Question

A force F x of magnitude 6.00 units act at the origin in a direction 30 degree above the positive x axis. A second force Fy of magnitude 5.00 unit act at the orign in the direction of positive y axis. 1) Find the magnitude and direction of the resultant force mathematically. 2) Also find the resultant graphically

Answer 1

Magnitude of vector addition: 10.6

Direction of vector addition: 16.4 degrees

For resultant graphically see attached image

Step-by-step explanation:

Mathematically the resultant is calculated using x and y components:

F1 = 6 units at 30 degrees, then its components are:

`F1_x= 6 * cos (30^o) = 6 * (√(3) )/(2) = 3\,√(3) \approx 5.196\\F1_y = 6 * sin(30^o) =6 * (1)/(2) = 3`

F2 = 5 at 0 degrees (on the x-axis), then the x and y components are:

F2x = 5

F2y = 0

The addition gives the following components:

Fx = 10.196

Fy = 3

Which result (via Pythagoras Theorem) in a magnitude of:

`|F|=√(10.196^2+3^2)\approx 10.6`

and angle:

`\theta= arctan(3/10.196) \approx 16.4^o`