The protocol for this assignment is As Directed.
References: Sections 3.1-3.3 of the text; Trigonometry: Math for 2-Dimensional Physics
In this assignment, you'll use the graphical and component methods of vector addition. The problem
you'll do is Chapter 3
end-of-chapter problem 20. Present
your solutions as described below. Due to the nature of these
exercises, you need not use the standard given, goal, etc. method.
The convention for giving the direction angle of a vector is to give the angle as measured counterclockwise from the +x-axis. You're expected to use this convention throughout the course.
using a symbol to represent a vector, always make it clear that
the quantity represented is a vector and not a magnitude.
For example, does A represent a vector or a scalar? Our
convention on a word-processed page like this is to put vectors
in bold type. Hence, A is
a vector and A is the vector's magnitude. On a hand-written page,
the quickest method is put an arrow above the A like this: . Thus, is a
vector and A is a magnitude.
Part A. Component Method of Vector Addition
- Study the following example of the component method of vector addition.
Example problem: Add the following
three vectors using the component method: A = 10.00 m, 60°; B = 6.00 m, 135°, C = 3.00 m, 270°. Determine the magnitude and direction angle of the sum.
- Organize the components into a table like the one below. Then add the components of the individual vectors to find the components of the vector sum.
magnitude of the vector sum. The vector sum is also known as the resultant.
- The direction angle of the resultant is the following. Note that the angle must be a Quadrant I angle, because both x- and y-components of the sum are positive.
- Carry out the method shown above for problem 3-20 of the text.
Part B. Graphical Method of Vector Addition
In the graphical method, the individual vectors are placed tip-to-tail. Then the resultant is drawn from the tail of the first vector to the tip of the last vectors. You've already had some experience with this from E.3.2. In that assignment, you drew freehand sketches. In the present assignment, you'll do a careful, scaled construction on graph paper.
Here are the specifics.
Download and print a sheet of graph
paper. You'll construct your vector drawing on this page and include the page in the file that you submit.
In constructing your drawing, do the following:
the drawing large. Remember that greater measurements
generally mean greater accuracy.
Draw the vectors to
scale. Select a convenient scale factor, say 1.0 major division (5 minor divisions) on the graph
paper represents 1.0 m of distance. In that case, vector A would
be drawn 10.0 major divisions long.
Use a protractor to
measure angles. Use a ruler to measure lengths and
draw the vectors straight.
Put arrowheads on
the ends of the vectors. Otherwise, they're just lines. Label
the vectors A, B, C.
Draw the vector sum A + B + C from the tail of A to the
tip of C. Label the vector D.
Measure the length
of D with your ruler. Then use your scale factor to
convert back to meters.
Measure the direction angle of D with your
protractor. Show clearly on your scale drawing the angle that you measured.
- When you've completed the above, compare the magnitudes and angles found with the
component and graphical methods. That means you need to say quantitatively how
close they are to each other. The way to do this is
to calculate the percentage difference:
% Difference = 100 ∙ (Value 1 - Value 2) ÷
(Value 1 + Value 2)