FRICTION
When an object lies on or moves along a surface, there is a contact force. It is convenient to
break that contact force into two components: one "normal" to the surface, the other
"tangential" to the surface. In fact, the two components are often discussed as if they are two
separate forces. Of course, as we saw previously in the force lab(s), it makes no difference to its
effect whether it is two forces or one force (addition of vectors).
θ
w
w
θ
The force normal (perpendicular) to the surface is called the normal force. The normal force
prevents the object from breaking through the surface. Its magnitude exactly balances the net
effect of all other forces in the normal (perpendicular to the surface) direction.
The force along the tangential direction is called the frictional force. Friction behaves slightly
differently depending on whether or not the object is moving relative to the surface.
•
Kinetic: If the object is moving (has a non-zero velocity) relative to the surface, then
friction opposes that motion, i.e., its direction is opposite to that of the velocity.
•
Static: If an object is not moving relative to the surface, then the friction opposes any
would-be motion, i.e. its magnitude is equal to and its direction opposite to the sum of
the other tangential forces. There is a limit to the force that static friction can
successfully oppose. When that limit is exceeded, motion results.
The frictional force is ultimately due to the interaction of the object atoms with the surface
atoms and vice versa. The strength (magnitude) of the frictional force might depend on the
following:
1. the number of atoms in contact (microscopic) or the surface area of contact
(macroscopic)
2. the distance between interacting atoms (microscopic) or the pressure (force per area)
exerted at the surface (macroscopic); the greater the pressure, the closer the atoms are
squeezed together
2012
3. the kind of atoms (microscopic) or the materials from which the block and surface are
made
In the first part of this course, we usually approximate objects by point particles. To keep
consistent with this approximation, we assume that the area dependences of the first two
considerations above exactly cancel. One is then left with the frictional force being proportional
to the force exerted perpendicular to the surface, that is, the normal force. Any material
dependence from the third consideration will be encoded in the proportionality constant called
the coefficient of friction.
Friction: Finding the coefficient of static friction
In a static situation, the magnitude of the friction force is whatever it has to be to balance other
tangential forces up to some limit, that is,
Ff < μs N,
where N is the magnitude of the normal force and μs is called the coefficient of static friction.
The expression μs N is the largest the static friction can be. If the opposing tangential forces
exceed it, motion results. The direction of the frictional force is opposite to the direction of
motion the object would have in the absence of friction.
Measurements
•
Set up a track as shown below
height
θ
•
•
Record the length of the track and masses of the various blocks.
Length of track
(
)
Mass of friction block
(
)
Mass of heavy metal block (
)
Make sure your track is clean. Sticky parts on the track will lead to non-uniform
coefficients of friction. Why?
- 2-
•
Place a friction block (two views of which are shown below) with the wide wooden
surface against the track. Starting at small angles, increase the angle until the block first
begins to move. Record the height, then use trigonometry to find the corresponding
angle. (The block just beginning to moves means we are at the upper limit for static
friction.)
•
Repeat this measurement two more times for a total of three trials for the wide wooden
surface of the friction block.
Repeat the measurements for the narrow wooden side, the wide felt side, and the
narrow felt side.
•
Height
Trial 1
( )
Height
Trial 2
( )
Height
Trial 3
( )
Angle
Trial 1
( )
Angle
Trial 2
( )
Angle
Trial 3
( )
μs
Trial 1
( )
μs
Trial 2
( )
μs
Trial 3
( )
μs
Ave.
( )
μs
St.Dev.
( )
Felt
Wide
Felt
Narrow
Wood
Wide
Wood
Narrow
•
Choosing either Felt Wide or Wood Wide, place one of the heavy metal blocks on top of
the friction block and repeat the measurements (three trials). You may need to tape or
in some other way to secure the weights onto the friction blocks. Place a second metal
block on the friction block and take another set of measurements.
Height
Trial 1
( )
Height
Trial 2
( )
Height
Trial 3
( )
Angle
Trial 1
( )
Angle
Trial 2
( )
Friction
Block
Alone
With
One
Heavy
Block
With
Two
Heavy
Blocks
- 3-
Angle
Trial 3
( )
μs
Trial 1
( )
μs
Trial 2
( )
μs
Trial 3
( )
μs
Ave.
( )
μs
St.Dev.
( )
Analysis
•
Once the block starts moving, does it seem to travel down the track at a constant
velocity? Or does it appear to be accelerating?
•
In your write-up, draw the set-up above. Draw all of the forces acting on the block (the
weight, the normal force and the frictional force).
•
Break the forces into their components in the coordinate system shown above.
•
At an angle just below the one at which the block began to move, the forces were in
equilibrium. Thus the net force was zero. This should provide you with two equations
(one for the x components, one for the y components).
•
Using these equations and the form above for the maximal static friction force, find an
expression for μs. (It should depend only on the angle.) We are looking here for an
expression using variables names, not specific numbers.
•
Use this expression to find μs for your three runs above. Find the standard deviation as
well.
•
What are the dimensions of μs?
•
Do you observe any dependence on the coefficient of friction you found on the area of
contact?
•
Do you observe any dependence on the material?
•
Do you observe any differences when you add the heavy block on top?
Friction: Finding the coefficient of kinetic friction
When the object is moving along the surface, we have what is called kinetic friction, and in our
approximation the formula is
Ff = μk N,
(In the case of kinetic friction we have an equation rather than an inequality; the equation
applies provided the object is moving.)
Measurements
•
Obtain the various masses: friction block, metal block.
Mass of friction block
(
)
Mass on hanger including hanger (
)
Mass of metal blocks
)
(
- 4-
•
Using a universal clamp, secure a Smart Pulley at the edge of the lab bench.
•
Plug the Smart Pulley into the Digital Channel 1 of the Data Studio Interface.
•
Start Data Studio, click on the digital plug icon into the Digital Channel 1 icon, and select
Smart Pulley from the menu. (It is also possible to make the measurements using a
Motion Sensor on the other end of the track.) Remember to set the Sampling Rate
(Frequency) high enough, e.g. 20 or 50 Hz. (50 Hz provides more data but is sometimes
problematic.)
•
Tie one end of a string to the friction block and the other end to a 50-g hanger.
•
Place the two heavy metal blocks on top of the friction block. Add enough mass to the
hanger so that it sets the friction block into motion. (We want a noticeable acceleration
here, not too big and not too small.)
•
Note the distance between the hanger and the floor so you can stop the friction block
before it travels that distance.
•
Click Start and the release the friction block.
•
Copy the position vs. time data and use Excel to graph it.
•
Fit it a polynomial of order two and extract the acceleration. (Remember to leave out
any data from the start or end where the "physics changed", e.g. if it hit the floor. If the
data is not reasonably well fit by a polynomial of order 2, consider retaking it.)
•
Repeat the process for each of the two wide surfaces of the friction block being in
contact with the track.
Acceleration
(
)
Felt Wide
Wood Wide
- 5-
Coefficient of
kinetic friction
(
)
Analysis
Looking at the forces acting on the block and the hanger and breaking the block forces into
components yields the following three equations:
Block
Y component
N b – mb g = 0
Block
X component
T b – μk N b = m b a b
Hanger
Y Component
mhg – Th = mh ah
where the subscript b indicates block and the subscript h indicates hanger. If the string and
pulley are considered massless, then Th=Tb. Furthermore, if the string does not stretch or break
then ah=ab.
Solve the set of simultaneous equations above for μk. Enter the value you find for the
coefficient of kinetic friction for each of the two types of blocks in the previous table.
What is the ideal acceleration, that is, the acceleration you would have in the absence of
friction?
What are the frictional forces?
What are the coefficients of friction?
Do you observe any dependence on the material?
How do the kinetic coefficients compare to the static coefficients?
- 6-