Vectors Addition

Name:

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.

Please notice that in this document a bold letter (F or R) indicate the symbol of a vector.

1) Use graph paper, a ruler and 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 by drawing a coordinate system. Draw the first vector F₁:use a protractor to draw it in the direction indicated by the angle and use a ruler to determine the length according to your scale. At the end of this vector draw an arrow and start drawing as before the second vector F₂. 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 =77^0. Your results will be differentbut if you did it right they will be close to the values of the Analytical method R=285 N and =75⁰

2) Use the analytical method (component or mathematical method) to find the resultant for the analytical column. Remember you will resolve the forces into their "x" and "y" components. F_x = Fcos, F_y = Fsin

Add the components Rx= F1x+F2x+... Ry= F1y+F2y+... and then use the Pythagorean Theorem to find the resultant R = R_x²+R_y²

The angle is given by: = tan^-1(R_y/R_x)

3) Complete the table, include the vector diagrams and thecalculationsin the lab report.

Include all the pictures in the word document andupload just one file. The accepted formats are word or pdf.

Please review the videos below for this lab.

Solved example illustrating both graphical and analytical methods of adding vectors:

Please notice the angles, the arrows at the end of the lines, the labels with vectors arrow hats.

F1x = 200cos 30 = 173

F1y = 200sin30 = 100

F2x = 200cos 120 = -100

F2y = 200sin120 = 173

Rx = 173-100 = 73

Ry = 100+173= 273

R= R = R_x²+R_y² = 283

= tan^-1(R_y/R_x) = tan^-1 (273/73) = 75⁰

Activity	Forces	Graphical R (N)	Graphical	Analytical R(N)	Analytical
1.Vector addition 1	F1 = 200 N, 1 =30 F2 = 200 N, 2 =120	280	770	283	750
2.Vector addition 2	F1 = 150 N, 1 =60 F2 = 300 N, 2 =180
3.Vector addition 3	F1 = 200 N, 1 = 20 F2 = 100 N, 2 = 80
4.Vector addition 4	F1 = 200 N, 1 = 0 F2 = 150 N, 2 = 90
5.Vector addition 5	F1 = 200 N, 1 =330 F2 = 150 N, 2 = 90 F3 = 100 N, 3 = 180