Force on a Particle: Find Direction of Movement from Rest

[uchicago2012]

Homework Statement

In the figure, force F_B has four times the magnitude of force F_A. 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 F_B + F_A, 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 P_x = ... and P_y = ... does not seem sufficient.

 

[kuruman]

Don't forget Newton's Second Law. It gives you the direction of the acceleration. What is that direction?

 

[uchicago2012]

Well, since all the forces that act on the particle are F_A and F_B and
F_Ax = F_A cos theta = F_A
F_Ay = F_A sin theta = 0
F_Bx = -4F_A cos theta = -F_A (2.83)
F_By = -4F_A sin theta = -F_A (2.83)

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

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

but is that even an answer? And I wasn't sure if I should just take F_Ax + F_Bx or F_Ax - F_Bx, 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.

 

[kuruman]

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?

 

[uchicago2012]

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.

 

[kuruman]

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?