Question

The vertical force F acts downward at A on the twomembered frame. Determine the magnitudes of the two components of F directed along the axes of AB and AC. Set F = 500N.

Answer 1

The question is incomplete. The complete question is attached as an image and explanation is provided below.

Step-by-step explanation:

Parallelogram Law for Vector Addition:

If a force F is to be resolved into components along two axes b and c, then start at the head of force F and construct lines parallel to the axes, eventually forming a parallelogram. The sides of this parallelogram becomes Fb and Fc

We have to find the component of force
`F_(AB)` and
`F_(AC)` exerted at point A in the diagram.

We can use law of sines as illustrated in the diagram.

To find
`F_(AB)`

`(F_(AB))/(sin60)  =(500)/(sin75)`

`{F_(AB)  =(500)/(sin75)sin60`

`{F_(AB)  =(500)/(0.965)0.866`

`F_(AB)=448.7 N`

To find
`F_(AC)`

`(F_(AC))/(sin45)  =(500)/(sin75)`

`F_(AC)  =(500)/(sin75)sin45`

`F_(AC)  =(500)/(0.965)0.7071`

`F_(AC)=366.3 N`