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

Answer:

$F=16.512\ N$

$\theta=74.38^{\circ}$

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.

$\frac{8.1}{sin\ (134-\theta)} =\frac{F}{sin\ (136)} =\frac{6.4}{sin\ (90+\theta)}$

Now, from the extreme left and extreme right term:

$\frac{8.1}{sin\ (134-\theta)} =\frac{6.4}{sin\ (90+\theta)}$

$\frac{8.1}{6.4} \times cos\ \theta=0.72\times cos\ \theta+0.7\times sin\ \theta$

$\theta=74.12^{\circ}$

Now, for calculating force F:

$\frac{F}{sin\ (136)} =\frac{6.4}{sin\ (74.12+\theta)}$

$F=16.25\ N$