The force F = 450 lb acts on the frame


The force F = 450 lb acts on the frame. Resolve this force into components acting along members AB and AC , and determine the magnitude of each component.

The force F = 450 lb acts on the frame

Solution:

Draw the components as follows.

The force F = 450 lb acts on the frame

The goal of drawing out the components is to find the missing angles. We can use the alternate interior angles theorem, corresponding angles theorem and consecutive angles theorem to figure out the values.

After we figure out the angles, we can draw the vector components separately as follows.

The force F = 450 lb acts on the frame

Use sine law to solve for F_{AB} and F_{AC}

\dfrac{F_{AB}}{\sin105^0} = \dfrac{450}{\sin30^0}

F_{AB} =869lb

 

\dfrac{F_{AC}}{\sin45^0} = \dfrac{450}{\sin30^0}

F_{AC} =636lb

 

Another similar example to look at is to analyze forces effecting a bracket.

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