(300 lb) = 396 lb

■ EXAMPLE 11.8
Problem : A 200-lb box is placed on a plane inclined at a 30° angle from the horizontal. The plane
has a static coefficient of friction of 0.66. What is the minimum push or pull force required to move
the box down the plane?

Solution:

F = (0.66)(200 lb × cos 30) = (0.66)(200 lb × 0.866) = (0.66)(173.2 lb) = 114 lb

Note, however that a component of the weight of the box is causing a force (due to gravity) to already
be acting in the downward direction of incline. This force is equal to W sinθ, or 200 × 0.50 = 50 lb.
Therefore, the only additional push/push force needed to get the box moving is

114 lb - 50 lb = 64 lb