Lab report 2. Components of a Vector PDF

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Lab report 2. Components of a Vector...

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Components of a Vector A vector is a quantity that has both magnitude and direction. --Britannica.com

Components of a Vector OBJECTIVE The purpose of this experiment is to test vectors and the importance of the concept of the vector components. The components will be found in this experiment graphically, analytically, and experimentally. And on the accuracy of the graphical and experimental methods compared to the analytic method.

MATERIALS 1. Force table 2. Slotted mass holder and masses 3. Ruler 4. Graph paper 5. Protractor

PROCEDURE General procedure Vector A 1. Determine the mass of the mass holder from the mass stamped on the mass holder. Convert that mass given from grams to kilograms. And record the answers to the data sheet. 2. Convert the mass required to be placed on the mass holder for vector A from grams to kilograms. And record the answers to the data sheet. 3. Calculate the total mass attached to the end of vector A using the following formula:

Total mass=Mass of mass h older+ Mass placed∈mass h older . And record

the answers to the data sheet.

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4. Calculate the magnitude of vector A using the following formula:

Magnitude = Mass∗Gravity . And record the answers to the data sheet. Vector B 1. Determine the mass of the mass holder from the mass stamped on the mass holder. Convert that mass given from grams to kilograms. And record the answers to the data sheet. 2. Convert the mass required to be placed on the mass holder for vector B from grams to kilograms. And record the answers to the data sheet. 3. Calculate the total mass attached to the end of vector B using the following formula:

Total mass=Mass of mass h older+ Mass placed∈mass h older . And record

the answers to the data sheet. 4. Calculate the magnitude of vector B using the following formula:

Magnitude = Mass∗Gravity . And record the answers to the data sheet. Vector C 1. Determine the mass of the mass holder from the mass stamped on the mass holder. Convert that mass given from grams to kilograms. And record the answers to the data sheet. 2. Convert the mass required to be placed on the mass holder for vector C from grams to kilograms. And record the answers to the data sheet. 3. Calculate the total mass attached to the end of vector C using the following formula:

Total mass=Mass of mass h older+ Mass placed∈mass h older . And record

the answers to the data sheet. 4. Calculate the magnitude of vector C using the following formula:

Magnitude=Mas s∗Gravity . And record the answers to the data sheet.

Analytical determination of the components of a vector Vector A 1. Calculate the magnitude of the components of vector A using the following formulas: the x-component= A x= A∗cosθ ,the y-component= A

y= A∗sinθ . Using the magnitude of vector A that was calculated, and the angle given, plug them in the formulas to get the magnitude of the components of vector A. And record the answers to the data sheet. Vector B

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1. Calculate the magnitude of the components of vector A using the following formulas: the x-component= B x=B∗cosθ ,the y-component= B y=B∗sinθ . Using the magnitude of vector B that was calculated, and the angle given, plug them in the formulas to get the magnitude of the components.of vector B. And record the answers to the data sheet. Vector C 1. Calculate the magnitude of the components of vector A using the following formulas: the x-component= C x=C∗cosθ ,the y-component= C

y=C∗sinθ . Using the magnitude of vector C that was calculated, and the angle given, plug them in the formulas to get the magnitude of the components.of vector C. And record the answers to the data sheet.

Experimental components of Vector Vector A 1. Set the force table and make sure that it is leveled using a level. 2. Put vector A at 40° and add 50 grams to the end of the string. 3. Then set A x at 180° and A y at 270°. 4. Add weights to each of the components A x and A y . Keep adding weights until Vector A and the two components are balanced. Remove the pins and if they balance then record the mass added to each component to the data sheet 5. To calculate the magnitude of the components use the following formula:

Magnitude = Mass∗Gravity . Plug in the mass recorded and gravity, 9.8, to find the magnitude of the components of vector A. Record the answers to the data sheet. Vector B 1. Set the force table and make sure that it is leveled using a level. 2. Put vector B at 120° and add 70 grams to the end of the string. 3. Then set B x at 0° and B y at 270°. 4. Add weights to each of the components B x and B y . Keep adding weights until Vector B and the two components are balanced. Remove the pins and if they balance then record the mass added to each component to the data sheet. 5. To calculate the magnitude of the components use the following formula:

Magnitude = Mass∗Gravity . Plug in the mass recorded and gravity, 9.8, to

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find the magnitude of the components of vector B. Record the answers to the data sheet. Vector C 1. Set the force table and make sure that it is leveled using a level. 2. Put vector C at 230° and add 100 grams to the end of the string. 3. Then set C x at 0° and C y at 90°. 4. Add weights to each of the components C x and C y . Keep adding weights until Vector C and the two components are balanced. Remove the pins and if they balance then record the mass added to each component to the data sheet. 5. To calculate the magnitude of the components use the following formula:

Magnitude = Mass∗Gravity . Plug in the mass recorded and gravity, 9.8, to find the magnitude of the components of vector C. Record the answers to the data sheet.

% Error To calculate the % error use the following formula:

% Error =(( experimented value−accepted value)/ accepted value)∗100 . Substitute in the experimented value and the accepted value calculated into the formula and get the % error. And record the answer to the data sheet.

DATA A. General Procedure

Vector

Mass to be Placed on Mass Holder (kg)

A

0.05

B

0.07

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Mass of MAss Holder (kg)

Total Mass Attached to End of String (kg)

Magnitude of Vector (N)

Direction with respect to x-axis (degrees)

0.05

0.10

0.98

40°

0.05

0.12

1.18

120°

C

0.10

0.05

0.15

1.47

230°

B. Analytical Determination of the components of a Vector

Vector

X-component (N)

Y-component (N)

A

0.75

0.63

B

-0.59

1.02

C

-0.94

-1.13

C. Experimental components of a vector Vector A

Mass of mass holder

Mass of Mass placed Mass placed mass holder on mass on mass holder holder

Total mass suspended from pulley

Total mass suspended from pulley

At 180° (kg) At 270° (kg) At 180° (kg) At 270° (kg) At 180° (kg) At 270° (kg) 0.05

0.05

0.027

0.01

0.077

0.06

Total mass suspended from pulley

Total mass suspended from pulley

Vector B

Mass of mass holder

Mass of Mass placed Mass placed mass holder on mass on mass holder holder

At 0° (kg)

At 270° (kg) At 0° (kg)

At 270° (kg) At 0° (kg)

At 270° (kg)

0.05

0.05

0.050

0.1

Vector C

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0.013

0.063

Mass of mass holder

Mass of Mass placed Mass placed mass holder on mass on mass holder holder

Total mass suspended from pulley

At 0° (kg)

At 90° (kg)

At 0° (kg)

At 90° (kg)

At 0° (kg)

At 90° (kg)

0.05

0.05

0.043

0.067

0.093

0.117

Experimental components (N)

% Error

A x

0.755

0.7

A

0.588

6.7

-0.617

4.6

0.980

3.9

C x

-0.911

3.1

C

-1.147

1.5

y

B x B

y

y

Total mass suspended from pulley

SAMPLE CALCULATIONS General procedure: To convert the mass of the mass holder from grams to kilograms use the following formula: kg=g/1000 , kilograms =grams /1000 . kg of t h e mass h older=50 / 1000 =0.05 kg . To convert the mass of the mass placed on mass holder from grams to kilograms use the following formula: kg=g/1000 , kilograms =grams /1000 . kg of 70 grams=70 /1000=0.07 kg .

To calculate the total mass attached to the end of the string use the following formula: Total mass=Mass of mass h older + Mass placed∈ mass h older , totalmass of vector B=0.05 + 0.07 =0.12 kg .

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To calculate the magnitude of vector use the following formula:

Magnitude = Mass∗Gravity ,

magnitudeif vector B=0.12∗9.8=1.18 N .

Analytical determination of the components of a vector: To calculate the magnitude of x-component of vector A, plug in the magnitude of vector A and the angle of vector A with respect to x-axis to this formula: A

x= A∗cosθ ,

A x=0.98∗cos 40=0.75 N .

To calculate the magnitude of y-component of vector A, plug in the magnitude of vector A and the angle of vector A with respect to x-axis to this formula: A

x= A∗sinθ ,

A x=0.98∗sin 40=0.63 N .

Experimental components of a vector: To calculate the total mass from pulley use the following formula:

Total mass=Mass of mass h older+ Mass placed ∈mass h older . The mass for vector B at 0° = 0.05 + 0.013 =0.063 kg . To calculate the magnitude of the components use the following formula:

Magnitude = Mass∗Grav i ty . B x=0.063∗9.8=0.617 N . % Error: To calculate the % Error use the following formula:

% Error=(( experimented value−accepted value )/ accepted value )∗100 . % Error of B y=(( 1.02−0.98 )/1.02 )∗100=3.9 % .

QUESTIONS 1. A scalar is a quantity that only has a magnitude and does not have directions, such as temperature and weight. While vector is a quantity that has both magnitude and direction, such as velocity and displacement. 2. The components of a vectors are the two parts that is the vector is broken into. They work together to have the same work or effect of the vector. Also when adding the squared value of the two components it equals the vector squared. 3. The major sources of error are: The force table is not level. If the force table is not leveled it will result in an inaccurate results because it would lean more towards one side than the other and

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that will result on a greater mass or less mass that needs to be added to the components to balance out with the vector. It can be reduced by using a level properly to make sure that the table is adjusted correctly. Wind can affect the results from the experiment. If any kind of wind acted on the force table, the vector, or the components, it will result on an inaccurate result because it would not show the exact mass needs to be added. Can be reduced by trying to eliminate all sources of wind in the place of the experiment. Human error. Human could cause a source of error in the experiment if someone accidentally hit the force table causing it to not be leveled. Or added mass to the components after recording the answer. It could also be a human error in counting how many grams he added to the mass holder or an error in recording the wrong number. To reduce the human error, the person has to double check the answers before recording it. As well as another person checking the answer. 2

4. The magnitude of the force is

35 ¿ ¿ 2 65 ¿ +¿ the angle of the force is: ¿ √¿

θ=Ta n−1 (Fy /Fx )=Tan−1 (35 / 65 )=28 ° . The resultant force is 73.8 N at 28° in the north east direction. 5. The x and y components are placed on the opposite side of vector A because the components and the vector need to balance out in order for the components to act on the vector. Also 180° and 270° are perpendicular, so we can calculate the magnitude of them.

CONCLUSIONS The objective of this experiment was to experiment the vectors and their components using different methods. And the objective was met successfully. Because in the lab analytical method was used and it played a role as the accurate and accepted value for the magnitudes of the components of the vectors. Also, experimental method was used and it showed how to apply vectors and the components in a real life situation. It also used different equations to be able to complete the experiment. For example,

Magnitude = Mass∗Gravity that was used to

calculate the magnitude of the components experimentally given gravity and by figuring out the mass. Also, it used the formula for % Error to calculate the percentage of error of the experimented magnitude of the components from the

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analytical magnited (the accepted). And by recording all the numbers calculated to the data sheet, it showed the accuracy and the difference between the two methods and how to do each of them.

ERROR ANALYSIS In this experiment many things can cause error in the experiment. Some of these things are: The force table is not level. If the force table is not leveled it will result in an inaccurate results because it would lean more towards one side than the other and that will result on a greater mass or less mass that needs to be added to the components to balance out with the vector. Wind can affect the results from the experiment. If any kind of wind acted on the force table, the vector, or the components, it will result on an inaccurate result because it would not show the exact mass needs to be added. Human error. Human could cause a source of error in the experiment if someone accidentally hit the force table causing it to not be leveled. Or added mass to the components after recording the answer. It could also be a human error in counting how many grams he added to the mass holder or an error in recording the wrong number.

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