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Static and Kinetic Friction
(One or two weights)
For one weight, complete Part I. Complete both Part I and Part II for two weights.
Recommended reading: R.A.Serway and J.W.Jewett, Jr. Physics for Scientists and Engineers 8th
ed. (Thomson, 2010). Chapter 5.8.
PREPARATORY QUESTIONS
B
C
Force
D
A
Time
1. The graph above is representative of the force applied to an object as it is pulled across a
horizontal surface. Draw a free-body diagram for each of the positions labeled in the graph
above. Describe the motion of the object for the positions labeled in the graph.
2. An object is at rest on the ramp with the angle of inclination θ. The object starts moving
down the ramp being just slightly pushed. What is the coefficient of static friction between
the object and the surface of the ramp?
3. Why do anti-lock brakes help to avoid automobile accidents?
INTRODUCTION
The purpose of this experiment is to find the coefficient of static friction and the coefficient of
kinetic friction for different surfaces on a leveled or inclined track. As it pulls a Friction Tray
from rest to a constant velocity, the Force Sensor can measure both the static friction and the
kinetic friction. A plot of each of these forces versus their respective normal forces yields both
coefficients.
THEORY
Consider an object is at rest on a horizontal surface and a force is applied to the object in the
horizontal direction. The object will not move until the force applied to it is greater than the
maximum force due to static friction. Until the maximum static frictional force is reached, the
static frictional force is equal to the force applied. The coefficient of static friction (s) is simply
the ratio between the maximum static frictional force (Fs,max) and the normal force (FN):
2
s 
Fs ,max
FN
To keep the object moving at a constant velocity, a force must be applied to the object equal to
the kinetic frictional force. Hence, the coefficient of kinetic friction (k) is the ratio between the
kinetic frictional force (Fk) and the normal force (FN):
k 
Fk
FN
EXPERIMENT
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Force sensor CI-6746
String
PASCO Universal Interface 850
Aluminum track
Bubble level
Stand with table clamp
PART 1: LEVELED TRACK
Level track
Connect the sensors. the interface to connect the PASCO Force Sensor Cl-6746 to Channel A.
Set the sample rate to 500Hz.
Setup Capstone. Display force vs time.
Manual data input. For each cart configuration, table of Normal Force and Static Friction, and
Normal Force and Kinetic Friction
Part 1 (b): Some training and verifying that μs ≥ μk
1. Use a bubble level to level the track in both along- and across-track directions.
2. Cut a string of about 10 cm; tie a knot to the cart and a loop to attach it to the force sensor.
3. Put any combination of masses in one of the carts and secure them to the base of the cart
using masking tape. This is to ensure that the mass and the cart are acting as a single object.
The tape can be obtained from the Resource Center.
4. Take this part as training for part 2. You will need practice pulling the cart very slowly and
steadily to maintain a constant velocity, as extra force will accelerate the carts which will
give a result that can significantly deviate from the theoretical value.
5. Click on START on DataStudio and press the TARE button on the force sensor (make sure
that no force is applied when pressing the TARE button, and the string attached to the force
sensor is not experiencing any tension)
6. Start pulling the cart horizontally to ensure no vertical component of the force is applied
which might influence the normal force. (Note: slowly apply tension to the string by
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gradually increasing the force applied until the cart starts moving. Applying a sudden and
abrupt force will result in a spike in the Force-Time graph which does not accurately reflect
the maximum static friction). Once the cart is moving, pull it at an approximately constant
velocity. Pull it in a straight line, using the groove on the sides of the track for guidance.
Moving the cart to cover at least half of the track.
7. ASTM Standard D-1894 (Standard Test Method for Static and Kinetic Coefficients of
Friction) states that the speed of the specimen should be 150mm/min. Although this speed is
practically too slow for this experiment, it suggests that the accuracy of the results can be
improved by moving the object slowly.
8. Repeat steps 3 to 6 for different combinations of mass (at least 3 different runs, one using
each cart). Label the runs appropriately in DataStudio. (Suggestion: It would be easier to
begin with cork cart with 300g mass added, felt cart with 300g mass added, and plastic cart
with 500g mass added).
9. Show that constant force is needed to maintain constant velocity of the cart by highlighting
the data points when the cart is moving and performing a linear fit. You should get a slope
value close to 0. If that is not the case, repeat from step 5.
10. Verify that μs ≥ μk by showing that the force needed to start moving the cart is greater than
(or equal to) the force needed to move the cart at constant velocity.
Part 1 (c): Estimating the coefficient of static friction and kinetic friction
1. Use the DataStudio file prepared earlier in the experiment in part 1(a).
2. Put one (or more) 100g masses into the plastic cart. Measure the mass of the cart with
mass(es) in it. Calculate the normal force and record it in the Data Table created earlier as
“Normal force”.
3. Start pulling the cart gently and carefully (as suggested in part 1(b)) while pressing START
on DataStudio (Don’t forget to press the TARE button). Stop it after moving a distance of
about 15-20 cm, but keep allowing force sensor to record the data. Start moving it again
from the stopped position. Repeat this for at least 5 times to collect data at different
locations of the track. After doing this, return the cart to the starting position on the track.
(We suggest repeating this for at least 3 times, for a total of 15 runs per data point to get
more accurate result).
4. Each run has a peak that corresponds to the maximum static friction and a near-to-constant
force that corresponds to the kinetic friction. Calculate the average of the maximum static
friction for this specific mass and specific type of cart and record it into the Data Table with
variable Y as Static Friction. Also average the kinetic friction and record it into the Data
Table with variable Y as Kinetic Friction.
5. Repeat step 2 to 4 for different combinations of mass in the plastic cart. Then repeat for the
other two types of cart. Take at least 3 different mass combinations for each type of cart for a
total of 9 runs.
6. For each type of cart, create a linear plot in the graph Friction vs Normal by dragging the
data from the tables into the graph. The slopes of Static Friction vs Normal and Kinetic
Friction vs Normal represent the coefficients of static friction and kinetic friction
respectively.
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7. In addition to DataStudio plot, try Microsoft Excel to perform error analysis for a graph with
error bars in it.
EXPERIMENT PART 2: INCLINED TRACK
Part 2 (a): Measuring static friction
1. This part will only involve the use of the plastic cart.
2. Use two PASCO large table clamps ME-9472 that come with metal rods to mount the track
at one end using the track rod clamps. Care is needed to prevent damaging the long track.
The end that is not mounted to the stand must be cushioned by PASCO Dynamics Track Feet
ME-8972.
3. This experiment will only use the plastic cart. Using results for the coefficient of static
friction from the previous part of the experiment, calculate the estimated height required for
each cart to begin sliding and explain why only the plastic cart can be used.
4. Set the track at a low inclination and put the plastic cart on the track. Add mass into the cart
and measure the total mass. Record this mass.
5. Loosen the screws on the track rod clamps and slowly adjust the angle of inclination by
increasing the height of the track. This process should be smooth and produce no vibrations
if the track is mounted properly. The track should be supported from the bottom using both
hands. Any vibrations will cause the cart to temporarily leave the track surface and start
moving, even if the critical angle has not been reached.
6. When the cart starts sliding down the track, stop adjusting the height and tighten the screws
on the rod clamps to secure the track in place.
7. Using a ruler, determine the height at which the cart starts to move. Extra care should be
taken to measure the height that gives the angle of inclination, as a small change in height
will produce a significant difference in the coefficient of static friction.
8. Repeat this step at least three more times, by having different masses in the cart. Remember
to reset the height of the inclined ramp and start from step 4.
9. Calculate the coefficient of static friction by using the formula that you have derived
answering question 5 of the Preparatory Questions.
Part 2 (b) Measuring kinetic friction
l
h1
h0
1. This part is performed with the plastic cart only.
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2. From the critical height determined in part 2(a), raise the track to a slightly higher
inclination. Use a bubble level to make sure the track is not slanted to either side. Measure
the angle of inclination as in the previous part.
3. Using the scale on the side of the track, determine the starting point of the cart.
4. Add mass into the cart and measure the total mass. A good mass to start with is 200g or
above; otherwise it will be difficult to keep the cart moving in a straight line.
5. Place the cart on the track and allow it to move down the track while starting the stopwatch
simultaneously. Do not give the cart an initial push so that the initial velocity is zero. Make
sure the cart starts at the middle of the track and is moving down the track in a straight line.
The result will be affected significantly if the cart collides with the scale on the track or with
the sides of the track. If the cart is colliding into the sides of the track, repeat the trial. It
may take a few trials to get well acquainted with the technique of making the cart moving in
a straight line.
6. Stop the stopwatch when the cart reaches the destination, i.e. the end of the track. Cushion
the cart before it hits the table to prevent damage to both the table and the cart. Measure the
distance traveled by the cart.
7. Repeat the experiment 3 times for at least 3 different masses in the cart.
8. Calculate the coefficient of kinetic friction using the formula that you have derived
answering question 6 of the Preparatory Questions.  k  tan  
2 s 1  tan 2 
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gt 2
Present results of all measurements in the table, calculate uncertainties and give the value of
coefficient of static friction for the pair of surfaces “cork – aluminum” and “felt-aluminum” with
their uncertainties.
Using the results of measurements of friction for the plastic cart, show the coefficient of static
friction and coefficient of kinetic friction for the plastic cart. Which method – of Part 1 or of Part
2 – gives more precise result?
Additional Exercise.
Design an experiment and perform measurements to prove or disprove your predictions for the
behavior of functions Force vs. Time and Frictional Force vs. Force, drawn in dashed lines in
your answer to question 4 of the Preparatory Question.
Compare the graphs of theoretically predicted functions and experimentally obtained data.
Written by Yih Tang Yeo and Jody Chan in June 2012
Revised by Natalia Krasnopolskaia in October 2012
Revised by Xingxing Xing in July 2015