Question

The two structural members, one of which is in tension and the other in compression, exert the indicated forces on joint O. Determine the magnitude of the resultant R of the two forces and the angle θ which R makes with the positive x-axis. The angle θ is measured counterclockwise from the positive x-axis.

Answer 1

R = 3.606 KN, θ = 24°

Step-by-step explanation:

Resolving the forces to the x-direction

Rx = 3cos60 + 2cos30

= 1.5 + 1.732 = 3.232 KN

Resolving the forces to the y-direction

Ry = -3sin60 + 2sin30

= -2.6 + 1 = -1.6 KN

Getting the resultant of the two forces

R =
`√(Rx^2 + Ry^2)`

Substituting the values of Rx and Ry, we obtain

R = 3.606 KN

tanθ = Ry/Rx = | -1.6/3.232 |

Then we have θ = 24°