Please assist with Vector addition using Graphical and Analytical methods - Horizontal Force Board

Question

After doing an experiment on vector addition using a Horizontal force board (Gravesand Apparatus), with the need to use graphical and analytical methods of vector addition. For the Horizontal force board, the force-meters were stretched into the alignment of a letter Y; the two force-meters at the top each had a reading of 1.55 N whilst the force-meter at the bottom (equilibrant) had a reading of 1.85 N. The angle in between the junction of the “Y” was 110°. Using a sketch with a scale of 1 cm = 0.5 N for the graphical method. With that in mind, how can I use this information in the analytical method to calculate the Size and the direction of the Resultant force, using the both the Parallelogram rule and vector tangent rule?

Please refer to the attached image for sketch:

https://ibb.co/xHRcbLS

(Please correct my calculations)

Experiment Data:

F_A = 1.55N

F_B= 1.55 N

F_C (Equilibrant) = 1.85 N

Angle of F_A relative to X-axis = 140°

Angle of F_B relative to X-axis = 35°

Answer 1

Analytical solution:

First split forces F_A and F_B in their respective horizontal and vertical components by

Applying definition of Trigonometric functions.

Force    Magnitude  Angle X-Horizontal Component      Y-Vertical Component

Vector   Newton N    Degrees°       F_x = F cos θ N                   F_y = F sin θ N

 F_A           1.55           140      1.55 x -0.766= -1.187       1.55 x 0.643= 0.997

 F_B           1.55            35       1.55 x 0.819 = 1.27           1.55 x 0.574= 0.889

                                                           ∑F_x = 0.08 N                    ∑F_y = 1.886 N

Resultant force= (∑F_x² + ∑F_y²)^1/2 = (0.08^2 + 1.886^2)^1/2 = 1.888 N and angle is 87.57°

Analytical solution is very close to experiment value 1.85 N

I hope this helps.

Sincerely,

Shailesh (Sky) Kadakia, Expert Tutor with WYZANT

Former Professor, University of Pittsburgh, Johnstown PA

Electrical Engineering Technology Department