2 PHY122 lab report

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Friction: Determination of μS and μK

Introduction When two bodies interact by direct contact of their surfaces, the interaction forces are called

contact forces. There are two kinds of contact forces: the normal force – a force perpendicular

to the contact surface, and the friction force - a force parallel to the contact surface. Experiments

show that a body moving on a horizontal surface slows down and finally stops if no external

force being applied to maintain its motion. That means there is a force acting on the moving

object in the direction opposite its motion and parallel to the contact surface. That force is called

friction force. We distinguish between two types of friction forces: static friction force – fs - acts

on an object at rest, prevents it from sliding; and kinetic friction force – fs- acts on an object in

motion.

Frictional forces are very complicated, however we can apply a simplified model according

to which the maximum magnitude of the static frictional force fs,max and the magnitude of the

kinetic friction force fk are proportional to the magnitude of the normal force N acting between

the two surfaces:

fs,max = µs N (1)

where µs is called the coefficient of static friction. That means in a particular situation Fs ≤ µs N.

Fk = µk N (2)

where µk is called the coefficient of kinetic friction.

The coefficient of static friction is the slope of a linear graph friction force vs normal force.

In this case, friction force is plotted on the vertical axis of a graph and normal force is on the

horizontal axis. Notice that the force of static friction can take on a range of values from zero to

its maximum. It changes proportionally as the applied force changes. This is an important

difference between static and kinetic friction since kinetic friction can have only one value.

(Figure 1.)

Figure 1. A graph of the friction force magnitude f as a function of the applied force F

The coefficient of static friction is always larger than the coefficient of kinetic friction. From

everyday life experience we know that on a horizontal surface, a larger force is required to make

an object moving than is required to keep it moving at a constant velocity (Fig. 2).

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a) a box is at rest: Fs = T1 b) a box is in uniform motion Fk =T2 < T1

Fig. 2. Horizontal forces acting on the box. (a) a box is at rest; (b) a box is in uniform

motion. T is the rope tension force; fs - static friction force; fk - kinetic friction force; fk < fs,

max.

You must overcome the maximum static frictional force to get the object moving, but once

this is accomplished, you need only to overcome the kinetic friction force (which is smaller than

the maximum static frictional force) to keep the object moving at a constant velocity. The

coefficient of friction changed from static to kinetic the moment you exceeded the maximum

static friction force.

In this lab, we will take measurements for which the random errors are relatively large (roughly

10% of the measured values). We will use a statistical analysis to determine a final measured

value with proper uncertainty.

Text Reference: Y&F 5.3

Objectives

To measure the coefficient of static and kinetic friction between the surface of the block and lab

table; to check if the collected experimental data fit normal distribution curve.

Equipment: weights, wooden block, force sensor, Data Studio. A sketch of the experimental

setup is shown below.

Procedure

You will pull a weighted block, using a force sensor ( an electronic “spring scale” ) and the

computer ( Data Studio ) to record the tension in the pulling string during the pull.

I. Calibrate the force sensor before beginning the formal experiment.

1) Open the Data Studio program: Labs/PHY 122/ Friction 2) Hang the sensor from the provided lab stand. 3) In the Data Studio program, choose “Setup”, then “Calibrate Sensor”, then “2-Point

Calibration”.

T 1

F

s

T

2

F

k

T 1 > T

2

3

4) With nothing hanging from the sensor, set the first value in Data Studio to zero, then press the “Tare” button on the force sensor itself, and finally select “Read from Sensor” in Data

Studio.

5) Put a 1.00 kg mass to hang from the sensor. Set the second value in Data Studio to 9.81, select “Read from Sensor”.

6) Check your calibration by taking 40 seconds of data with the 1.00 kg mass hanging from the sensor. You should see a line with a zero slope at 9.81 N.

Let each group member record a practice run or two. Endeavor to make five to eight

smooth, short, straight line pulls, each one starting from rest during the 40 second recording

time. Your data should resemble the figure. Note that each of the pulls has three distinct sections

(labeled on the first pull in the figure): (a) before the block starts moving, (b) while the block is

moving with approximately constant speed, and (c) while the block is stopping. We are not

interested in section (c).

II. Experiment

1) Use two weights of the wooden block (the wide wooden side of the block should be down) and make runs for 40 short pulls.

2) Do Analysis Part I and II. 3) Remove one weight and repeat step one. Write down the remaining weight. 4) For Data collected in step (3) you need to do only Analysis Part I.

Figure 1. Three pulls are shown in the figure. Tension is on the vertical axis and time is on the

horizontal axis.

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Analysis Part I:

1) Your need to determine two values for each short pull: (1) the maximum force of static friction (ƒs

max), and (2) the force of kinetic friction (ƒk).

2) The force of static friction is taken to be equal to the measured tension just before the block begins to slip (labeled in the figure for pulls one and three).

3) The force of kinetic friction is taken to be the average tension while the block is slipping with approximately constant speed (indicated in pull two of the figure).

4) Use Data Studio’s “Smart Tool” icon for determining ƒs max. To determine ƒk, highlight the

selected region and choose “Σ” icon and “mean” from the drop down menu.

5) Record the 40 values of ƒs max and ƒk in separate columns in GA and find the mean

( max

s f and

k f ) and standard deviation (σn-1). Calculate the uncertainties in both types of

friction forces.

6) Calculate the coefficient of static (μS) and kinetic friction (μK) and their uncertainties. For this calculation the uncertainty in the weight may be ignored in comparison to the large

uncertainties in the frictional forces.

Analysis Part II:

1) If the errors are truly random and normally distributed, then there is a 68% chance that your mean value is within one stand. dev. of the mean value (±σn-1) which would be obtained by

an infinite number of measurements.

2) Make a histogram for one of your columns of friction data; mark ±σn-1 and ±2σn-1 on your histogram.

3) In your conclusion, discuss whether or not this column of data is normally distributed; are ~95% of the data points within 2σn-1’s of measurements?

Notes and Hints:

What is below is not meant to be an exhaustive list of what should be put in your reports, but

should be thought of reminders of things to think about during your lab period.

1) Make sure you attach a properly labeled histogram to your report. Are the data in the histogram normally distributed? Explain how you arrive at your answer.

2) You should include in your report: a table with a properly reported values of μS and μK and their errors for the experiment with one added weight and a second table for properly reported

values of μS and μK and their errors for the experiment with two added weights. Make sure to

include the calculations for how you arrive at your values of μS and μK and their errors in Data

Analysis.

3) Compare the μS and μK results of the class as a whole. Are the values consistent? Are the results independent of the weight being added to the cart? If another group reported results are not consistent with the class as a whole there is no need to speculate as to why, just note the

inconsistency. If your results are inconsistent with the class as a whole, please be sure to

address in detail reasons why that happened. Don’t forget the general requirement of error

discussion as outlined in the syllabus.

__MACOSX/2/._Lab Manual - Friction.pdf