Vector addition using Vertical force board

Question

After doing an experiment on vector addition using a Vertical force board (Gravesand Apparatus), with the need to use graphical and analytical methods of vector addition. For the Vertical force board, the weights at the outer ends were each 70 g, which equates to 0.686 N, while the equilibrant weight was 90 g (0.882N). For the graphical method used a scale of 1 cm = 0.245 m. 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?

Experiment Data:

F_A = 0.686 N

F_B = 0.686 N

F_C = 0.882 N

Angle of F_A relative to x-axis: 140°

Angle of F_B relative to x-axis: 40°

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           0.686         140      0.686 x -0.766= -0.526     0.686 x 0.643= 0.441

 F_B           0.686          40       0.686 x 0.766= 0.526        0.686 x 0.643= 0.441

                                                           ∑F_x = 0 N                    ∑F_y = 0.882 N

Resultant force = (∑F_x² + ∑F_y²)^1/2 = (0 + 0.882^2)^1/2 = 0.882 N and angle is 90 ° y-axis

Analytical solution matches with force of equilibrium weight.

I hope this helps.

Sincerely,

Shailesh (Sky) Kadakia, Expert Tutor with WYZANT

Former Professor, University of Pittsburgh, Johnstown PA

Electrical Engineering Technology Department