Force on a Particle: Find Direction of Movement from Rest

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The discussion revolves around determining the direction of a particle's movement when acted upon by two forces, FB and FA, with FB being four times stronger than FA. The participant expresses confusion about how to relate the net force's direction to the particle's movement, particularly when starting from rest. They calculate the components of the forces and derive the net force, but question whether they should add or subtract the components due to their opposing directions. The participant concludes that the angle of acceleration, approximately 237 degrees counterclockwise from a reference line, indicates the particle's movement direction, which is down and to the left. The relationship between the acceleration direction and the particle's motion is clarified, emphasizing the importance of understanding net force and acceleration in this context.
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Homework Statement


In the figure, force FB has four times the magnitude of force FA. Find the direction in which the particle moves, if it starts from rest.
See figure 1

The Attempt at a Solution


I was a bit confused about what exactly my answer is going to look like. I can find the x and y components of FB + FA, but that would be the net force on the object, not its direction. Can I say the direction of the net force is the direction of the particle? How exactly does one say that? The direction is Px = ... and Py = ... does not seem sufficient.
 

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Don't forget Newton's Second Law. It gives you the direction of the acceleration. What is that direction?
 
Well, since all the forces that act on the particle are FA and FB and
FAx = FA cos theta = FA
FAy = FA sin theta = 0
FBx = -4FA cos theta = -FA (2.83)
FBy = -4FA sin theta = -FA (2.83)

(I used theta = 225 degrees because I drew FB in the third quadrant.)

then Fnet = (-1.83 FA)x - (2.83 FA)y
Fnet = ma, so
a = [(-1.83 FA)x - (2.83 FA)y ] / m

but is that even an answer? And I wasn't sure if I should just take FAx + FBx or FAx - FBx, since they're in opposite directions. But FBx is already negative to account for that, which is what I believe I did when I measured its angle from the positive direction of the x axis.
 
Can you specify the direction of the acceleration in terms of an angle measured counterclockwise with respect to the dotted line in the drawing? How is the direction of the acceleration related to the direction of motion if the particle starts from rest?
 
I can find theta, how interesting. I found theta equals about 237 degrees with respect to the dotted line. I don't know if I can relate that to the given coordinate system though- the particle is just moving down and to the left.
 
All you need to specify is theta counterclockwise with respect to the dotted line. If it is 237 degrees, isn't that down and to the left?
 

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