Friction -- Chapter 8
Introduction
Laws of Dry Friction. Coefficients of Friction
Angles of Friction
Problems Involving Dry Friction
2
Problems Involving Dry Friction
Examples and Problems for Dry Friction
Wedges
docsity.com
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Guidelines and tips
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Friction Part 1-Basic Mecanical Engineering-Lecture Slides, Slides of Mechanical Engineering
Prof. Dasmaya Sidhu delivered this lecture at National Institute of Industrial Engineering for Basic Mechanical Engineering course. It includes: Laws, Dry, Friction, Coefficients, Angles, Wedges, Slide, Transmission, Brakes, Horizontal, Force
Typology: Slides
2011/2012
1 / 55
This page cannot be seen from the preview
Don't miss anything!
Related documents
Partial preview of the text
Download Friction Part 1-Basic Mecanical Engineering-Lecture Slides and more Slides Mechanical Engineering in PDF only on Docsity!
Friction -- Chapter 8
Introduction
Laws of Dry Friction. Coefficients of Friction
Angles of Friction
Problems Involving Dry Friction
2
Problems Involving Dry Friction
Examples and Problems for Dry Friction
Wedges
When a body moves or tends to move on another body, a force appearsbetween the surfaces. This force is called force of friction and it actsopposite to the direction of motion
Friction - Introduction
Friction force occurs when one contacting surfacetends to slide along another
3
Frictional Friction is useful in power transmission by belts. It is useful inappliances like brakes, bolts, screw jack
force
is
undesirable
in
bearing
and
moving
machine parts where it results in loss of
energy and, thereby, reduces
efficiency of the
machine and its effect is needed to be minimized
For the body shown in the figure tobe in equilibrium,
the following must be true:
F = P,
(All forces in x direction)
N
W,
and
Friction - Introduction
5
N
W,
and
(All forces in y direction)
Wx = Ph (moment about O)
“N” acts at a distance “
x
” to the right of the line of action of “W”. This distance is necessary to
balance the “tipping effect” caused by “P”For example if “P” is applied at a height “h” from the surface the moment about point “O” issatisfied if
W
x
=Ph
or
x
= Ph/W
where
F
f
is the friction force.
is the coefficient of friction. (depends on materials)
F
f
F
n
Friction - Introduction
6
is the coefficient of friction. (depends on materials)
F
n
is the normal force exerted between the surfaces,
(which is equal to W in this diagram).
If P is small, the block will not move; some other horizontal force must therefore exist, whichbalances P. This other force is the static-friction force F
There are two types of frictional forces
Static friction Kinetic friction
If the force P is increased,
the friction force F alsoincreases, continuing to oppose P, until its magnitude reaches a certain maximum value F
max
Maximum Value of Static Friction
8
Motion cannot begin until the applied force is higher than themaximum friction force
F
max
μμμμ
S
F
n
Kinetic Friction When a body moves relative to another body, the resisting force betweenthem is called kinetic or sliding friction
F
k
μμμμ
k
x F
n
Kinetic Friction
9
μ
k
coefficient of kinetic friction
It has been experimentally found that the
kinetic friction is less than the maximum static friction
It is based on the concept that it takes more force to accelerate a mass from rest than to keep it moving The force of friction is always exerted in a direction that opposes movement (kinetic friction)
or
Potential movement (for static friction) between the two surfaces.
COEFFICIENT OF FRICTION
The ratio between the maximum static frictional force and the normal reaction is known ascoefficient of static friction denoted by Greek letter
μ μ
μ μ
s
Coefficient of Friction
The coefficient of friction , is a dimensionless (scalar) value so it has no units.
11
The coefficient of friction , is a dimensionless (scalar) value so it has no units. (This is because it is a ratio between two forces). The coefficients of friction
μ
s
and
μ
k
do not depend upon the area of the surfaces in contact.
Both coefficients, however, depend strongly on the nature of the surfaces in contact
The coefficient of friction is measured experimentally, and cannot be found throughcalculations. Rougher surfaces tend to have higher effective values. Most dry materials in combination have friction coefficient values between 0.3 and 0.6. Values outside this range are rarer, but teflon, for example, can have a coefficient as low as0.04. A value of zero would mean no friction at all,
Coefficient of Friction
12
A value of zero would mean no friction at all,
However,
if
the
applied
force
P
has
a
horizontal
component
P
x
which tends to
move the block, the force
R will have a horizontal component
F and, will form a
certain angle with the vertical
If P
x
is increased until motion becomes
impending, the angle between R and the
Angle of Friction
14
s
s
s
m
s
N
N
N
F
μ
φ
μ
φ
tan tan
impending, the angle between R and the vertical grows and reaches a maximum value This value is called angle of friction and denoted by
φ
k
k
k
k
k
N
N
N
F
μ
φ
μ
φ
tan tan
- It is sometimes convenient to replace normal force
N
and
friction force
F
by their resultant
R
Angle of Friction
15
No friction
Motion impending
No motion
s
s
s
m
s
N
N
N
F
μ
φ
μ
φ
tan tan
Motion
k
k
k
k
k
N
N
N
F
μ
φ
μ
φ
tan tan
docsity.com
Consider block of weight
W
resting on board with variable inclination angle
Angle of Friction- For inclined plane
ANGLE OF INCLINATION IS INCREASING
8 - 17
No friction
No motion
Motion impending
Motion
The maximum friction force
is attained just before the block begins to
move (a situation that is called “impending motion”).
The value of the force is found using F
s
s
N,
where
s
is called the coefficient of static friction. The value of
s
depends on the materials in contact.
18
Once the block begins to move, the frictional force typically drops andis given by
F
k
=
μ μ
μ μ
k
N.
Example 8.
The uniform crate shown in the fig has the mass of 20 kg.if a force P=80 N is applied to the crate Determine whether it remains in equilibrium? The static coefficient of friction is
μ
s= 0.
20
Example 8.
Free Body Diagram The resultant Normal force N
C
must act at a distance x from the crates center line to counteract
the tipping effect caused by “P” There are three unknowns
F, Nc, and x
which can be derived using three equations of
equilibrium
0
F
30
cos
80
0
F
o
x
=
=
−−−−
====
∑ ∑
∑ ∑
21
0
2
.
196
N
30
sin
80
0
F
0
F
30
cos
80
0
F
C
o
y
o
x
====
− −
− −
− −
− −
====
=
=
−−−−
====
∑ ∑
∑ ∑
∑ ∑
∑ ∑
F= 69.3NN
C
= 236 N
max
C
s
max
F
F
N
8
.
70
)
236
(
3
.
0
N
F
<<<<
====
=
=
====
μ
Since F=69.3 N< 70.8 N the crate will not slip but very close to slip