Module 2 Lab 2 Vector
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Northern Virginia Community College *
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Course
201
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
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NOL PHY 201
Lab - Vectors
Name __Michelle Balderrama_ Before starting, please scroll through the worksheet to check the page numbers and get all the information. Complete all activities before submitting the lab.
Each lab counts for 20 points and is about 1.42% of the total grade.
Lab Goals
This lab will help you learn the following:
how to add and subtract vectors graphically and by components
using critical thinking and ingenuity in building a physics problem rooted in a real-life experience. Introduction
This Lab uses the simulation provided by PhET at the University of Colorado Boulder, Vector addition
.
It is divided into two activities.
If any physical quantity has both magnitude (size) and direction
, it is called a vector. For example, displacement is a vector. It has magnitude and direction. The displacement is how far an object displaced itself from the starting position. Distance instead is a scalar and it has only magnitude. Other examples of vectors are velocity, acceleration, force, momentum. Examples of non- vectors, therefore scalar quantities, are temperature, energy, voltage.
Consider the vector ⃗
v
=
(
20,10
)
. The
numbers 20 and 10 are called
components of the vector, they help to
visualize the vector's position. The
horizontal component is v
x
=
20
and
vertical component is v
y
=
10
; The
magnitude of the vector v
is obtained with
the
v
=
√
(
v
x
)
2
+(
v
y
)
2
=
√
(
20
)
2
+(
10
)
2
=
√
400
+
100
=
√
500
=
22.4
Here, units are not included because v
could be any physical quantity that is a vector, like displacement, velocity, acceleration, force, momentum. The direction of the vector is obtained with the Page 1 of 6
NOL PHY 201
θ
=
arctan
(
10
20
)=
26.6
o
In the simulation, the magnitude is called ‖
⃗
v‖
and the components are called v
x
and v
y
Using trigonometry we can find the components of the vector with the following formulae:
v
x
=
v
cos
(
θ
)
and v
y
=
v
sin
(
θ
)
Where v
corresponds to the magnitude of the vector, in the simulation it is marked as
‖
⃗
v‖
and cos
(
θ
)
means cosine of the angle theta.
The sum or the difference between vectors is obtained adding or subtracting their corresponding components.
⃗
C
=
⃗
A ±
⃗
B
when C
x
=
A
x
± B
x
and C
y
=
A
y
±B
y
Graphically, with the parallelogram method, the sum and the difference of the two vectors are given by the diagonals of the parallelogram formed by the vectors as shown on the diagrams below:
Graphically, with the head-tail method the sum of two or more vectors is given by the vector that connects the first tail with the last head like in the diagrams below:
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NOL PHY 201
Set up
1.
Open the simulation
Vector Addition
. Select the tab called “Equations”.
2.
On the simulation, create the same setup marked (1), (2) and (4) on the picture below. On the screen, you want to see the grid, the vectors, but not their components.
3.
Notice that the origin of the reference frame may be placed in any location of the screen. Do not mix the colors of the vectors, use only pink or only blue.
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NOL PHY 201
Activity 1: Addition and subtraction of Vectors
1.
On the “Base Vectors”, point (3) on the image above, adjust the components of the vectors ⃗
a
and ⃗
b
with numbers of your choice.
-
The vectors are a (7,2) and b (-10,5).
2.
Insert here a screenshot of your two vectors. [Screenshot]
:
3.
Determine the magnitude and the direction of the vectors ⃗
a
and ⃗
b
. Give the angle
direction from the x-positive axis. [Answer, show your work with the numbers] 4.
Complete Table below. 5.
Does the simulation confirm your calculations? Yes/
No
6.
Complete the Table below with all the information obtained from the next steps. (10pt)
Page 4 of 6
NOL PHY 201
●
Determine the components of the vector sum ⃗
c
=
⃗
a
+
⃗
b
●
Determine the magnitude and direction of the vector sum.
●
Determine the components of the vector difference ⃗
c
=
⃗
a
−
⃗
b
●
Determine the magnitude and direction of the vector difference.
●
Compare your results with the simulation. To obtain the sum or the difference of vectors use the option marked (5) on the picture above. On the simulations, the components, the magnitude, and the angle will be reported on the option (6) marked on the picture above.
7.
Include two screenshots of your vectors sum and difference.
8.
**Include a screenshot of your work on paper, if you prefer, instead of writing it directly on the table.
Activity 2: Building a problem with vectors
For this activity you want to use the simulation at the tab “Lab” and select “Show the angles”. In the simulation always use
the same vector color, for example
blue, because the "Sum" works only
for vectors with the same color.
In the problem below, you want to fill
in the blank with numbers of your
choice. The rhino walks along three
different vector displacements, you
decide how far and in which direction.
Page 5 of 6
NOL PHY 201
Use the simulation to build the path of the rhino along these three vectors. For example,
in the image, you see three vectors placed one after the other.
The problem
To protect a rhino, volunteers are following its steps with air monitoring devices and ground cameras. The rhino starts on the first day from ground camera O (
the origin of your reference frame
) and walks for _18____ km east along a straight line (Vector 1). The rhino then moves __16__ km in a direction of ___75____degrees from the x-axis (Vector 2). In this location the rhino finds water and food, therefore the animal stays for the night. On the second day, the rhino moves ________ km in a direction of ____270_____degrees from the x-axis (Vector 3). 5
a)
Report the three vectors on your simulation page. Use the head-tail method only.
b)
Determine the displacement of the rhino. The displacement is the "SUM" of the three vectors. c)
Report here the magnitude___17.36_____ and direction ___142.9_ of the vector SUM. d)
Include a screenshot of your three vectors and of their SUM.
e)
Write here the components of all your three vectors, and the components of the vector displacement. f)
Show that the sum of the x- components equal the x- component of the displacement.
g)
Show that the sum of the y- components equal the y- component of the displacement.
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