Question

3. Use the polygon method to determine the resultant of the following forces: a) 8 lb at 40°, b) 9 lb at 110°, 11 lb at 160°, and 12 lb at 200°. (Graphical Solution)

Answer 1

To get the graphical solution, plot these four force vectors on the graph paper. Let's name the 4 vectors. Let F1= 8lb, F2=9lb, F3=11lb and F4=12lb. Follow the below mentioned steps to plot:

(Please note that these steps can be used for any number of vectors and for any vector)

1. Choose an appropriate scale to represent the magnitude of the vector. In this case, I am choosing 1 cm = 2lb. You can choose whatever you want to depending on the size of your graph sheet.

2. Draw a horizontal line. This will be used as your base line from where you will measure your angles.

3. Mark a point, say A, on this line. This will be the starting point, I.e, start F1 from here. Measure 40^o from the base line and draw a 4 cm line (since 8/2=4) in that diection.

4. Now place the protractor on the head of F1 and parallel to the base line and measure an angle of 110^o. Draw a line of length 4.5 cm in that direction ( 9/2= 4.5). This will be F2.

5. Follow the same procedure for F3. Place protractor on the head of F2 and parallel to the base line and measure an angle of 160^o. Draw a line of 5.5 cm (11/2= 5.5) in that direction. This wil give you F3.

6. For F4, follow the same steps but since the angle is 200^o, measure 20^o below the base line.

7. For the resultant, join the tail of F1 to the head of F4. The length of this line multiplied by the scale factor will give the magnitude of the resultant ( in this case it is approximately coming to around 11 cm. So magnitude is 11x2= 22 lb) The angle of the resultant vector can be measured using a protractor from the base line. (Since the angles are not drawn to scale, I have marked it as y^o.)