HOUSTON COMMUNITY COLLEGE
SYSTEMS SOUTHWEST COLLEGE
COLLEGE PHYSICS I – PHYS 1401
Experiment Three
Coefficient of Friction
Professor: Robert Hage
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PRE LAB QUESTIONS
Due before lab begins.
1) Explain briefly the different types of frictional forces.
2) How does the coefficient of friction depend upon the area of contact? Explain.
3) Give some examples in which the force of friction causes the object to accelerate.
4) If you push on a heavy box that is at rest, you must exert some force to start its
motion. However, once the box is in motion you need a smaller force to maintain
that motion. Why?
5) Find the force needed to pull a mass of 30 kg at constant velocity on a rough incline
making an angle of 400 with horizontal and with µk = 0.3
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OBJECTIVE
The nature of the frictional force between two wooden surfaces will be investigated. This
will lead to the observation of the properties of friction. The following objectives will be
accomplished:
1. the determination of the coefficients of static friction, µs , and kinetic friction, µk ,
between two wood surfaces by sliding the block down the board.
2. Determination of the coefficient of friction by using the board as an inclined
plane.
3. Comparison of the two values of µs from the two different methods.
4. Demonstration that the coefficients of friction are independent of the surface area
of contact.
5. Verification that the coefficient of static friction, µs, is in general slightly larger
than the coefficient of kinetic friction, µk, for any same type of surfaces.
MATERIALS
1. Wooden Block
3. Wooden Board
5. Triple-beam balance
7. Protractor
9. Paper towel
2. Weight hanger
4. Slotted weights
6. Pulley
8. String
10. Two sheets of Cartesian graph paper
INTRODUCTION
Friction is a resistive force that occurs due to motion between two contacting surfaces.
The two surfaces must either be sliding or attempting to slide over another resulting in a
force that is tangent to the two surfaces and in a direction that tends to oppose the motion
of each surface. In general, frictional force depends on the nature and physical properties
of the surfaces in contact. It slows down the motion of an object and is directed along the
two surfaces in contact in the opposite direction of the motion. Friction is always called a
non-conservative force because some energy is needed to overcome it.
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The following conclusions can be made of friction, Friction between two surfaces is:
(i)
(ii)
(iii)
(iv)
Independent of the surface area of contact
Independent of the sliding speed of the surfaces
Proportional to the normal force acting on the surfaces
Acts in a direction opposite to the direction of motion of each surface.
On the other hand the coefficients of friction µs and µk , which are constants, depend on
the nature of the surfaces in contact and are independent of the normal force.
THEORY:
There are two types of frictional forces:
a) Static friction ( fs)
This exists when the object is at rest relative to the surface. This force must be
overcome in order to make the object start moving. It is given by fs ≤ µs n.
b) Kinetic friction ( fk)
This exists when the object is in motion and is given by fk =
µk n (where µs and µk are the coefficient of static and
kinetic friction respectively, and n is the normal force
which presses the two surfaces together). In general, f s > fk
and µs > µk because it takes a larger force to start an object
sliding (static friction) than to keep it sliding (kinetic
friction). As mentioned above the coefficient of friction, µ,
(pronounced mu) is depends on the nature of the surfaces
and is independent of the area of contact.
In this experiment, using the board in a horizontal position,
we measure the frictional force fk and fs as they vary with respect to the normal force
n. Using the second law of motion, we can calculate the coefficients of friction
between block and board.
Another way to find µs is to set up the board as an incline plane.
The coefficient of friction µs is related to the maximum angle θm to
which the board can be elevated before the block starts its motion is:
In the case of an inclined plane, θm can be adjusted.
When the block is placed on the plane, the angle is
slowly increased till a point is reached at which
the block begins to slip. Accordingly, the forces on block include the normal force, N,
which acts perpendicularly to the plane, and the components of the weight of the
block, mgcosθm, which acts in the opposite direction. Since the plane is in equilibrium
as far as perpendicular motion is involved, these two forces are equal, thus
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N = mgcosθm
(1)
Where is the angle at which the block just begins to slip down the inclined plane. There
are also two forces parallel to the plane. There are the component of the weight of the
block, mgsinθm, which acts down the plane, and the frictional force fs which acts up the
plane. At the point that the blockb just slips, the maximum frictional force is exerted, and
these two forces are equal, that is
fs =
µsN
= mgsinθm
(2)
but N == mgcosθm in equation (1) above. When the two equations are combined, the
result is
µs = mgsinθm = mgsinθm = tanθm
N
mgcosθm
(3)
Hence µs = tanθm in this case.
EXPERIMENTAL PROCEDURE
1. Weigh the wooden block on the triple beam balance and record its weight
2. Set up the block on the board with the
largest surface in contact with the board
surface and string attached to the block run
over a pulley. Place some weights on the
weight hanger. Slightly increase the load on
the weight hanger until the block begins to
move slowly with a constant speed after it has been started with a very small
push. Make sure you wipe away any dust from the surfaces. Record the weight
placed on the weight hanger including the mass of the weight hanger. 200 g on the
surface of the block. Slowly increase the load on the hanger until the block starts
slowly moving with constant speed after given a small push. Don’t forget to
include the mass of the hanger.
3. Repeat Procedure 2 above placing masses of 200, 400, 600, 800 and 1000 g
successively on top of the wood block. Record the total weights placed on the
weight hanger including the weight hanger. The coefficient of kinetic friction can
be obtained from these data.
4. Turn and place the smallest side of the wood block on the board and repeat
Procedure 2 above.
5. Set up the block again as in procedure 2 and place a mass of 600 g on it. Place
weights gently on the hanger and increase them slowly until the block just starts
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its motion without any push. Repeat a total of 3 independent trials and record your
data. With this data you can find the coefficient of static friction.
6. Remove the pulley and set up the board as an inclined plane. Place the wood
block on it with its largest surface being in contact. Gently and smoothly tip the
board until block starts to slide down the plane. Measure the angle θm with a
protractor and record it in the table. Repeat this procedure 3 independent times.
REPORT FORM
Weight of block _________
Procedure 2 Normal and Friction force for kinetic friction
Total Normal Force, N Friction Force, N
Mass on block
200 g
400 g
600 g
800 g
1000 g
µk from graph ________
Procedure 3
Mass on block
Normal and Friction force for static friction
Total Normal
Force, N
Friction Force, N
600 g
600 g
600 g
Averages
Procedure 4 Inclined plane for static friction
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µs
Deviation
Measurement
1
2
3
Averages
Percent difference between
the two values for µs
Angle θm
µs
Deviation
______________
CALCULATIONS
1) From procedure 2, draw a graph using the data of the force of friction as the
ordinate and those of the normal force as the abscissas. Draw the best straight
line joining most of the points. Obtain the slope of this graph. The slope so
obtained is the coefficient of kinetic friction, µk, between the wooden block and
board.
2) From procedure 3, calculate the value for µs between block and board. Obtain
their average value and average deviation.
3) From procedure 4, calculate the value for µs between block and board. Find their
average value and average deviation. Compare the two values for µs for wood on
wood by calculating their percent difference which is given by:
Percent difference = [difference of the two values/ average] x 100 %
POST LAB QUESTIONS
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1. Explain why the block should move at constant speed in procedure 2.
2. Derive equation 1, µs = tan θm
( apply 2nd law of motion for constant velocity)
3.
In procedure 4 , find the acceleration of the block as it breaks away if µk = 0.2 and
θm = 200
4.
Compare your experimental value with the book value for the coefficient of kinetic
friction for wood( µk = 0.2). Find the percent error and give reasons for it.
5.
Is the frictional force in this experiment only due to the surface of contact between
block and board? Explain.
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