Forces act on the screw eye


Two forces act on the screw eye. If F=600 N, determine the magnitude of the resultant force and the angle θ if the resultant force is directed vertically upward.

Forces act on the screw eye

Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

Solution:

Let us first draw the vector components as follows:

Two forces act on the screw eye

Note that we drew the resultant force vertically upward as stated in the question.

Now, we can draw the vectors tail to tail.

Two forces act on the screw eye

Let’s apply the law of sines to figure out θ. (Forgot the law of sines?)

\frac{\sin \theta}{600}=\frac{\sin 30^0}{500}

\theta = 36.87^0

Now that we have θ, we can figure out \phi.

\phi=180^0-(30^0+36.87^0) (Remember, all interior angles in a triangle must add up to 180^0)

\phi=113.13^0

Now that we have both θ and \phi, we can use the law of sines to figure out F_R.

\frac{F_R}{\sin 113.13^0}=\frac{500}{\sin 30^0}

F_R=919.61N

This question can be found in Engineering Mechanics: Statics (SI edition), 13th edition, chapter 2, question 2-23.

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