Lab 01- Physics
docx
keyboard_arrow_up
School
North Lake College *
*We aren’t endorsed by this school
Course
2425
Subject
Mathematics
Date
Feb 20, 2024
Type
docx
Pages
4
Uploaded by PrabinNorthlake
Lab 1: Vector Addition and Subtraction
Name:
____Prabin Shrestha_________________________________
EXPERIMENTAL DATA
Table 1
. Vector data.
Vector
Magnitude
Angle (Direction)
(degrees)
X component
Y component
⃗
a
5.0
90.0
0.0
5.0
⃗
b
7.1
45.0
5.0
5.0
⃗
c
(Part 1)
11.2
63.4
5.0
10.0
⃗
c
(Part 2)
5.0
180.0
-5.0
0.0
⃗
c
(Part 3)
11.2
-116.6
-5.0
-10.0
Questions
1
. Calculate the components of vector ⃗
c
using the rectangular components of vectors ⃗
a
and ⃗
b
,
and then calculate the magnitude and direction of ⃗
c
using these calculated components:
c
x
= a
x
+ b
x
= 0+5= 5
c
y
= a
y
+ b
y
= 5+5= 10
c
=
√
c
x
2
+
c
y
2
= (
125)^1/2= 5(5)^1/2
θ
=
tan
−
1
(
c
y
c
x
)
+
adjustment if necessary
θ
=
tan
−
1
(
10
5
)
AGB_DallasCollege
Lab 1: Vector Addition and Subtraction
θ
=
¿
63.4 degree
2
. You used the head-to-tail
geometrical method for vector addition in steps 5 and 6. Does the
order in which you placed the vectors to be added head-to-tail matter? Why?
The head-to-tail geometrical method for vector addition is a graphical way to add vectors. It
doesn’t matter in which order we placed the vector to be added because we still get the same
answer irrespective of any order. As vectors possess commutative property, the result of A+B
will be equal to B+A.
3
. Calculate the components of vector ⃗
c
using the rectangular components of vectors ⃗
a
and ⃗
b
,
and then calculate the magnitude and direction of ⃗
c
using these calculated components:
c
x
= a
x
– b
x
= 0-5= -5
c
y
= a
y
– b
y
= 5-5 = 0
c
=
√
c
x
2
+
c
y
2
= 5
θ
=
tan
−
1
(
c
y
c
x
)
+
adjustment if necessary
θ
=
tan
−
1
(
0
−
5
)
θ
=
¿
0 degree θ
=
¿
0 +180 = 180 degree
( θ
= 0 degree in the first quadrant and the answer we have in the table is 180 degree that is
second quadrant as we have x component negative ) AGB_DallasCollege
Lab 1: Vector Addition and Subtraction
4
. When geometrically subtracting vectors, we do not place the vectors to be subtracted head-
to-tail, but tail-to-tail
instead, as you did in step 11. Explain why this geometrical method used
in step 11 for vector subtraction is the same
method as the head-to-tail geometrical method for
vector addition.
The geometrical method used in step 11 for vector is indeed conceptually the same method as
the head-to-tail geometrical method for vector addition. By connecting the tail of vector B to
the tail of the resultant vector (C) in step 11 of the vector subtraction process, we are
essentially doing the head-to-tail approach reversed. When vector C is added to vector B, it
equals vector A.
Therefore, although the geometric representation for vector subtraction (tail-to-tail) can
appear to be different, it actually operates on the same basic principle as the head-to-tail
method for vector addition. Both approaches center on identifying the vector that, when paired
with another vector, produces a particular outcome. 5
. Calculate the components of vector ⃗
c
using the rectangular components of vectors ⃗
a
and ⃗
b
,
and then calculate the magnitude and direction of ⃗
c
using these calculated components:
c
x
= – (a
x
+ b
x
) = -(0+5) = -5
c
y
= – (a
y
+ b
y
) = -(5+5) = -10
c
=
√
c
x
2
+
c
y
2
= (125)^1/2 =5*(5)^1/2
θ
=
tan
−
1
(
c
y
c
x
)
+
adjustment if needed
θ
=
tan
−
1
(
−
10
−
5
)
θ
=
¿
63.4 degree
θ =63.4 - 180= - 116.6
63.43 degree belongs in the first quadrant and the result in the table as shown is -116.6 degree
that will be in the third quadrant as x and y component are negative . (63.4-180=-116.6)
AGB_DallasCollege
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Lab 1: Vector Addition and Subtraction
6
. In Part 3, vectors ⃗
a
, ⃗
b
, and ⃗
c
form a closed polygon, which is something that must happen
when the vectors add up to zero. Is this consistent with the head-to-tail geometrical method for
vector addition? Explain.
Yes, the statement that vectors a ⃗
, b ⃗
, and c ⃗
form a closed polygon is consistent with the head-
to-tail geometrical method for vector addition. This method involves sequentially aligning
vectors by connecting the endpoint of one vector to the starting point of the next. Eventually, it
formed a closed polygon illustrating that the vectors cancel each other out in terms of
displacement or motion, resulting in no net change in position. Mathematically represented as (
a ⃗
+b ⃗
+c ⃗
=0 ⃗
).
So, in summary, when vectors are arranged head-to-tail to form a closed polygon,
it is visually consistent with the vectors summing up to zero.
AGB_DallasCollege