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Introduction

Friction is a small measurement that can have a monumental effect on any daily

routine such as driving or even walking.  Friction can dictate whether someone slips on

the ice or if there is a car crash on I-75 that will make you 45 minutes late for your big

interview.  It also plays a role in the medical industry with replacement joints.  Many

famous people have studied friction and its factors, including Leonardo Da Vinci in 1490.

It was researched whether the surface area of an object had an effect on the coefficient of

friction. Could having wider or narrower tires on your car decrease the stopping distance

and prevent that crash? Simple questions like these can affect the overall safety of daily

life that is taken for granted.

With so many practical uses of friction it is important to understand how the

concept works. Friction is the force on an object that opposes motion. The purpose of this

experiment was to determine if the surface area would affect the coefficient of static

friction. The global usage of the results of this experiment could go towards increasing

the safety and maximizing the efficiency of motor vehicles. The coefficient of friction

could be used to decrease the stopping distance of a vehicle or it could be used to resize

bearings to find the highest efficiency of bearings with certain surface areas.

On a smaller scale, understanding friction could be put to use in the athletic

world. Understanding frictional forces could lead to the innovation of newer, better

basketball and volleyball shoes which could allow a person to run faster, stop faster, and

jump higher.

This experiment was conducted through the use of wood blocks, rubber, and a

pulley. The contact between the rubber, on the bottom of the block, and the table the

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block was on caused the frictional force that was measured. The block was connected to a

force sensor via string and the force sensor was attached to a weight. When the weight

was dropped on the pulley, the block would slide across the table at a constant

acceleration. This constant rate, along with uniform mass between the blocks, ensured

that the surface area was the only thing being tested in the experiment.

The importance of friction comes with its practical uses. Understanding friction

and what could potentially affect it can lead to the innovation of new technology which

can produce the best coefficient of friction for the material and the scenario. This results

of this experiment can be utilized in the future for this new innovation.

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Review of Literature

The purpose of this experiment was to determine if surface area has a statistically

significant effect on the coefficient of friction.  This was tested using two wood blocks,

one with half the surface area of the other, with a rubber layer on the bottom.

The experiment was conducted by attaching a force sensor to the blocks. The

force sensor was also attached to a weight. The weight, on a string, was connected to a

pulley system, in which the weight was dropped from a constant height to pull the block

at a constant rate. The data from the force sensor was then analyzed and the force needed

to get the block moving was used to calculate the coefficient of static friction.

MCMILLAN WANTS GONE Friction is the force exerted on an object that opposes

motion. Static friction is the frictional force used to start the movement of an object while

kinetic friction is the force required to keep an object in motion. Many of the other

experiments found tested multiple variables, such as surface area and normal force. In

this experiment however, only surface area was tested, to show that it would have no

effect on the coefficient of static friction.

The coefficient of friction and all friction forces have an effect on daily life and a

large effect in engineering.  Friction is the resistance of two objects when they are in

contact.  Static friction is the force of friction when the objects are stuck together and is

greater than that if the kinetic friction - when the objects are moving relative to each

other.  Friction also plays a role in medical purposes as well. In one study, the frictional

forces on the hip joint were measured when people walk. The study was conducted in an

attempt to understand how these frictional forces can affect a hip replacement, in the

hopes that the results will lead to a better replacement that can prevent wear on the

implant (Damm, et al.).  

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        Many other previous experiments have been done regarding friction.  One

experiment tested the effect of the normal force and temperature on the coefficient of

friction.  It was concluded that as the normal force on an object increased, the coefficient

of friction also increased (Babu, Manisekar, and Starvin).  Another experiment done by

Leonardo da Vinci also stated that the increase in the normal force directly increased the

coefficient of friction (Eriksson, Bergman, and Jacobson).  Normal force is a relationship

between the mass of an object and gravity - it is the force exerted by the surface that an

object rests on. The normal force can be found by multiplying the mass of the object by

gravity. This was why the mass of the two blocks were held constant in the experiment -

to make sure that surface area was the only thing changing and therefore the only factor

tested.   

The following formula is used to calculate the coefficient of friction,:

        F represents the force in Newtons that was required to overcome the static friction

and move the wood block.  N represents the normal force acting on the wood block.  The

normal force is the mass multiplied by the acceleration of gravity (mg).  This is the equal

and opposite force from the weight that was pushing back up on the object.  Mu

represents the coefficient of friction..

        Experiments and studies have been done by Amonton and Coulomb, both

accomplished French physicists, on frictional forces (Desplanques).  Amonton

demonstrated by experiment the dependence of friction on the normal load, and the area

of contact between the two sliding surfaces.  Coulomb used an oak table with a sleigh and

a load plate to test the difference that normal force and surface area had on the coefficient

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of friction.  One of his explanations of friction was that the coefficient of friction

increased as the normal load increased (Desplanques). This background information led

to the hypothesis that the surface area would not affect the coefficient of friction in any

way as long as the normal force remained constant.

        Another article that supported the hypothesis that the coefficient would remain the

same regardless of the surface area stated Coulombs law (Hildenbrand, Bretault, and

Hoshimoto).  The law states:

with Ft representing the lateral force that is acting on the object from the pulley and

weight, and Fn representing the normal force that is acting on the object (Hildenbrand,

Bretault, and Hoshimoto).  Mu represents the coefficient of friction.  Since the normal

force of the object is calculated by multiplying the mass of the object with the

acceleration of gravity (mg), the normal force will remain the same as long as the mass

remains the same.  As long as the mass is held constant throughout the experiment and on

both blocks, the coefficient of friction of each block with a different surface area should

remain the same.  This also supports the current hypothesis that the researchers tested.

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Problem Statement

Problem:

To see if increasing or decreasing the surface area has an effect on the coefficient

of static friction on an object if the mass is held at a constant.

Hypothesis:

If the surface area of an object is changed while the mass is held constant, then

the coefficient of friction will remain the same.

Data Measured:

The surface area is the independent variable, and the coefficient of friction is the

dependent variable. The mass was held constant. The force used to overcome the static

friction was found and then converted to find the coefficient of friction. The coefficients

of the friction were analyzed and compared using a two sample t-test. Fifty trials were

run for each of the blocks.

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Experimental Design

Materials:

(2) Wood Block (8.1x8.1 cm and 11.4x11.4 cm)(2) Rubber Pads (8.1x8.1 cm and 11.4x11.4 cm)String (1m)Lab-QuestClay (100g)

Vernier Force SensorLogger ProScale (0.01 precision)Smart PulleyVernier LabQuestHanging Weights (50g and 20g)

Procedures:

1. Randomize the trials using the random integer function on the TI-nspire. Assign the number one to the large surface area and the number two to the small surface area. Randomize for 100 total trials.

2. Use clay to make the mass of each block equal to each other at 195 grams.

3. Attach a piece of rubber that has the same surface area as one side of the block to the bottom of the block using super glue. See Appendix B for instructions on how to build the blocks.

4. Tie a knot to make a loop on both ends of the string to connect it to the wood block and the force sensor.

5. Connect the force sensor to the Lab-Quest.

6. Drape a string connected to the force sensor over the pulley wheel and connect the weight to the string.

7. Drop the weight on the pulley to pull the force sensor at a constant rate. Allow the block to move across a flat surface to collect the lateral force to overcome the frictional force.

8. Stop the trial and analyze the force needed to overcome the static friction using the Logger Pro software. See Figure 3 below.

9. Wipe off the rubber and the counter that the block is sliding against. This will help eliminate outside factors, like dust, that will affect the results.

10. Divide the lateral force found by the normal force of the block to convert the Newtons found into the coefficient of static friction

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11. Repeat 49 times to get a total of 50 trials for each block.

12. Repeat Steps 4-10 for the second block.

Diagram:

Figure 1. Lab Setup

A picture of the lab setup is shown in Figure 1 above. Shown is a block of wood

attached to the force sensor. On the wood is one of two different pieces of rubber to cause

a frictional force and clay to balance the mass of each block. The force sensor is

connected to a LabQuest, which is connected to a computer to utilize the Logger Pro

software. The force sensor is also connected to a pulley and a weight. The weight will be

dropped on the pulley, thus pulling the wood block at a constant speed.

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Data and Observations

Table 1Data for Large Block

Trial

Surface Area (m2)

Force (N)

Coefficient of Static Friction

Trial Surface Area (m2)

Force (N)

Coefficient of Static Friction

1 129.96 0.962 6.54E-04 26 129.96 1.06 7.21E-042 129.96 0.993 6.76E-04 27 129.96 0.993 6.76E-043 129.96 0.993 6.76E-04 28 129.96 0.923 6.28E-044 129.96 1.03 7.01E-04 29 129.96 0.962 6.54E-045 129.96 0.962 6.54E-04 30 129.96 0.993 6.76E-046 129.96 1.03 7.01E-04 31 129.96 0.993 6.76E-047 129.96 0.993 6.76E-04 32 129.96 0.931 6.33E-048 129.96 0.962 6.54E-04 33 129.96 0.897 6.10E-049 129.96 0.993 6.76E-04 34 129.96 1.03 7.01E-0410 129.96 0.993 6.76E-04 35 129.96 1.06 7.21E-0411 129.96 0.993 6.76E-04 36 129.96 0.932 6.33E-04

12 129.96 0.962 6.54E-04 37 129.960.999

6 6.80E-0413 129.96 0.993 6.76E-04 38 129.96 1.03 7.01E-0414 129.96 0.993 6.76E-04 39 129.96 0.976 6.64E-0415 129.96 0.962 6.54E-04 40 129.96 1.03 7.01E-0416 129.96 0.962 6.54E-04 41 129.96 1.09 7.41E-0417 129.96 1.03 7.01E-04 42 129.96 1.02 6.94E-0418 129.96 0.962 6.54E-04 43 129.96 1.03 7.01E-0419 129.96 0.936 6.33E-04 44 129.96 1.07 7.28E-0420 129.96 1.06 7.21E-04 45 129.96 0.991 6.74E-0421 129.96 1.09 7.41E-04 46 129.96 0.962 6.54E-0422 129.96 0.934 6.33E-04 47 129.96 1.08 7.35E-0423 129.96 0.993 6.76E-04 48 129.96 1.02 6.94E-0424 129.96 0.933 6.33E-04 49 129.96 1.02 6.94E-0425 129.96 1.03 7.01E-04 50 129.96 1.08 7.35E-04

Table 1 above shows the results of each trial for the larger of the two blocks. The

tables show the surface area of the block, held constant, the force, and the calculated

coefficient of friction for each trial. Trial number 33 had the smallest coefficient of

friction at 6.10x10-4. The largest coefficient of friction occurred on trials 21 and 41, at a

value of 7.41x10-4. The range for the coefficient of friction of this block is 1.31x10-4.

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Table 2Observations for the Large BlockTrial Observations

1 The block accelerated slowly.2 The string fell off of the pulley at the end.3 The table was not wiped.4 The trial ran perfect.5 The force sensor disconnected and was reconnected.6 The block accelerated fast.7 The block accelerated slowly.8 Trial ran smooth.9 The table was wiped more than once.10 Trial ran smooth.11 The force sensor disconnected again.12 Trial ran smooth.13 The table had wired in the way.14 The block moved very slowly.15 The string fell off the pulley at the end.16 A different force sensor was used.17 The trial ran smoothly.18 The block seemed to be stuck.19 The trial went well.20 The block stuck more.21 The block seemed to stick to the table.22 The trial ran perfect.23 The block seemed to move faster than normal.24 Trial ran smooth.25 The block moved faster.26 The trial ran perfect.27 Trial ran smooth.28 The block was not wiped.29 Perfect trial.30 The block moved at a seemingly fast pace.31 String fe1l off of pulley.32 The block seemed to be stuck.33 The weights were dropped roughly.34 The block accelerated very slowly.35 The block seemed to move slower than normal.36 The blocked moved faster than normal.37 The block jerked forward.38 The trial ran perfect.

Trial Observations39 The lab quest died and had to be charged.

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40 The trial ran perfect.41 The block accelerated constantly.42 The trial ran perfect.43 The block had trouble starting to move.44 The trial ran perfect.45 The force sensor wire was stick in the blocks hook.46 The block moved smoothly.47 The block seemed to stick to the table.48 The block seemed to jerk forward.49 The table was not wiped.50 The block accelerated rapidly.

Table 2 above shows the observations for the large block. On trial 33, which had

the smallest coefficient of friction, the weight on the pulley was dropped more roughly

than other trials, possibly jerking the block and causing it to move more easily on the

table, thus lowering the coefficient of friction. The two trials which had the highest

coefficient, 21 and 41, the block seemed to stick to the table more (trial 21) and seemed

to accelerate at a constant rate (trial 41).

Table 3

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Data for Small BlockTrial Surface

Area (m2)Force (N)

Coefficient of Static Friction

Trial Surface Area (m2)

Force (N)

Coefficient of Static Friction

(µ)1 65.61 1.03 7.01E-04 26 65.61 0.935 6.36E-042 65.61 1.03 7.01E-04 27 65.61 1.05 7.14E-043 65.61 0.962 6.54E-04 28 65.61 0.962 6.54E-044 65.61 1.03 7.01E-04 29 65.61 0.962 6.54E-045 65.61 1.05 7.14E-04 30 65.61 0.962 6.54E-046 65.61 0.972 6.60E-04 31 65.61 1.02 6.94E-047 65.61 0.9996 6.80E-04 32 65.61 0.991 6.74E-048 65.61 0.982 6.68E-04 33 65.61 1.02 6.94E-049 65.61 1.06 7.21E-04 34 65.61 0.935 6.36E-0410 65.61 0.952 6.48E-04 35 65.61 1.02 6.94E-0411 65.61 0.983 6.67E-04 36 65.61 0.935 6.36E-0412 65.61 1.02 6.94E-04 37 65.61 0.932 6.34E-0413 65.61 1.06 7.21E-04 38 65.61 0.934 6.35E-0414 65.61 0.946 6.44E-04 39 65.61 0.934 6.35E-0415 65.61 1.004 6.83E-04 40 65.61 0.991 6.74E-0416 65.61 1.004 6.83E-04 41 65.61 0.991 6.74E-0417 65.61 1.07 7.28E-04 42 65.61 0.962 6.54E-0418 65.61 0.991 6.74E-04 43 65.61 0.935 6.36E-0419 65.61 1.02 6.94E-04 44 65.61 1.02 6.94E-0420 65.61 1.02 6.94E-04 45 65.61 0.935 6.36E-0421 65.61 1.02 6.94E-04 46 65.61 0.934 6.35E-0422 65.61 1.05 7.14E-04 47 65.61 0.991 6.74E-0423 65.61 0.935 6.36E-04 48 65.61 0.962 6.54E-0424 65.61 1.02 6.94E-04 49 65.61 0.935 6.36E-0425 65.61 0.935 6.36E-04 50 65.61 0.935 6.36E-04

Table 3 above shows the results of each trial for the smaller of the two blocks.

This table, like Table 1, shows the surface area of the small block, held constant, the

force, and the calculated coefficient of friction. The smallest coefficient of friction

happened on trial 34 at a value of 6.36x10-4. Trial 17 had the largest coefficient of friction

at 7.28x10-4. The range of coefficient of friction for the small block 0.92x10-4.

Table 4.Observations for the Small Block

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Trial Observations1 Trial ran smoothly.2 Block accelerated slowly.3 Table was not wiped.4 Trial ran smoothly.5 String came off the pulley.6 The weight was hit.7 Trial ran smoothly.8 Trial ran smoothly.9 Block accelerated quickly.10 Trial ran well.11 Table was not wiped.12 Block moved slowly.13 Wires were tangled.14 String came off the end of pulley.15 The weight hit the table.16 Force sensor hit the pulley.17 Trial went well.18 Block jerked forward.19 String tangled with the cord.20 Table and block not wiped.21 Block moved slower.22 Trial ran smoothly.23 Block went quickly.24 Force sensor hit the cord.25 LabQuest hit the force sensor.26 Trial went well.27 Block was not wiped off.28 Table was not wiped.29 Block stuck to table.30 String came off the pulley.31 Force sensor hit the cord.32 Trial ran smoothly.33 Trial ran smoothly.34 Block moved faster than normal.35 Block was not wiped off.36 Force sensor was hit.37 Trial went well.38 Block moved smoothly.

Trial Observations39 Trial ran well.40 Trial went well.41 The weight was dropped harshly.42 String fell off pulley.43 Trial ran smoothly.44 Trial ran well.45 Table was not wiped.46 Smooth trial.47 Block moved slowly.48 Trial went well.49 Block was not wiped.50 Trial ran smoothly.

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Table 4 above shows the observations for the smaller block. On trial 34,

mentioned above as having the smallest coefficient of friction for the smaller block, the

block seemingly moved faster than normal, meaning the block may have faced less

resistance. This could be the reason for the small coefficient of friction. The trial with the

highest coefficient of friction, trial 17, seemed to run well. This could indicate that the

value for this trial could be the actual coefficient of friction for this block.

Figure 2. Procedure Process

In Figure 2 above, two pictures are displayed, showing the process of

experimentation. In the first picture, the block is connected to the force sensor, which is

connected to the pulley and the weight. The string is being held to prevent the weight

from falling and therefore keeping the block from sliding. In the second picture, the string

was let go so the weight would pull the block and data could be collected.

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Figure 3. Logger Pro Data

In Figure 3 above, a screenshot of the Logger Pro software is shown. On the

graph is the data collected from an example trial. The area contained within the brackets

was analyzed to find the maximum point. This maximum is the force needed to get the

block moving, or the lateral force, that was applied to the block. This value was then

divided by the normal force of the block (its mass multiplied by the value of gravity) to

get the coefficient of friction for that trial as shown in Table 1 and Table 3. The

maximum of this particular trial is 1.031N.

μ= FN

= Fmg

Figure 4. Coefficient of Friction Equation

Figure 4 above shows the equation used to calculate the coefficient of static

friction for each block. Mu (μ) is the symbol for the coefficient of friction. The numerator

in the fractions, F, stands for the lateral force, which was the value collected from the

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Logger Pro software in each trial as shown in Figure 3. The denominator in the first

fraction represents the normal force of the block, which is equal to the mass of the block

multiplied by the value of gravity (9.8 m/s2) as shown in the denominator of the second

fraction. See Appendix A.1 for a sample calculation using this formula to find the

coefficient of friction.

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Data Analysis and Interpretation

The data collected from the experiment can be considered reliable because the

trials were randomized which helps eliminate bias and unknown interactions between the

trials. The trials were randomized by assigning the number one to the small block and the

number two to the bigger block. Using the random integer function on the TI-Nspire, the

trials were randomized for fifty trials for each of the blocks. The trials were repeated

many times which helps to reduce variability and allowing the effect of surface area to be

the only variable tested. This ensures consistent outcomes throughout the experiment and

allows any outliers to become apparent. Using the LoggerPro software, the force sensor

was zeroed between each trial to serve as a control for the experiment, keeping the trials

from affecting one another.

Figure 5. Box Plots of Data

Figure 5 above shows the box plots created of the data collected. The top box plot

shows the data from the small block trials and the bottom box plot shows the data from

the large block trials. Neither box plot has outliers. The top box plot is normally

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distributed, while the bottom box plot is slightly right skewed. The medians for the box

plots are fairly close to one another. The median for the top box plot is 6.755x10-4 and the

median for the bottom box plot is 6.741x10-4. The mean of the top box is 6.79x10-4 and

the mean for the bottom box plot is 6.71x10-4. There is overlap between both box plots

between their medians and maximums indicating that the surface area of the block did not

affect its coefficient of static friction.

To test if the surface area had an effect of the coefficient of static friction, a two

sample t-test was used. This test was used because means from two independent

populations were being compared and the standard deviation was unknown. A confidence

interval was also conducted at 90% confidence because the alternate hypothesis (shown

below) was that the two means were not equal to each other, and the alpha value used

was 0.05. Since the alternate hypothesis stated the means were not equal, the 0.05 had to

be on both sides, leaving the confidence interval at 90% confidence.

In order to run the two sample t-test, some assumptions had to be met. These

assumptions are that a simple random sample (SRS) was conducted, the populations are

independent, each population size is at least ten times the size of its respective sample

size, and each sample comes from a normal population. The first assumption, the SRS,

was met with the randomization of the trials. The second assumption of independent

populations was met with the randomization of the trials to ensure that one trial did not

affect another. The next assumption that the population is ten times the sample size is met

because the experiment can be run an infinite number of times. The final assumption,

normal populations, was met. Each block had at least 30 trials, thus by the central limit

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theorem (CLT), which states that 30 or more data points will produce a normal sampling

distribution, it can be assumed that this data came from a normal distribution.

H 0 : μ1=μ2

H a : μ1≠ μ2

Figure 6. t test Hypotheses

Figure 6 above shows the null and alternative hypothesis for the two sample t test.

The null hypothesis states that the coefficient of friction for the small block is equal to the

coefficient of friction for the large block. The alternative hypothesis states that the coefficient of

friction for the small block is not equal to the coefficient of friction for the large block.

Figure 7. T-Test Results

In Figure 7, shown above, the results from the two sample t test are displayed.

The t-value, p-value, and degrees of freedom are shown, as well as the sample means,

sample standard deviations, and the sample sizes from each block. The t-value of 1.28724

yielded a p-value of 0.201072. Fail to reject the null hypothesis, because the p-value is

greater than the alpha level of 0.05. There is significant evidence that the coefficient of friction of

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the small block is equal to the coefficient of friction for the large block. The p-value of 0.201072

is larger than the alpha level of 0.05. There is a 20% chance of getting these results by chance

alone if the null hypothesis is true. A sample calculation for finding the t-value is shown in

Appendix A.2.

Figure 8. Confidence Interval Results

Figure 8 above shows the results from the confidence interval at a 90%

confidence level. The lower bound of the confidence interval is -0.000002 and the upper

bound is 0.000018. It can be said, with 90% confidence, that the true population

difference of the coefficients of friction lies between the boundaries of the confidence

interval. The difference of nearly zero falls between the boundaries of -0.000002 and

0.000018, thus supporting the null hypothesis of the test and the hypothesis of the

experiment by showing that there is no difference in the coefficients of friction of the two

blocks. A sample calculation for the confidence interval can be found in Appendix A.3.

Based on the results of the data, the boxplots, and the test conducted, it was

concluded that the surface area of the blocks did not have an effect on the coefficient of

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friction of the block. The t-test conducted showed that the null hypothesis should not be

rejected, thus indicating what the normally distributed, overlapping box plots showed –

the surface area of the block did not have an effect on the coefficient of friction of the

block. The data collected also supported this because the values received were fairly

close to each other, having nearly identical sample means of 0.000679 and 0.000671 for

the small block and large block respectively.

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Conclusion

        The purpose of this experiment was to see if changing the surface area of a block

would affect its coefficient of static friction. To test this, rubber was added to the bottom

of wood blocks. The larger wood block had a surface area exactly twice that of the small

block. The mass of the blocks was held constant, at 195 grams, by adding clay to the

blocks. The blocks were then pulled across a flat surface at a constant acceleration. This

was accomplished by connecting the block to a pulley and a weight. The weight would

fall from a constant distance at a constant acceleration, thus pulling the block at a

constant acceleration. The force needed to start the block moving was collected from

trials and the data was used to calculate the coefficients of static friction, which were then

analyzed.

        This experiment was similar to many others that have previously been done.

However, this experiment sought to understand the relationship between surface area and

the coefficient of static friction directly, while other experiments focused on the

interactions between surface area and other factors. Some of these other factors included

differentiating the materials used to create the frictional force and the slope of the flat

surface that the block was moved on.  Another factor that was tested was how water

might affect the coefficient of friction by scientists Lasse Makkonen and Maria

Tikanmäki (“Improving the Reliability…”).

        The hypothesis stated that the surface area would have no effect on the coefficient

of static friction on wood blocks, so long as the mass was held constant. The analysis

performed agreed with this hypothesis. A p-value of 0.201072 meant the coefficient of

static friction would be the same for both surface areas. The data collected also supports

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this hypothesis that the change in surface area would not affect the coefficient of static

friction as long as mass was held constant, with a mean coefficient of friction for the

small block of 6.79x10-4 and a mean coefficient of friction of 6.71x10-4 for the larger. The

average coefficient of static friction for the blocks were nearly the same, with a

difference of 8.0x10-6, thus supporting that surface area has no effect on the coefficient of

friction.

        These results make sense in terms of scientific accuracy. The reason that the

surface area of an object will not affect the object’s coefficient of static friction is

because it is dependent on the force of friction and the normal force, and the normal force

of the object does not change. For example, if the coefficient of static friction of two

blocks, one longer than the other, is found, the coefficient of friction between the two will

be the same, assuming they are made of the same materials. This is because the two

blocks will have the same mass thus the same normal force because the normal force is

equal to its mass multiplied by its acceleration of gravity. Even though one block has a

smaller area, its pressure will be higher than the other block (Holzner). Pressure is the

force exerted on an object by another that it is in contact with.

p= fa

P represents the pressure of the object, and f represents the normal force of the object

while A is the surface area. The normal force is divided by the area to find the pressure

of the object. This inverse relationship between area and pressure ensures that the force

of friction needed to pull it will be the same for each surface area and the mass of the

object is not affected.  It is because of this reason that the static friction coefficient of one

block will be equal to that of the other block.  

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The results of this experiment agree with the current findings in the scientific

field. Experiments done previously have also concluded that the surface area of an object

does not affect its coefficient of friction if the normal force is held constant. The normal

force of an object is the product of its mass and gravity; it is the force at which the object

is being pulled down by gravity. Experiments done by Amontons, a famed physicist,

yielded results that agree with those of this experiment. His results led him to conclude

two things about friction. The first of Amontons’ laws states that frictional force is

independent of contact area (surface area). The second law states that frictional forces are

proportional to the applied load (normal force) so as long as the normal force remains the

same, the frictional force will also remain the same (Baragiola).  Amontons partially

based his laws off the experiments done by Coulomb, another famed physicist, as well as

his own experiments. Coulomb came to the same conclusions as Amontons, and the work

he did led to the following equation:

μ=F t

Fn,

with F trepresenting the translational force and Fn representing the normal force of the

blocks (Hildenbrand). This equation was used in this experiment to calculate the

coefficient of static friction.

The value of this research comes in its real-life applications. Understanding that

surface area has no effect on friction can lead to better innovations in the engineering and

medical fields. For example, knowing that surface area will not affect its friction, a

medical engineer can design a hip replacement that has a size that will maximize comfort

for the patient.

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During the course of the experiment several errors were found. The first of which

was dust that collected on the table and the block. To combat this, both were wiped off

with a rag, however, this was not done between every trial. The dust could have made the

block move more easily on the table, thus reducing that trial’s coefficient of friction.

Another error occurred towards the end of trials when the rubber began to wear out. This

too could have reduced the force needed to move the block, and consequently its

coefficient of friction. There were also technology issues throughout the experiment. At

one point, the LabQuest being used had to be replaced because it had malfunctioned.

Also the force sensor would periodically hit the pulley. The force sensor could have also

created more drag, which could have raised the coefficient of friction. If the experiment

was to be repeated, the above errors would be corrected to ensure the data collected is as

accurate as possible.

Further research could widely expand the factors that are tested.  A wider range of

surface areas could have been tested along with additional factors.  Water or moist

surfaces could be tested along with variations in the temperature of one of the surfaces or

both.  Another factor that could have been tested was the shape of the object, as well as

the materials used to cause a frictional force.

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Appendix A: Sample Calculations

1

μ= FN

= Fmg

μ= FN

= 0.962150∗9.8

μ=¿0.000654 = 6.54x10-4

Figure 1. Coefficient of Friction Sample Calculation

Figure 1 above shows how the coefficient of friction was calculated for trial 1 for

the bigger block. To solve for mu (μ), the lateral force (F), mass of the block (m), and

gravity (g), were plugged into the equation. Then the lateral force was divided by the

normal force (N) to get the coefficient of friction. For this trial, the coefficient of friction

was 6.54x10-4.

2

t=x̄1− x̄2

√ S12

n1+

S22

n2

t= 0.000679−0.000671

√ 0.00003250

+ 0.00002950

t=1.28724

Figure 2. Two Sample t Test Sample Calculation

Figure 1 shows how the t value was found for the entire experiment. To solve for

t, the mean of the large block (x̄2) was subtracted from the mean of the small block ( x̄1),

then that was divided by the square root of the sample standard deviation squared of the

small block (S12) divided by the number of trials (n1), plus the sample standard deviation

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squared of the large block (S22) divided by the number of trials (n2). The t value was

found to be 1.28.

3

CI=( x̄1− x̄2 )± t ¿√ S12

n1+

S22

n2

CI=¿(0.000679−0.000671¿± 1.645(√ 0.00003250

+0.000029

50)

CI=−0.000002¿0.000018

Figure 3. 90% Confidence Interval Sample Calculation

Figure 3 above shows the sample calculation for the 90% confidence interval. To

find the lover boundary, the mean of the large block (x̄2) was subtracted from the mean of

the small block (x̄1), then the square root of the sample standard deviation squared of the

small block (S12) divided by the number of trials (n1), plus the sample standard deviation

squared of the large block (S22) divided by the number of trials (n2) was all multiplied by

the t star (t ¿¿ value and subtracted from the difference in the means. To find the upper

boundary, the whole square root times the t star (t ¿¿ value was added to the difference in

the means.

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Appendix B: Block Construction

To construct the block, the rubber and its respective block must have the same

dimensions. Once the dimensions of the rubber and the block are the same, the rubber

may be attached to the bottom of the block using super glue. Once the glue has dried the

hook must be inserted into one side of the block. To do this, drill a hole in the side of the

block with a diameter slightly smaller than the hook. Then, insert the hook into the block

and make sure that the hook is secure and will not fall out of the block. Repeat this

process on the other block.

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