Question

1 = (60)(cos 20 + sin 20)

2 = (13)( 20+45°)

3 = (65) cos(20 − 6 ⁄ )

a) Find the value of the resultant force. b) Show the vectors F1, F2, F3, and ΣF on the rotating vector and trigonometric diagram.

Answer 1

To find the value of the resultant force, we need to add the vectors F1, F2, and F3.

a) Resultant Force:

1 = 60(cos 20° + sin 20°)

2 = 13(20° + 45°)

3 = 65cos(20° − 6/°)

To find the resultant force, we can add the x-components and the y-components of the vectors separately.

X-component:

F1x = 60cos(20°)

F2x = 13cos(20° + 45°)

F3x = 65cos(20° − 6/°)

Y-component:

F1y = 60sin(20°)

F2y = 13sin(20° + 45°)

F3y = 65sin(20° − 6/°)

Now, we can calculate the resultant force:

Resultant Force (Rx) = F1x + F2x + F3x

Resultant Force (Ry) = F1y + F2y + F3y

Then, the magnitude of the resultant force can be found using the Pythagorean theorem:

Resultant Force (R) = sqrt(Rx^2 + Ry^2)

b) To show the vectors F1, F2, F3, and the resultant force ΣF on the rotating vector and trigonometric diagram, we would need the specific angles and lengths of each vector. Please provide the angle and length information for each vector, and I can assist you in creating the diagram.