Experiment 2: Vector Addition
Physics 2125 (16008)
HCC-Scarcella Science & Technology
September 2, 2016
Objective

##### We have textbook solutions for you!

**The document you are viewing contains questions related to this textbook.**

**The document you are viewing contains questions related to this textbook.**

Expert Verified

The first objective of this experiment was to calculate the number of forces acting on a body and
then calculate the resultant of the same forces by drawing a vector diagram to scale to find its
magnitude and direction. Once this was done, we calculated the resultant using analytical
methods, most notably the law of cosine for magnitude and the law of sine in order to obtain the
direction in one instance. The components method is also used.
Equipment
1. Force table
2. Weight holders (#4).
3. Pulleys (#4).
4. Slotted weights
5. Strings for suspending the masses
6. A ring
7. A metal pin
8. A protractor
9. Graph paper.
Theory and Equations
Vectors such as force, displacement, velocity are physical quantities with both magnitude and
direction. In contrast, a scalar value is a physical quantity that only has magnitude. Examples of
include speed, temperature and distance. A vector
A
can be written as the sum of two vectors
A
x
and
A
y
and can be drawn along the x and y-axis respectively.
A
x
and
A
y
are called
the
components of vector
A
and are given by
:
A
x
= A
cosα (Equation 1)
A
y
= A
sinα
α (≤ 90
0
)
is the angle vector
A
makes with the x-axis. (Equation 2)
To find the resultant,
R
, of the vectors
A, B, C
etc we much follow the following steps:
1.
Obtain the
A
x,
B
x,
C
x ...
and
A
y,
B
y,
C
y
....
components of each vector using the above two
equation. We must keep in mind that the Vector value can be positive or negative
depending in its direction.
2.
Once we have the above values we write them down as:
R
x
=
A
x
+ B
x
+ C
x
+ …
R
y
=
A
y
+ B
y
+ C
y
+ …
3.
The magnitude of
R
can now be calculated using the equation
[R
x
2
+
R
y
2
]
½
and the
direction of
R
can be calculated using the equation θ = tan
-1
[R
y
/ R
x
]
where θ is the
angle between
R
and x axis.

If θ > 0 then
R
is either in the 1
st
or 3
rd
quadrant