Kinetic Friction Experiment
Discussion
Kinetic friction forces are the forces that sliding surfaces exert on each other parallel to their surfaces. Kinetic friction forces are cumulative effects of the forces between all the microscopic contact points of the sliding surfaces. As a result, friction forces vary with the types of surfaces in contact, the state of each surface (smoothness, surface dirt or impurities, etc.), and the pressure of one surface against the other. Even for the same surfaces tested under similar conditions, the friction will not be exactly reproducible from one trial to the next.
The coefficient of kinetic friction (
μ k
) is defined as the ratio of the kinetic friction force to the normal force (the perpendicular force of each surface on the other.) Because doubling the normal force usually doubles the friction force, the coefficient (
μ k
) remains the same.
Even though friction forces vary from run to run, for any pair of surfaces they usually don’t vary very much, so similar values of
μ k
can be expected from different trials. For most pairs of surfaces, it is found that
μ k
is approximately independent of normal force, contact area, and speed. In this experiment these properties of kinetic friction will be tested for two surface pairs; wood on aluminum, and felt on aluminum.
Theory
In Figure 1, block M accelerates along a horizontal track, pulled by a string which passes over a pulley and is attached to load m. T is the tension in the string. (Note that T is not equal to the weight mg.)
Figure 1a A schematic diagram of the experiment showing the direction of acceleration of the masses
Figure 1b. A free body diagram of M showing the forces and the components of the weight.
Figure 1c. A free body diagram of m showing the forces on it.
For block M, since there is no acceleration perpendicular to the plane, the forces N and
Mg cos
θ
are balanced, so
N = Mg (1)
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Therefore
F k
=
μ k
N =
μ k
Mg (2)
Considering the forces parallel to the track, Newton’s second law gives
F
NET
= Ma
T – f k
= Ma
Substituting for f
K
from eq. 2 ,
(3 )
T- Ma
Solving this for T,
T =
μ k
Mg + Ma (4)
Applyi ng Newton’s second law to the hanging mass m gives
F
NET
= ma mg – T = ma (5)
Solving for T,
– )
S etting the two expressions for T equ gives ,
μ k
Mg + Ma = mg – ma
Rearranging this to sol ve for
μ k
,
μ k
= mg −
( m
Mg
+ M
) a
(8)
(7)
Pre-Lab Assignment
A student doing the friction experiment with a horizontal track obtains the following data for four trials.
M (sliding block) = .150 kg
m (hanging load) = .060 kg
The values of acceleratio n measured using the motion sensor are
2 a = .3 m/s
Calculate
μ k
from each trial, using equation (8). Program the calculation on an Excel spreadsheet, using the methods explained on the Excel reference sheet. Using the defined statistical f unctions in the spreadsheet program to calculate the average value of the coefficient friction.
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Object: The object of the experiment is to investigate the behavior of kinetic friction to determine if type of surface, surface area, normal force or speed affects the coefficient of kinetic friction.
Apparatus
Pasco 750 Interface
Pasco Motion Sensor
1.2 meter dynamics track
Friction block with wood and felt sides
Hanging mass holder (50 grams) and set of masses.
2 – 500 g slotted masses
Thread
Procedure and Analysis for Kinetic Friction Experiment
I. Set-up of computer and interface
1.
Turn on the PASCO 750 interface first. Verify that the indicator light is on.
2.
Turn on the computer.
3.
Start Data Studio, choose Create Experiment
4.
Select the motion sensor icon and drag it to the interface
5.
Select 100 Hz for the sample rate.
6.
Turn off (uncheck) all measurements except velocity. You want to measure the velocity of the block as a function of time.
II . Set-up of Track and Taking Data
Figure 2. The apparatus used for the kinetic friction experiment set up and ready for measurement
1.
Set up the 1.2 meter track as shown in Figure 2 with the motion sensor clipped onto the end of the track.
2.
Use a scale to weigh the friction block. Record the mass of the friction block.
3.
Place the wood side of the block against the track and add 500 g of mass on top of the friction block. (What is the mass that will now slide along the track?) The block should be at least 30 cm in front of the motion sensor.
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4.
Attach a pulley as shown in Figure 2. Place the larger area wood surface of the friction block on the track. Run the string from the friction block over the pulley and down to the hanging mass holder. Make sure the string is parallel to the track, place a sheet of foam on the floor where the masses will hit.
5.
Attach enough weight on the hanging mass holder so that it starts slowly moving along the track. Add 50 grams more to the holder and collect data for the velocity as a function of time.
NOTE: The graph of the data must be a straight line.
6.
Select a linear fit to the data. Choose the best straight line portion of your data, and determine the slope (acceleration of the block) from your data. Record this acceleration. Repeat step 4 and this step until you have a total of 3 trials.
7.
Average the acceleration from these three trials.
8.
Add another 50 g to the mass of the hanger, collect velocity data for this mass and repeat steps 6 and 7.
9.
For two additional runs add another 50 g to the mass of the hanger, collect data, and repeat steps 6 and 7 until you have an average value for 4 different accelerations.
10.
Don’t forget to print representative graphs of the data you are collecting.
III. Collecting data for a different normal forces and surfaces.
1.
Add another 500 g to the friction block (total of 1000 g on top of the friction block) and repeat II.
2.
Repeat II placing the felt surface against the track and placing 500 g on the friction block.
IV. Calculations
Determine
μ k for each of the average accelerations you recorded from the above procedure.
Conclusions
Your report should include your observations about the following:
1. Is the coefficient of friction constant depending only on the types of surface in contact?
(Remember it is very difficult to reproduce exactly the same value for the coefficient of friction on each run.)
2. Does the normal force change the coefficient of friction?
3. Does the surface area change the coefficient of friction?
4. Did the coefficient of friction vary significantly with acceleration?
5. What are your sources of experimental error?
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