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- Homework Statement
- I need to present Fay and Fax using Fa and cos(a) and sin(a). I seem to be missing a minus, why?
- Relevant Equations
- None
There are two ways to think of this.Edwardy said:Homework Statement:: I need to present Fay and Fax using Fa and cos(a) and sin(a). I seem to be missing a minus, why?
Relevant Equations:: None
View attachment 315305
Thank you,topsquark said:There are two ways to think of this.
1) The vector ##F_A## is in the 3rd Quadrant. So both of its vector components will point in the negative directions, thus ##F_{Ax}## and ##F_{Ay}## will be negative.
2) Again, the vector ##F_A## is in the 3rd Quadrant. So the angle it makes with the +x axis is actually ## \theta = 180 + \alpha##. (Or, equivalently, ##\theta = 360 - \alpha ##.) In the 3rd Quadrant ##sin( \theta )## and ##cos( \theta )## are negative.
-Dan
I have left the vector notation off here (it messes up the LaTeX for some reason.) The vector ##F_A## has vector components ##F_{Ax}## and ##F_{Ay}##. These are vectors so they have magnitude and direction. The magnitudes of the vectors ##\mid F_A \mid = F_A##, ## \mid F_{Ax} \mid = F_{Ax}##, ## \mid F_{Ay} \mid = F_{Ay}## are just numbers, taken to be positive by convention. The x component of ##F_A## is ##F_{Ax} ( - \hat{i} )## where ##\hat{i}## is the unit vector in the +x direction. The negative is attached to the unit vector direction, not the magnitude.Edwardy said:Thank you,
I have one more question though. From my understanding, we are not thinking of Fa as a vector here (hence the arrow above it is missing), so why wouldn't Fa be negative itself? It would have both negative coordinates?
Welcome!Edwardy said:Homework Statement:: I need to present Fay and Fax using Fa and cos(a) and sin(a). I seem to be missing a minus, why?
Relevant Equations:: None