Friction
CEE 210: Engineering Mechanics
North South University
Basics
• Friction is a force that resists the movement of
two contacting surfaces that slide relative to
one another.
• This force always acts tangent to the surface
at the points of contact and is directed so as
to oppose the possible or existing motion
between the surfaces.
• We study dry friction , or Coulomb friction
Equilibrium: No Apparent Impending Motion
F < 𝐹𝑠
𝐹𝑠 = 𝑇ℎ𝑒 𝐿𝑖𝑚𝑖𝑡𝑖𝑛𝑔 𝐹𝑟𝑖𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝐹𝑜𝑟𝑐𝑒 𝑤ℎ𝑒𝑛 𝑀𝑜𝑡𝑖𝑜𝑛 𝑆𝑡𝑎𝑟𝑡𝑠
Moment of Equilibrium
distributed normal and frictional
loadings is indicated by their resultants N
and F on the free-body diagram
N acts a distance x to the right of the line of action
of W. This location, which coincides with the centroid or
geometric center of the normal force distribution in the figure, is necessary
to balance the “tipping effect” caused by P.
moment equilibrium about point O is satisfied
if Wx = Ph or x = Ph/W.
Equilibrium: Impending Motion at All Points of
Contact
P is slowly increased; F correspondingly increases
until it attains a certain maximum value Fs, called
the limiting static frictional force,
limiting static frictional force Fs is directly
proportional to the resultant normal
force N.
the constant of proportionality, ms (mu “sub” s ),
is called the coefficient of static friction.
Equilibrium: Impending Motion at All Points of
Contact
The angle fs (phi “sub” s) that
Rs makes with N is called the
angle of static friction .
Coefficients of static friction
MOTION
If P>F
the frictional force at the contacting surface will be Fk.
kinetic frictional force. the magnitude of the kinetic
friction force is directly proportional to the magnitude
of the resultant normal force.
the resultant force at the surface of contact, Rk,
has a line of action defined by Fk. This angle is
referred to as the angle of kinetic friction,
where,
the constant of proportionality, Фk, is called the
coefficient of kinetic friction.
• F is a static frictional force if
equilibrium is maintained.
• F is a limiting static frictional
force Fs when it reaches a
maximum value needed to
maintain equilibrium.
• F is a kinetic frictional force Fk
when sliding occurs at the
contacting surface.
Equilibrium: Impending Motion at some Points
of Contact
if the surface is very rough (large ms ) then the resultant
normal force will shift to the corner, x = b/2, At this point the
crate will begin to tip over. The crate also has a greater
chance of tipping if P is applied at a greater height h above
the surface, or if its width b is smaller.
Example
Example
It is observed that when the bed of the dump truck
is raised to an angle of Ѳ = 25º the vending machines
will begin to slide off the bed. Determine the static
coefficient of friction between a vending machine
and the surface of the truck bed.
The spool of wire having a weight of 300 lb rests on the
ground at B and against the wall at A. Determine the force
P required to begin pulling the wire horizontally off the
spool. The coefficient of static friction between the spool
and its points of contact is µs = 0.25.