Resolve each force acting on the support 2


Resolve each force acting on the support into its x and y components, and express each force as a Cartesian vector.

Resolve each force acting on the support

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 each force separately on it’s own coordinate plane and break each vector into it’s x and y components. Each force is separately drawn below:

Resolve each force acting on the support solution

Resolve each force acting on the support solution

Resolve each force acting on the support solution

Carefully analyze each force and it’s components. Now, we can write each component using the i,j,k Cartesian coordinate system.

For force F_1 we see that it has two components, i and j which are both positive. So we can write F_1 as follows:

\vec{F_1} = \left\{800 \cos60^0(i)+800\sin 60^0(j)\right\}N

\vec{F_1} = \left\{400i+693j\right\}N

 

For force F_2 we see that it also has two components, but note that the i component is negative.

\vec{F_2} = \left\{600 \sin45^0(-i)+600\cos45^0(j)\right\}N

\vec{F_2} = \left\{-424i+424j\right\}N

 

Finally, for force F_3, note that the j component is negative.

\vec{F_3} = \left\{650(\frac{12}{13})(i)+650(\frac{5}{13})(-j)\right\}N

\vec{F_3} = \left\{600i-250j\right\}N

This question can be found in Engineering Mechanics: Statics (SI edition), 13th edition, chapter 2, question 2-39.

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