How do you find magnitude of the resultant force and the angle between the resultant and each force?

Question

Forces of 3 lbs and 8 lbs act at an angle of 90° to each other.

Answer 1

Hi Joy,

 

                                           A

                                           ∧

                                           |
                                           |
                                           | 3 Ib
                                           |  
                                           |
                                           |

O--------------------------------->

           8 Ib

If you draw a straight line from point O to point A that will form the resultant force, if the angle between that line and

the  8 Ib force is θ then the angle between the 3 Ib force will be 90-θ. Note that these three forces form a right triangle.

 

R² = (8 Ib)² + (3 Ib)² = 73 Ib²

 

R = √(73 Ib²) ~ 8.54 Ib 

 

The resultant force is 8.54 Ib

 

tanθ = 3 Ib/8 Ib    gives θ = tan^-1(3/8) =20.55° ,     90 - θ = 69.45° 

The angle between the 8 Ib force and the resultant is 20.55°

The angle between the 3 Ib force and the resultant is 69.45°