Friction

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Friction

• ENGR 221
• March 24, 2003

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Lecture Goals

• The Laws of Dry Friction
• Coefficient of Static Friction
• Coefficient of Kinetic Friction
• Angles of Friction
• angle of static friction
• angle of kinetic friction
• angle Repose

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Example Problem Shear and Bending Moment Diagram
Draw the shear and bending moment diagram
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Example - Shear and Bending Moment Diagram
Free-body diagram
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Example - Shear and Bending Moment Diagram
Look at the shear
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Example - Shear and Bending Moment Diagram
Look at the shear diagram
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Example - Shear and Bending Moment Diagram
Find the moments
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Example - Shear and Bending Moment Diagram
Draw the moment diagram
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Friction
A friction force is a shear force that acts
tangent to the surface of contract between two
bodies. This force opposes sliding motion
between bodies.
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Friction
The force of static friction is maximum when the
two bodies in contact are just ready to slip
relative to each other. The maximum force of
friction increases as the normal force between
the bodies increases.
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Friction
There are two force horizontal forces, Pmax,
which is the magnitude of maximum horizontal
force which the object can resist. where ms is
the coefficient of static friction and N is the
normal force.
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Friction
The other horizontal force, Fk, due to friction
is the kinetic-friction force which the object
can resist. where mk is the coefficient of
kinetic friction and N is the normal force.
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Friction
The coefficients of friction ms and mk do not
depend upon the area of the surfaces in contact.
Both coefficients depend strongly on the nature
of the surface contact. metal on metal ms
- 0.15 - 0.6 metal on wood ms - 0.20 -
0.6 wood on leather ms - 0.25 - 0.5
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Friction
Four different situation may occur when a rigid
body is in contact with a horizontal surface.
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Friction
Note
Since there is no evidence that the maximum value
of the static-friction force has been reached the
equation can not be used to determine the
friction force.
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Friction
Four different situation may occur when a rigid
body is in contact with a horizontal surface.
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Angle of Friction
It is sometimes found convenient to replace the
normal force N and friction force F by their
resultant R.
The angle fs is known as the angle of static
friction.
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Angle of Friction
The four cases are
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Angle of Friction
The four cases are
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Angle of Friction
Another example that will show how the angle of
friction may be used to advantage in the analysis
of certain types of problems. For block on an
incline.
The block is in not motion and friction force is
not overcome.
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Angle of Friction
If we continue to increase the angle of
inclination, motion will soon become impending.
At the time, the angle between R and the normal
will have reached its maximum value fs. The
value of the angle of inclination corresponding
to impending motion is called the angle of
repose.
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Solving Friction Problem
There are three groups, All of the applied forces
are given and the coefficients of friction are
known are determined whether the body considered
will remain at rest or slide. All applied forces
are given and the motion is known to be
impending we are to determine the value of the
coefficient of static friction. The coefficient
of static friction is given, and it is known that
motion is impending in a given direction, we are
to determine the magnitude or the direction of
one of the applied forces.
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Example Problem Friction I
A 100-lb force acts on a 300-lb block on an
inclined plane. The coefficient of friction
between the block and the plane are ms 0.25 and
mk 0.2. Determine whether or not the block is
in equilibrium and find the value of the friction
force.
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Example Problem Friction I
Determine the value of the friction force
required to maintain equilibrium.
The force needed to maintain equilibrium is an
80-lb force directed up and to the right, the
tendency is for the block to move down the
incline.
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Example Problem Friction I
Maximum friction force is may be computed.
Since the value of the force required to maintain
equilibrium (80-lb) is larger tan the maximum
value which may be obtained (60-lb) equilibrium
will not be maintained and the block will slide
down the plane.
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Example Problem Friction I
Actual value of friction force The magnitude of
the actual friction force is obtained.
The forces acting on the block are not balanced ,
the resultant is
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Class Problem Friction I
Workers are pulling a 400-lb crate up an incline.
The coefficient of friction between the crate
and the surface is 0.2 and the rope on which the
workers are pulling is horizontal.
(a) Determine the force P that the workers must
exert to start the crate up the incline. (b) If
one of the workers lets go of the rope for a
moment determine the minimum force the other
workers must exert to keep the crate from sliding
back down the incline.
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Example Problem Friction II
Two blocks are connected by a light, flexible
cable that passes over a friction-less pulley.
Block A weighs 500 N and block B weighs 200 N.
The coefficient of static friction between block
A and ramp is ms 0.3.

• Determine whether the two blocks are in
  equilibrium
• Determine whether block A will slide down the
  ramp after the cable is cut.

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Example Problem Friction II
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Example Problem Friction II
Maximum friction force is may be computed.
Since the value of the force sign is -100 N
assume sense of F is wrong. The blocks are in
equilibrium, since Fs does not exceed the maximum
static frictional force 120N.
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Example Problem Friction II
The cable is cut and the tension is zero.
The force exceeds the friction resistance 120 N
so the block will slide down the ramp.
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Example Problem Friction II
The second part can be obtained by comparing the
ramps angle of inclination f to the angle of
repose fs.
Since force f gtthe angle of repose fs, the ramp
is inclined at an angle greater tan the angle of
repose.
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Class Problem Friction II
Two blocks are connected with a flexible cable
that passes over a friction-less pulley. The
weight of block A is 25 lb, and the coefficient
of friction is 0.20 on both inclined surfaces.
Determine the maximum and minimum weights for the
block B if the system remains in equilibrium.
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Example Problem Friction III
The movable bracket shown may be placed at any
height on 3-in. diameter pipe. If the
coefficient of static friction between the pipe
and bracket is 0.25, determine the minimum
distance x at which the load W can be supported.
Neglect the weight of the bracket.
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Example Problem Friction III
Determine the value of the friction force
required to maintain equilibrium.
FA mNA and FBmNB ,which from sum in the x
direction will give FA FB
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Example Problem Friction III
Determine the value of the friction force
required to maintain equilibrium.
Use the moment about A to determine the
distance,x.
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Example Problem Friction III
Using the moment about A to find x.
The x12 in.
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Class Problem Friction III
The 200-lb block is sitting of a 30o inclined
surface. The coefficient of friction between the
block and the surface is 0.50. A light
inextensible cord is attached to the block,
passes around a friction-less pulley, and is
attacked to a second block of mass M. Determine
the minimum and maximum masses, Mmin and Mmax,
such that the system is in equilibrium. Is
impending motion by slipping or by tipping?
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Homework (Due 3/31/03)
Problems
9-1, 9-4, 9-6, 9-7, 9-24
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Example Problem Friction IV
A large rectangular shipping crate of height h
and width b is at rest on the floor. It is acted
on by a horizontal force P. Assume that the
material in the crate is uniformly distributed so
that the weights acts at the centroid of the
crate.
(a) Determine the conditions for which the crate
is on the verge of sliding. (b) Determine the
conditions under which the crate will tip about
point A.
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Example Problem Friction IV
Draw the free-body diagram, look at the equations
of equilibrium.
If FP and NW substitute into the moment equation
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Example Problem Friction IV
If the crate is on the verge of sliding FmsN
where the coefficient of static friction .
If the crate is on the verge on tipping it is on
the verge of rotation about point A, that is the
crate and the floor are in contact only at A.
Therefore x0
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Example Problem Friction IV
Note that tipping will occur before sliding,
provided that Psliding gt Ptipping, therefore if P
increases until motion occurs tipping will occur
before sliding if