Mechanical Engineering Principles

FRICTION 171

Transposing gives:

frictional force =μ×normal force,

i.e. F=μN

The direction of the forces given in this equation is
as shown in Figure 15.2.

Frictional

force, F= mN

Normal

force, N

Applied

Force, P

Figure 15.2

The coefficient of friction is the ratio of a force to
a force, and hence has no units. Typical values for
the coefficient of friction when sliding is occurring,
i.e. the dynamic coefficient of friction, are:

For polished oiled metal surfaces less than 0.1
For glass on glass 0. 4
For rubber on tarmac close to 1.0

The coefficient of friction (μ) for dynamic friction
is, in general, a little less than that for static friction.
However, for dynamic friction,μ increases with
speed; additionally, it is dependent on the area of
the surface in contact.

Problem 1. A block of steel requires a

force of 10.4 N applied parallel to a steel

plate to keep it moving with constant

velocity across the plate. If the normal force

between the block and the plate is 40 N,

determine the dynamic coefficient of friction.

As the block is moving at constant velocity, the
force applied must be that required to overcome
frictional forces, i.e. frictional force,F = 10 .4N;
the normal force is 40 N, and sinceF=μN,

μ=

F

N

=

10. 4

40

= 0. 26

i.e.the dynamic coefficient of friction is 0.26

Problem 2. The surface between the steel

block and plate of Problem 1 is now

lubricated and the dynamic coefficient of

friction falls to 0.12. Find the new value of

force required to push the block at a constant

speed.

The normal force depends on the weight of the block

and remains unaltered at 40 N. The new value of the

dynamic coefficient of friction is 0.12 and since the

frictional forceF=μN,F= 0. 12 × 40 = 4 .8N.

The block is sliding at constant speed, thus the

force required to overcome the frictional force is

also 4.8 N, i.e.the required applied force is 4.8 N.

Problem 3. The material of a brake is being

tested and it is found that the dynamic

coefficient of friction between the material

and steel is 0.91. Calculate the normal force

when the frictional force is 0.728 kN.

The dynamic coefficient of friction,μ= 0 .91 and

the frictional force,F= 0 .728 kN=728 N

SinceF=μN, then normal force,

N=

F

μ

=

728

0. 91

=800 N

i.e.the normal force is 800 N.

Now try the following exercise

Exercise 75 Further problems on the coef-

ficient of friction

1. The coefficient of friction of a brake pad
   and a steel disc is 0.82. Determine the
   normal force between the pad and the disc
   if the frictional force required is 1025 N.
   [1250 N]


2. A force of 0.12 kN is needed to push a
   bale of cloth along a chute at a constant
   speed. If the normal force between the
   bale and the chute is 500 N, determine
   the dynamic coefficient of friction.
   [0.24]


3. The normal force between a belt and
   its driver wheel is 750 N. If the static
   coefficient of friction is 0.9 and the
   dynamic coefficient of friction is 0.87,
   calculate (a) the maximum force which