Optional Unit V: Applications of Kinematics and Dynamics
B. Frictional Forces
Key Concepts
Frictional forces act to oppose motion.
Frictional forces negate the possibility of perpetual motion.
A force is needed to overcome static friction and to
initiate motion.
It takes more force to make an object move from rest than to keep
it moving once it is in motion.
For an object at rest, as more force is applied, more friction is
encountered, until the limiting static
frictional force has been attained. Additional force applied
beyond that will initiate motion.
Frictional forces that oppose the motion of moving objects are
due to kinetic friction.
Various methods can be used to reduce or increase the amount of
friction between surfaces in contact. The particular application
usually determines those methods which would be most effective.
A surface exerts an upward normal force ( or R in some
texts) on objects resting upon it.
On horizontal surfaces this normal force opposes the force of
gravity. (On an inclined plane the normal force opposes the force
of gravity acting on the plane: , where the angle is defined as
the angle between the plane and the horizontal.)
These forces can be considered to act concurrently through the
centre of mass of an object. Forces that act at a common
point are said to be concurrent.
The coefficient of kinetic friction can be found
experimentally by determining the force needed to keep an object
moving at a constant velocity along some particular surface.
The kinetic frictional force on an object is directly
proportional to the normal force on an object.
where is the force due to kinetic friction, is the
coefficient of kinetic friction, and is the
normal force. (Strictly speaking, the equation is not quite
correct at high velocities.)
A coefficient is a scalar quantity having no units.
The coefficient of static friction is important in
determining the minimum amount of force needed to initiate
motion.
The minimum force needed to initiate motion is equal to
the maximum static frictional force.
where is the static frictional force, is the coefficient
of static friction, and is the normal force.
The coefficient of static friction exceeds the value of the
coefficient of kinetic friction (with some rare exceptions,
such as Teflon on Teflon, where ).
Coefficients of friction depend on the nature of the materials
making up the surfaces in contact, temperature, phase, surface
area in contact, etc.
Learning Outcomes
Students will increase their abilities to:
- Define the following terms: limiting static frictional force,
static friction, kinetic friction, normal force, centre of mass,
coefficient, coefficient of kinetic friction, kinetic frictional
force, coefficient of static friction, static friction,
concurrent forces.
- Explain that frictional forces usually act to oppose motion.
- Give examples of some moving objects which will eventually
come to rest due to friction.
- Explain that a sufficient force needs to be applied to an
object before it will begin to move.
- Identify situations in which it is desirable to increase or
reduce the amount of friction between surfaces in contact.
- Give examples of various ways in which frictional forces can
either be increased or decreased.
- Explain that the normal force acts to oppose the force of
gravity.
- Explain that the normal force must be equal in magnitude and
opposite in direction to the force of gravity for the object to
remain in equilibrium.
- Explain that the structure supporting an object must be
capable of producing a normal force to withstand the force of
gravity acting on the structure by the object, otherwise the
structure will undergo failure.
- Draw free body diagrams to illustrate forces acting
concurrently through the centre of mass of an object.
- Solve problems involving kinetic or static friction.
- Compare the static and kinetic frictional forces acting on an
object.
Teaching Suggestions, Activities and Demonstrations
- To demonstrate the effect that friction has on objects, a
discussion about the possibility of a perpetual motion machine
might be used. If friction could be eliminated completely, or if
there were no heat loss in energy conversions, then perpetual
motion might become a possibility.
Several examples of attempts that have been made in the past to
create perpetual motion machines could be used for illustration.
- Investigate the effects of static or kinetic friction on
different objects.
- Experimentally determine the coefficient of static or kinetic
friction acting on an object under some particular circumstances.
- Place a wooden block on a board. Slowly raise the board at
one end until the block begins to slide down the ramp. Record the
angle of the ramp at which the block first begins to move. Draw a
free body diagram of the forces acting on the block
.
Repeat with the block resting on its narrow side. Soap the bottom
of the block and repeat. Glue a piece of sandpaper on the block
and repeat.
- Research the historical use of animal fat on sled runners to
reduce friction.
- Run a string up from a block to a pulley at the top of an
inclined plane. Place weights on the free end of the string until
the block begins to move up the ramp with a slight starting push.
Repeat at different ramp angles, and with different conditions
between the surface of the block and the ramp. Analyze the
results to develop a relationship for the coefficient of sliding
friction.
- Design an experiment to test the effects of different types
of ski waxes on cross-country or downhill skis, or sled runners.
Variables such as the characteristics and temperature of the
snow, the air temperature, the relative humidity, etc.,
would have to be monitored to determine if different waxes were
needed under different conditions.
A group of students could research the types of waxes used on
cross-country or downhill skis and present a report to the class.
- Attach a spring balance to the end of an empty box. Determine
the force needed to start the box in motion, and then to keep it
moving at a constant velocity. Place objects inside the box to
increase its weight. Repeat the experiment. Develop
generalizations regarding the coefficients of static and kinetic
friction.
- Athletic events involving motion at high speed pay particular
attention to reducing air resistance. Examples include such
sports as downhill skiing, cycling. speed skating, and
bobsledding.
Students might enjoy researching some of the ways in which
frictional forces are minimized in such sports.
One way to do this activity is to divide the class into groups.
Each group could research a different topic and make
presentations to the class.
- Investigate ways in which the ends of a travois could be cut
to reduce friction.