# Homework Help: Forces on a Particle

1. Sep 18, 2010

### uchicago2012

1. The problem statement, all variables and given/known data
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

3. 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.

#### Attached Files:

• ###### Figure1.jpg
File size:
3.8 KB
Views:
98
2. Sep 18, 2010

### kuruman

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

3. Sep 18, 2010

### uchicago2012

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.

4. Sep 18, 2010

### 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?

5. Sep 18, 2010

### 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.

6. Sep 18, 2010

### 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?