Solving a Statics Problem with F=80N

[ebinesos]

hey all. I'm having problems with what should be a simple statics problem.

"The Magnitude of force F is 80.0 N. What are the madnitude of its components a) F\ab and b) F\ac that are parallel to the bars AB and AC respectively."

The picture: Force F pointing straight down. bar AB pointing 30 left of straight up (NW), and and bar AC pointing 70 degrees left of straight up (NW also).

I know i need to use the dot product somehwhere, but I can't determine what i need to do it with respect to. But I did rotate the problem 90 degrees CCW, and had the resulting equation:

|80*F\ac|cos110 + |80*F\ab|cos150=0

additional question: will F\ab + F\ac = 80. When adding up all those forces this problem doesn't seem to be in static equallibrium...

Thanks

 

[haynewp]

No, adding the force onto each bar will not equal the original force.

Each component part of your equation is right, but I do not understand why you are trying to add the components. When you see a force written as F=#i+#j, the 'i' and 'j' are 90 degrees apart.

 

[piercas]

for reaching out for help with your statics problem. It seems like you have a good understanding of the problem and are on the right track with using the dot product. To solve for the magnitude of the components, you will need to use the dot product with respect to the direction of each bar, AB and AC. This will give you two equations with two unknowns (F\ab and F\ac) that you can solve simultaneously.

Regarding your additional question, yes, F\ab + F\ac should equal 80N. This is known as the principle of superposition, which states that the total force on an object is equal to the sum of all the individual forces acting on it. If the forces do not add up to 80N, then there may be an error in your calculations or assumptions.

It is also important to note that in a statics problem, the forces should add up to zero in order for the object to be in equilibrium. If your equations are not resulting in a zero sum, double check your calculations and make sure all forces and angles are accounted for correctly.

I hope this helps you solve your problem. If you continue to have trouble, don't hesitate to reach out for further assistance. Good luck!