Experiment 2

__Objectives__:

The objective is to (1) practice the polygon
method of vector addition that is a graphical method, and (2) compare
the results with calculation (analytical method) to get an idea of
how accurate the graphical method is**.**

__Equipment__:

A protractor, a Metric ruler, and a few sheets of graphing paper

__Theory__:

The resultant of
two or more vectors is a single vector that is equivalent in its physical effects to
the action of the original vectors**.** For example, if three force vectors
were acting on an object, these three forces could be replaced by their
resultant, and the object would experience the same net effect**.**

**Note:** In the following sections, "gf" means gram-force**.** 1gf is
the force of gravity on the mass of one gram**.**

*Example:*

**Given** **A*** =*
20

find *R = A + B + C*,
(1) by *graphical method*,
and (2) by* **analytical method*.

**Solution: **

**1)***
Graphical Method *(Here the

As shown above, a polygon is drawn with
the given vectors * A,
B, C* by
placing the vectors one after another, on a tail-to-tip basis

** 2) Analytical Method**
(Here the

a) Calculate
the **x** and **y **component of each of * A, B,*
and

b) Sum the components in
the** x-**direction to obtain *R*_{x }.

c)** **Sum the components in the **y-**direction
to obtain *R*_{y }.

d) Compute the magnitude and direction of the resultant using

e) Draw a sketch of **R _{x}** and

The x- and y-components of the vectors are:

* A_{x} =
*20

* B_{x }=*
15

* C_{x}= *25

**R _{x}** =

*R* = (*R _{x}+ R_{y}*)

__Procedure__:

Three vectors ** A, B, and C** are
given in

The purpose is *
use a ruler and a protractor* and

R_{1} =
A + B |
R_{2} = A
+ B
+ C |
R-_{3} =
A + B
C |

For each of **R _{1},_{ }R_{2},**

*
1)* Choose a

*
2)* Add
the vectors by

*
3)* Solve
for the same resultant that you found in Step
2, but
this time by using the analytical method (by calculation and use of
trigonometry)

*
4)* Calculate
a % error on magnitude and a % error on direction and record them in the space
provided in

__Data:__

Table 1

Vector |
Magnitude | Direction |

A |
25.0N |
35.0^{o} |

B |
10.0N |
120.0^{o} |

C |
15.0N |
155.0^{o} |

Table 2

Resultant |
Measured |
Calculated (Accepted) |
%error on Magnitude | %error on Direction | ||

Magnitude (N) | Angle (^{o}) |
Magnitude (N) | Angle ( ^{o} ) |
|||

R1 = A+ B |
||||||

R2 = A+
B+C |
||||||

R3 = A+B -C |

Show sample calculation, for example, the complete calculation for R_{1}.

**
Comparison
of the results:**

Provide the percent error formula used as well as the calculation of the
percent errors**.**

** Conclusion:**

State your conclusions of the experiment**.**

__Discussion__:

Provide a discussion if necessary**.**

__Questions__:

Which method is the most precise, graphical or analytical method?

Why is the polygon method generally considered to be the most reasonable graphical technique?