Question

The 8.1 N weight is in equilibrium under the influence of the three forces acting on it. The F force acts from above on the left at an angle of with the horizontal. The 6.4 N force acts from above on the right at an angle of 46? with the horizontal. The force 8.1 N acts straight down What is the magnitude of the force F? Answer in units of N. *******NOTE******** I have already gotten this part, which is 5.66N, but I am having difficulties of answering the second portion of this problem, which is: What is the angle of the force F as shown in the figure? Answer in units of

Answer 1

`F=16.512\ N`

`\theta=74.38^(\circ)`

Step-by-step explanation:

Given:

Observe the schematic showing the angle direction and magnitude of the forces acting on the center of the mass.

Here we find that there are 3 forces acting on a point and we can build a relation among the forces and the angle between them using Lami's Theorem.

`(8.1)/(sin\ (134-\theta)) =(F)/(sin\ (136)) =(6.4)/(sin\ (90+\theta))`

Now, from the extreme left and extreme right term:

`(8.1)/(sin\ (134-\theta)) =(6.4)/(sin\ (90+\theta))`

`(8.1)/(6.4) * cos\ \theta=0.72* cos\ \theta+0.7* sin\ \theta`

`\theta=74.12^(\circ)`

Now, for calculating force F:

`(F)/(sin\ (136)) =(6.4)/(sin\ (74.12+\theta))`

`F=16.25\ N`