Physics Lab

Lab Report Unit 3: FREE FALL & REACTION TIME 1

Lab Report Unit 3

Coefficient of Friction and Angle of Repose

Diego Abad

Broward College

PHY2048L, Physics Cal I Lab

Dr. Delonia Wiggins

February 26th, 2021

Lab Report Unit 3: FREE FALL & REACTION TIME 2

I did the measurements of the height from where a coin, a button, and a wooden toothpick

started sliding over a meter stick and then converted the centimeter units into meter, and I also

use an online simulator to measure the force used to move an object of different masses over

three different surfaces, and then I proceeded to height of the objects to calculate the value of its

coefficient of friction, and then calculate the percent error in relation to internet values of the

material, and for the simulation I proceed to use the forces to calculate the surfaces coefficient

of static and kinetic friction. The results I get for the coin μ=0.315 with a percent error of

1.61%, for the button μ=0.294 and % error = 26.5%, and for the wooden toothpick μ=0.486 and

% error = 2.8%, and the first surface had a 𝜇𝑠 = 0.936 𝑎𝑛𝑑 𝜇𝑘 = 0.403, the second surface

had a 𝜇𝑠 = 0.513 𝑎𝑛𝑑 𝜇𝑘 = 0.225,and the third surface had a 𝜇𝑠 = 0.629 𝑎𝑛𝑑 𝜇𝑘 = 0.571. I

conclude that the experiment coefficient of friction for my objects (except the button) are close to

the actual values, and that the surfaces don’t change their coefficient of friction regardless of

mass.

Introduction:

This lab will calculate the coefficient of friction of three different object sliding over a

meter-stick, which will be elevated until the object starts moving, to then record the height at which

the objects started sliding. Moreover, we will use a simulator of an object being dragged by a

tensional force along a surface, to then calculate the coefficient of friction for 7 different masses,

in which all 7 masses are dragged along three different surfaces. Also, during the experiment we

will be deriving their respective formulas to calculate their respective coefficients of friction, to

then calculate the mean and briefly compare how off from each mass value the mean is.

General Principles:

Lab Report Unit 3: FREE FALL & REACTION TIME 3

For Part 1, we will have to know how to convert centimeters into meters, by using the

following formula:

𝑿𝒄𝒎 ∗ 𝟏𝒎

𝟏𝟎𝟎𝒄𝒎 =

𝑿

𝟏𝟎𝟎 𝒎

Then, we will be using the formula for the mean, the uncertainty, the standard deviation,

and the relative error from the Lab 1 Manual:

Formula for the mean:

�̅� = 𝟏

𝑵 ∑ 𝑴𝒊

𝑵

𝒊

Formula to find Relative error steps bellow:

𝒅𝒊 = 𝑴𝒊 − �̅�

Formula for the standard deviation:

𝑶𝒊 = √ 𝟏

𝑵 √∑|𝒅𝒊|

𝟐

𝑵

𝑰

Formula for the relative error:

𝜀 = 𝑶𝒊

�̅�

Then, we will have to know the Second Law of motion, which states that if an object

if moving with a constant velocity, the sum of all forces (net force) equals 0.

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After that, we will need to know the formula of how to find the force of friction, how to

find the angle of a triangle, how to find the base of a triangle, and how to derive the force of the

x-component of an object falling from a specific angle, as well as the force of the y-component.

𝑭𝒇 = 𝑭𝒏 ∗ 𝝁

𝜽 = 𝐚𝐫𝐜𝐬𝐢𝐧 ( 𝒉𝒆𝒊𝒈𝒉𝒕

𝒉𝒚𝒑𝒐𝒕𝒉𝒆𝒏𝒖𝒔𝒆 )

Base = √𝒉𝒚𝒑𝒐𝒕𝒉𝒆𝒏𝒖𝒔𝒆𝟐 − 𝒉𝒆𝒊𝒈𝒉𝒕𝟐

𝑭𝒈𝒙 = 𝐬𝐢𝐧(𝜽) 𝒎𝒈

𝑭𝒈𝒚 = 𝐜𝐨𝐬(𝜽) 𝒎𝒈𝝁

Finally (for Part 1), we will need to use the formula to find the percentage error of an

experimental value and the expected value:

𝑷𝒆𝒓𝒄𝒆𝒏𝒕 𝑬𝒓𝒓𝒐𝒓 = |𝑬𝒙𝒑𝒆𝒓𝒊𝒎𝒆𝒏𝒕𝒂𝒍 𝒗𝒂𝒍𝒖𝒆 − 𝑬𝒙𝒑𝒆𝒄𝒕𝒆𝒅 𝒗𝒂𝒍𝒖𝒆|

𝑬𝒙𝒑𝒆𝒄𝒕𝒆𝒅 𝒗𝒂𝒍𝒖𝒆 ∗ 𝟏𝟎𝟎

For Part 2, we will be using the same concept to find the coefficient of friction (Newton’s

Second Law).

Methods:

For Part 1, I will start by using a meter stick to slide the coin, the button, and the wooden

toothpick, which must be lifted until the objects starts moving. I will record the height at which

the object starts moving by using 2 30cm rulers, and then I will convert each height into meters.

After that, I will calculate each objects’ mean, standard deviation, and relative error by using the

formulas stated in the General principles tab. Then, I will measure the mass of each object by using

Lab Report Unit 3: FREE FALL & REACTION TIME 5

an small kitchen balance used to measure small amounts of condiments. After that, I will derive a

formula for the coefficient of friction by knowing that the objects are moving a constant velocity,

to then calculate the angle at which each object starts falling using the angle formula that can be

found on the general principles tab. Then, I will calculate the base of the triangle that all objects

formed while sliding, and then I will calculate the value of the coefficient of friction by using the

derived formula I calculated before. Finally, I will use coefficient of frictions found on the internet

to calculate the percent error of each of my experimental values.

For Part 2, I will use a simulator that it is provided by the Lab Manual 3, to then calculate

the coefficient of friction (both static and kinetic) of an object, changing its mass 7 times and each

time I will test it in three different surfaces. After that, I’ll derive the formula for the coefficient of

friction, which will be different than the other one calculated in Part 1 since in this case the object

doesn’t have an angle of inclination (but the tension inflicted in the object could have). This

simulation displays the graph of the force used over time, so in other to find the coefficients, I will

look at the graph and record how much force is needed to move the object. For the static coefficient

of friction, I will use the highest amount of force use to move the object in the first place, and for

the kinetic coefficient of friction I will use the constant force used to move the object along the

surface. After that, I’ll calculate the mean of all surface’s coefficients of friction in order to

compare it to each coefficient of friction found it in each surface for each mass.

Results:

Part 1

1. Finding the mean

a. Coin

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Height of inclination (cm) Height of inclination (m)

30.5 0.305

30 0.3

29.5 0.295

30.3 0.303

29.8 0.298

Height of inclination (cm) Height of inclination (m)

28.5 0.285

28.3 0.283

27.9 0.279

28.4 0.284

28.6 0.286

Actual Value (m) Round Value (m)

Mean 0.3002 0.3

Actual Value (m) Round Value (m)

Mean 0.2834 0.283

Height of inclination (cm) Height of inclination (m)

43.5 0.435

43.8 0.438

43.6 0.436

43.9 0.439

43.6 0.436

Actual Value (m) Round Value (m)

Mean 0.4368 0.437

Height of inclination (m) Uncertainity Uncertainity squared

0.305 0.005 0.000025

0.3 0 0

0.295 -0.005 0.000025

0.303 0.003 9E-06

0.298 -0.002 4E-06

Standard Deviation 0.003549648 0.004

b. Button

c. Toothpick Wood

2. Finding the standard deviation

a. Coin

b. Button

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Height of inclination (m) Uncertainity Uncertainity squared

0.285 0.002 4E-06

0.283 0 0

0.279 -0.004 0.000016

0.284 0.001 0.000001

0.286 0.003 9E-06

Height of inclination (m) Uncertainity Uncertainity squared

0.435 -0.002 4E-06

0.438 0.001 1E-06

0.436 -0.001 0.000001

0.439 0.002 4E-06

0.436 -0.001 0.000001

Standard Deviation 0.00244949 0.002

Standard Deviation 0.00148324 0.001

Relative Error 0.007067138 0.007

Relative Error 0.013333333 0.013

Relative Error 0.00228833 0.002

Mass 0.003 kg

c. Toothpick Wood

3. Finding the Relative Error

a. Coin

b. Button

c. Toothpick Wood

4.

a. Coin

Lab Report Unit 3: FREE FALL & REACTION TIME 8

Mass 0.00083 kg

Mass 0.00004 kg

b. Button

c. Toothpick Wood

5.

Deriving the formula for coefficient of friction and finding the angle

∑ 𝑭 = 𝒎𝒈𝒔𝒊𝒏(𝜽) − 𝒎𝒈𝒄𝒐𝒔(𝜽)𝝁 = 𝟎 −→ 𝒎𝒈𝒔𝒊𝒏(𝜽) = 𝒎𝒈𝒄𝒐𝒔(𝜽)𝝁 −→ 𝝁 = 𝐭𝐚𝐧 (𝜽)

a. Coin

Angle 𝜽: 𝒔𝒊𝒏−𝟏(𝟎. 𝟑/1.0) =17.457 ≈ 17.5 °

b. Button

Angle 𝜽: 𝒔𝒊𝒏−𝟏(𝟎. 𝟐𝟖𝟑/1.0) ≈ 16.4°

c. Toothpick Wood

Angle 𝜽: 𝒔𝒊𝒏−𝟏(𝟎. 𝟒𝟑𝟕/1.0) =25.913 ≈25.9 °

6.

Base of Triangle

a. Coin

B = √𝟏𝟐 − 𝟎. 𝟑𝟐 = 𝟎. 𝟗𝟓𝟒𝟑𝟗 ≈ 𝟎. 𝟗𝟓𝟒𝒎

b. Button

Lab Report Unit 3: FREE FALL & REACTION TIME 9

B ≈ 𝟎. 𝟗𝟓𝟗𝒎

c. Toothpick Wood

B ≈ 𝟎. 𝟖𝟗𝟗𝒎

7.

Friction coefficient

a. Coin

𝝁 = tan (𝟏𝟕. 𝟓°) = 𝟎.𝟑

𝟎.𝟗𝟓𝟒 ≈0.315

b. Button

𝝁 ≈ 𝟎. 𝟐𝟗𝟒

c. Toothpick Wood

𝝁 = 𝟎. 𝟒𝟖𝟔

8.

Friction coefficient Internet Values

a. Coin

𝝁 =0.2 to 0.5

b. Button

𝝁 =0.4

c. Toothpick Wood

Lab Report Unit 3: FREE FALL & REACTION TIME 10

Percentage Error (%) Round Percentage Error (%)

1.612903226 1.61

Percentage Error (%) Round Percentage Error (%)

26.5 26.5

Percentage Error (%) Round Percentage Error (%)

2.8 2.8

𝝁 =0.25 to 0.5

9. Percent Error

a. Coin

𝑼𝒔𝒊𝒏𝒈 𝒂𝒏 𝝁 = 𝟑. 𝟏 𝑰𝑵𝑻𝑬𝑹𝑵𝑬𝑻 𝑽𝑨𝑳𝑼𝑬

𝑷𝒆𝒓𝒄𝒆𝒏𝒕 𝑬𝒓𝒓𝒐𝒓 = |𝟎.𝟑𝟏𝟓−𝟎.𝟑𝟏|

𝟎.𝟑𝟏 𝒗𝒂𝒍𝒖𝒆 ∗ 𝟏𝟎𝟎 = 1.6129 ≈ 𝟏. 𝟔𝟏

b. Button

𝑼𝒔𝒊𝒏𝒈 𝒂𝒏 𝝁 = 𝟒 𝑰𝑵𝑻𝑬𝑹𝑵𝑬𝑻 𝑽𝑨𝑳𝑼𝑬

c. Toothpick Wood

𝑼𝒔𝒊𝒏𝒈 𝒂𝒏 𝝁 = 𝟓. 𝟏 𝑰𝑵𝑻𝑬𝑹𝑵𝑬𝑻 𝑽𝑨𝑳𝑼𝑬

Part 2

Question 1 to 4: Record values and Surface

Lab Report Unit 3: FREE FALL & REACTION TIME 11

Question 5: Deriving formula for the coefficient of friction

∑ 𝑭 = (𝑻 ∗ 𝒄𝒐𝒔(𝜽)) − 𝒎𝒈𝝁 = 𝟎−→ 𝑻 = 𝒎𝒈𝝁 −→ 𝝁 = 𝑻𝒄𝒐𝒔(𝜽)

𝒎𝒈

Question 6 to 7: Finding the coefficient of friction (static and kinetic), as well as the max force

used.

Mass 1:

Surface #1:

𝒇𝒎𝒂𝒙 = 𝟖. 𝟑𝑵

Glass on Glass Wood on Lab Table Aluminium on Steel

Trial Changed mass (g) Changed mass (kg) Surface #1 Surface #2 Surface #3

#1 906 0.906

#2 880 0.88

#3 1010 1.01

#4 1192 1.192

#5 1310 1.31

#6 1133 1.133

#7 1265 1.265

Lab Report Unit 3: FREE FALL & REACTION TIME 12

𝝁𝒔 = 𝟖. 𝟑𝑵𝒄𝒐𝒔(𝟎)

𝟎. 𝟗𝟎𝟔𝒌𝒈 ∗ 𝟗. 𝟖 𝒎 𝒔𝟐

= 𝟖. 𝟑𝑵

𝟖. 𝟖𝟕𝟖𝟖𝑵 = 𝟎. 𝟗𝟑𝟒𝟖𝟏𝟏𝟎𝟏𝟎𝟓 ≈ 𝟎. 𝟗𝟑𝟓

𝒇𝒌 = 𝑭𝑵 = 𝟑. 𝟓𝑵

𝝁𝒌 = 𝟑. 𝟓𝑵𝒄𝒐𝒔(𝟎)

𝟎. 𝟗𝟎𝟔𝒌𝒈 ∗ 𝟗. 𝟖 𝒎 𝒔𝟐

= 𝟑. 𝟓𝑵

𝟖. 𝟖𝟕𝟖𝟖𝑵 = 𝟎. 𝟑𝟗𝟒𝟏𝟗𝟕𝟒𝟏𝟒 ≈ 𝟎. 𝟑𝟗𝟒

Surface #2:

𝒇𝒎𝒂𝒙 = 𝟒. 𝟓𝑵

𝝁𝒔 = 𝟒. 𝟓

𝟎. 𝟗𝟎𝟔 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟓𝟎𝟕

𝒇𝒌 = 𝑭𝑵 = 𝟐𝑵

𝝁𝒌 = 𝟐

𝟎. 𝟗𝟎𝟔 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟐𝟐𝟓

Lab Report Unit 3: FREE FALL & REACTION TIME 13

Surface #3:

𝒇𝒎𝒂𝒙 = 𝟓. 𝟗𝑵

𝝁𝒔 = 𝟓. 𝟗

𝟎. 𝟗𝟎𝟔 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟔𝟔𝟓

𝒇𝒌 = 𝑭𝑵 = 𝟒𝑵

𝝁𝒌 = 𝟒

𝟎. 𝟗𝟎𝟔 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟒𝟓𝟏

Mass 2:

Surface #1:

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𝒇𝒎𝒂𝒙 = 𝟖. 𝟏𝑵

𝝁𝒔 = 𝟓. 𝟗

𝟎. 𝟖𝟖 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟗𝟑𝟗

𝒇𝒌 = 𝑭𝑵 = 𝟑. 𝟓𝑵

𝝁𝒌 = 𝟑. 𝟓

𝟎. 𝟖𝟖 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟒𝟎𝟔

Surface #2:

Lab Report Unit 3: FREE FALL & REACTION TIME 15

𝒇𝒎𝒂𝒙 = 𝟒. 𝟒𝑵

𝝁𝒔 = 𝟒. 𝟒

𝟎. 𝟖𝟖 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟓𝟏𝟎

𝒇𝒌 = 𝑭𝑵 = 𝟏. 𝟗𝑵

𝝁𝒌 = 𝟏. 𝟗

𝟎. 𝟖𝟖 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟐𝟐𝟎

Surface #3:

𝒇𝒎𝒂𝒙 = 𝟓. 𝟒𝑵

𝝁𝒔 = 𝟓. 𝟒

𝟎. 𝟖𝟖 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟔𝟐𝟔

𝒇𝒌 = 𝑭𝑵 = 𝟒𝑵

𝝁𝒌 = 𝟒

𝟎. 𝟖𝟖 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟒𝟔𝟒

Lab Report Unit 3: FREE FALL & REACTION TIME 16

Mass 3:

Surface #1:

𝒇𝒎𝒂𝒙 = 𝟗. 𝟏𝑵

𝝁𝒔 = 𝟗. 𝟏

𝟏. 𝟎𝟏 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟗𝟏𝟗

𝒇𝒌 = 𝑭𝑵 = 𝟒𝑵

𝝁𝒌 = 𝟒

𝟏. 𝟎𝟏 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟒𝟎𝟒

Lab Report Unit 3: FREE FALL & REACTION TIME 17

Surface #2:

𝒇𝒎𝒂𝒙 = 𝟓. 𝟏𝑵

𝝁𝒔 = 𝟓. 𝟏

𝟏. 𝟎𝟏 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟓𝟏𝟓

𝒇𝒌 = 𝑭𝑵 = 𝟐. 𝟏𝑵

𝝁𝒌 = 𝟐. 𝟏

𝟏. 𝟎𝟏 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟐𝟏𝟐

Surface #3:

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𝒇𝒎𝒂𝒙 = 𝟔. 𝟏𝑵

𝝁𝒔 = 𝟔. 𝟏

𝟏. 𝟎𝟏 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟔𝟏𝟔

𝒇𝒌 = 𝑭𝑵 = 𝟒. 𝟕𝑵

𝝁𝒌 = 𝟒. 𝟕

𝟏. 𝟎𝟏 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟒𝟕𝟓

Mass 4:

Surface #1:

Lab Report Unit 3: FREE FALL & REACTION TIME 19

𝒇𝒎𝒂𝒙 = 𝟏𝟎. 𝟗𝑵

𝝁𝒔 = 𝟏𝟎. 𝟗

𝟏. 𝟏𝟗𝟐 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟗𝟑𝟑

𝒇𝒌 = 𝑭𝑵 = 𝟒. 𝟗𝑵

𝝁𝒌 = 𝟒. 𝟗

𝟏. 𝟏𝟗𝟐 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟒𝟏𝟗

Surface #2:

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𝒇𝒎𝒂𝒙 = 𝟔𝑵

𝝁𝒔 = 𝟔

𝟏. 𝟏𝟗𝟐 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟓𝟏𝟒

𝒇𝒌 = 𝑭𝑵 = 𝟐. 𝟕𝑵

𝝁𝒌 = 𝟐. 𝟕

𝟏. 𝟏𝟗𝟐 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟐𝟑𝟏

Surface #3:

𝒇𝒎𝒂𝒙 = 𝟕. 𝟓𝑵

𝝁𝒔 = 𝟕. 𝟓

𝟏. 𝟏𝟗𝟐 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟔𝟒𝟐

𝒇𝒌 = 𝑭𝑵 = 𝟓. 𝟓𝑵

𝝁𝒌 = 𝟓. 𝟓

𝟏. 𝟏𝟗𝟐 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟒𝟕𝟏

Lab Report Unit 3: FREE FALL & REACTION TIME 21

Mass 5:

Surface #1:

𝒇𝒎𝒂𝒙 = 𝟏𝟏. 𝟓𝑵

𝝁𝒔 = 𝟏𝟏. 𝟓

𝟏. 𝟑𝟏 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟖𝟗𝟔

𝒇𝒌 = 𝑭𝑵 = 𝟓. 𝟎𝑵

𝝁𝒌 = 𝟓

𝟏. 𝟑𝟏 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟑𝟖𝟗

Surface #2:

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𝒇𝒎𝒂𝒙 = 𝟔. 𝟖𝑵

𝝁𝒔 = 𝟔. 𝟖

𝟏. 𝟑𝟏 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟓𝟑𝟎

𝒇𝒌 = 𝑭𝑵 = 𝟐. 𝟗𝑵

𝝁𝒌 = 𝟐. 𝟗

𝟏. 𝟑𝟏 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟐𝟐𝟔

Surface #3:

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𝒇𝒎𝒂𝒙 = 𝟕. 𝟔𝑵

𝝁𝒔 = 𝟕. 𝟔

𝟏. 𝟑𝟏 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟓𝟗𝟐

𝒇𝒌 = 𝑭𝑵 = 𝟔𝑵

𝝁𝒌 = 𝟔

𝟏. 𝟑𝟏 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟒𝟔𝟕

Mass 6:

Surface #1:

𝒇𝒎𝒂𝒙 = 𝟏𝟎. 𝟖𝑵

𝝁𝒔 = 𝟏𝟎. 𝟖

𝟏. 𝟏𝟑𝟑 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟗𝟕𝟑

𝒇𝒌 = 𝑭𝑵 = 𝟒. 𝟓𝑵

𝝁𝒌 = 𝟒. 𝟓

𝟏. 𝟏𝟑𝟑 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟒𝟎𝟓

Lab Report Unit 3: FREE FALL & REACTION TIME 24

Surface #2:

𝒇𝒎𝒂𝒙 = 𝟓. 𝟕𝑵

𝝁𝒔 = 𝟓. 𝟕

𝟏. 𝟏𝟑𝟑 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟓𝟏𝟑

𝒇𝒌 = 𝑭𝑵 = 𝟐. 𝟓𝑵

𝝁𝒌 = 𝟐. 𝟓

𝟏. 𝟏𝟑𝟑 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟐𝟐𝟓

Surface #3:

Lab Report Unit 3: FREE FALL & REACTION TIME 25

𝒇𝒎𝒂𝒙 = 𝟕𝑵

𝝁𝒔 = 𝟕

𝟏. 𝟏𝟑𝟑 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟔𝟑𝟎

𝒇𝒌 = 𝑭𝑵 = 𝟓. 𝟒𝑵

𝝁𝒌 = 𝟓. 𝟒

𝟏. 𝟏𝟑𝟑 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟒𝟖𝟔

Mass 7:

Surface #1:

Lab Report Unit 3: FREE FALL & REACTION TIME 26

𝒇𝒎𝒂𝒙 = 𝟏𝟏. 𝟗𝑵

𝝁𝒔 = 𝟏𝟏. 𝟗

𝟏. 𝟐𝟔𝟓 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟗𝟔𝟎

𝒇𝒌 = 𝑭𝑵 = 𝟓𝑵

𝝁𝒌 = 𝟓

𝟏. 𝟐𝟔𝟓 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟒𝟎𝟑

Surface #2:

Lab Report Unit 3: FREE FALL & REACTION TIME 27

𝒇𝒎𝒂𝒙 = 𝟔. 𝟐𝑵

𝝁𝒔 = 𝟔. 𝟐

𝟏. 𝟐𝟔𝟓 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟓𝟎𝟎

𝒇𝒌 = 𝑭𝑵 = 𝟐. 𝟗𝑵

𝝁𝒌 = 𝟐. 𝟗

𝟏. 𝟐𝟔𝟓 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟐𝟑𝟒

Surface #3:

𝒇𝒎𝒂𝒙 = 𝟕. 𝟖𝑵

𝝁𝒔 = 𝟕. 𝟖

𝟏. 𝟐𝟔𝟓 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟔𝟑𝟎

𝒇𝒌 = 𝑭𝑵 = 𝟔𝑵

𝝁𝒌 = 𝟔

𝟏. 𝟐𝟔𝟓 ∗ 𝟗. 𝟖 ≈ 𝟎. 𝟒𝟖𝟒

Mean Coefficient of Static Friction of Surface #1:

Lab Report Unit 3: FREE FALL & REACTION TIME 28

𝝁𝒔̅̅ ̅ = 𝟏

𝟕 ∑ 𝝁𝒔𝒊 =

𝟎. 𝟗𝟑𝟓 + 𝟎. 𝟗𝟑𝟗 + 𝟎. 𝟗𝟏𝟗 + 𝟎. 𝟗𝟑𝟑 + 𝟎. 𝟖𝟗𝟔 + 𝟎. 𝟗𝟕𝟑 + 𝟎. 𝟗𝟔

𝟕 = 𝟎. 𝟗𝟑𝟔𝟒 ≈ 𝟎. 𝟗𝟑𝟔

𝟕

𝒊

Mean Coefficient of Kinetic Friction of Surface #1:

𝝁𝒌̅̅̅̅ = 𝟏

𝟕 ∑ 𝝁𝒌𝒊 =

𝟎. 𝟑𝟗𝟒 + 𝟎. 𝟒𝟎𝟔 + 𝟎. 𝟒𝟎𝟒 + 𝟎. 𝟒𝟏𝟗 + 𝟎. 𝟑𝟖𝟗 + 𝟎. 𝟒𝟎𝟓 + 𝟎. 𝟒𝟎𝟑

𝟕 = 𝟎. 𝟒𝟎𝟐𝟗 ≈ 𝟎. 𝟒𝟎𝟑

𝟕

𝒊

Mean Coefficient of Static Friction of Surface #2:

𝝁𝒔̅̅ ̅ ≈ 𝟎. 𝟓𝟏𝟑

Mean Coefficient of Kinetic Friction of Surface #2

𝝁𝒌̅̅̅̅ ≈ 𝟎. 𝟐𝟐𝟓

Mean Coefficient of Static Friction of Surface #3:

𝝁𝒔̅̅ ̅ ≈ 𝟎. 𝟔𝟐𝟗

Mean Coefficient of Kinetic Friction of Surface #3

𝝁𝒌̅̅̅̅ ≈ 𝟎. 𝟒𝟕𝟏

Conclusion:

For Part 1, I found out that the mean of the coin is 0.3m, of the button is 0.283m, and of

the wooden toothpick is 0.437m. After that, I find that the coin has a standard deviation of 0.004

and a relative error of ±𝟎. 𝟎𝟏𝟑, the button has a standard deviation of 0.002 and a relative error

of ±𝟎. 𝟎𝟎𝟕, and the wooden toothpick has a standard deviation of 0.001 and a relative error of

±𝟎. 𝟎𝟎𝟐. After measuring with the balance, I determined that the mass of the coin is 0.003kg, of

Lab Report Unit 3: FREE FALL & REACTION TIME 29

the button is 8.3*10-4 kg, and of the wooden toothpick is 4*10-5 kg. Then, I found out that the

coefficient of friction is equal to tan (𝜽), and then I found that the angle for the coin is 17.5°, for

the button is 16.4°, and for the wooden toothpick is 25.6°. I, then, I find that the length of the base

of the triangle of the coin is 0.954m, of the button is 0.959m, and of the wooden toothpick is

0.899m. After, I calculated the coefficient of friction for each object, being for the coin 𝝁 = 𝟎. 𝟑𝟏𝟓

, for the button 𝝁 = 𝟎. 𝟐𝟗𝟒, and for the wooden toothpick 𝝁 = 𝟎. 𝟒𝟖𝟔; and then I find out the

percent error in comparison with the values that I find out in the internet (metal to wood = 0.31,

plastic to wood = 0.4, wood to wood = 0.5), being the percent of error for the coin 1.61%, for the

button 26.5%, and for the wooden toothpick 2.8%. Since the values of the metal to wood and the

wood to wood can vary, I decided to use a value that will be close to my experimental values to

get a smaller percent error (this, however, couldn’t be done for the plastic-wood value since I

couldn’t find another coefficient of friction value that was close to my experimental coefficient for

plastic). I conclude that for Part 1, that since mass cancels out (or at least doesn’t affect the value

of the coefficient of friction) we don’t need to know the mass of the objects to find the coefficient

of friction, and my experimental coefficients of friction were within the range of the value of the

coefficient of friction that I found out on the internet, except for the button. This can be because I

could not get the exact material that the button was made of, leading me to search for plastic-on-

wood coefficient of frictions, which are hard to find. Moreover, I could have a better environment

to do the procedure since slipping the objects on the meter stick was hard to do without making

the object fall on the side.

For Part 2, I found out that since the block moving in the simulation has a constant velocity,

meaning that there is no acceleration, and therefore the sum of all forces exerting in the block in

the simulation must add to 0. By knowing this, I can calculate that the coefficient of friction will

Lab Report Unit 3: FREE FALL & REACTION TIME 30

always be 𝝁 = 𝑻

𝒎𝒈 . After that, I started calculating all coefficient of frictions (static and kinetic)

for all 7 masses of the block in 3 different surfaces. By the end of the experiment, I decided to

calculate the mean of the static coefficient of friction and kinetic coefficient of friction for the three

surfaces (since showing each individual value for each mass in each can be found in the

calculations tab), with the Glass-on-Glass surface having a static coefficient of friction of 0.936

and a kinetic coefficient of friction of 0.403, the Wood-on-Lab Table having a static coefficient of

friction of 0.513 and a kinetic coefficient of friction of 0.225, the Aluminum-on-Steal having a

static coefficient of friction of 0.629 and a kinetic coefficient of friction of 0.471. These values are

close to the actual values of the coefficients of friction of each mass; therefore, I conclude that no

matter how heavy the object may be, the coefficient of friction of a surface will remain being the

same. The mean could have been more accurate if I could determine exactly on the graph the max

force was (for the static coefficient of friction), and if I could determine how much exactly was

the constant force to move the object. Rounding errors could also affect the result, but in this case

the mean was not that far from each mass value, which leads me to believe that the rounding in

this experiment could not have a great impact in the results.

Lab Report Unit 3: FREE FALL & REACTION TIME 31

References

[1] Eml2322l -- friction coefficients. (n.d.). Retrieved February 20, 2021, from

https://mae.ufl.edu/designlab/Class%20Projects/Background%20Information/Friction%20coeffic

ients.htm

[2] Friction and friction coefficients. (n.d.). Retrieved February 20, 2021, from

https://www.engineeringtoolbox.com/friction-coefficients-d_778.html