Vectors Addition
In this lab you will use two different methods to find the resultant of various combinations of forces, and
then compare your results. These forces are given in column 2 of Table 1. Force is a vector.
Both the symbols (F1) and the geometrical lines indicating vectors have arrows.
In the book and in this lab report you will see also the Bold font F1 to indicate a vector where F1 represents
the magnitude of the vector.
1) Use graph paper, a ruler and a protractor to find the resultant for the graphical method or ”tail to tip”
method. This method is fast and it gives accurate results if you measure and draw accurately.
Do not forget to use an appropriate scale, example: 50N for 2 cm.
Start drawing a coordinate system. Then draw the first vector F1 (purple vector in my example): use a
protractor to draw it in the proper direction and use a ruler to determine the proper length according to your
scale. At the end of this vector draw an arrow and start drawing as before the second vector F2 (red vector in
my example). To measure correctly the angle for the second vector, draw the coordinate system again. The
resultant R connects the “tail” of the first vector with the “tip” of the last vector.
Find the angle of the resultant with a protractor and the length of the resultant with a ruler. Change then the
length back into Newton using your scale. Record the values of the magnitude (length) and direction (angle)
in the table under “Graphical”. My example has R=280 N and θ=770. Your results will be different but if you
did it right they will be close to the values of the Analytical method R=285 N and θ=750
2) For the analytical method or components method (adding vectors by components method) you will use
your calculator. Make sure it is set to degrees for sin, cos, tan-1 calculations to find the resultant. This method
gives the exact values of the magnitude and angle of the resultant.
Remember you will resolve the forces into their “x” and “y” components. Fx = Fcosα, Fy = Fsinα
Add the components Rx= F1x+F2x+… Ry= F1y+F2y+… and then use the Pythagorean Theorem to find the
resultant R =√ Rx2+Ry2
The angle is given by: θ = tan-1(Ry/Rx)
Follow the example below.
3) Complete Table 1, attach your graphs and calculations, and turn in the lab report. If you cannot scan and
attach the graphs, take a picture of your work for graphical method and inserted in the word doc along with
the table. Solved Example:
Vector addition ( F1 the purple vector, F2 the red vector and the black is the resultant R)
1 F1x = 200cos 30 = 173
F1y = 200sin30 = 100 R
R
R F2x = 200cos 120 = -100
F2y = 200sin120 = 173 F2 Rx = 173-100 = 73
Ry = 100+173= 273 F1 R= R =√ Rx2+Ry2 = 283
θ = tan-1(Ry/Rx) = tan-1 (273/73) = 750 Forces (N )
Vector
addition 1 F1 = 200 N, 1 =30˚
F2 = 200 N, 2 =120˚ Vector
addition 2 F1 = 200 N, 1 = 20˚
F2 = 150 N, 2 = 80˚ Vector
addition 3 F1 = 200 N, 1 = 0˚
F2 = 150 N, 2 = 90˚ Vector
components F = 200 N, 1 = 60˚ Vector
addition 4 Resultant (R magnitude and θ direction)
Graphical
Analytical
770 280 283 N 750 Fx Fx = 100 N Fy Fy F1 = 100 N, 1 =30˚
F2 = 150 N, 2 = 90˚
F3 = 200 N, 3 = 225˚ 2

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