# Force on a Particle: Find Direction of Movement from Rest

• uchicago2012
In summary, the problem involves finding the direction in which a particle will move when starting from rest, given that force FB has four times the magnitude of force FA. Using Newton's Second Law and the given forces, the net force on the particle is calculated to be (-1.83 FA)x - (2.83 FA)y. The direction of acceleration can be specified as theta counterclockwise with respect to the dotted line, which is found to be 237 degrees in this case. This corresponds to the particle moving down and to the left.
uchicago2012

## 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.

#### Attachments

• Figure1.jpg
3.8 KB · Views: 346
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?

## 1. What is force on a particle?

Force on a particle refers to the physical quantity that causes an object to accelerate or move in a certain direction. It is typically measured in Newtons (N) and is represented by the symbol F.

## 2. How is force on a particle calculated?

Force on a particle is calculated using the equation F=ma, where F is force, m is mass, and a is acceleration. This equation is known as Newton's second law of motion.

## 3. Can the direction of movement of a particle be determined from rest?

Yes, the direction of movement of a particle can be determined from rest. This can be done by analyzing the forces acting on the particle and determining the net force, which will indicate the direction of movement.

## 4. What factors influence the direction of movement of a particle?

The direction of movement of a particle is influenced by the magnitude and direction of the applied force, as well as the mass and initial velocity of the particle.

## 5. How does friction affect the direction of movement of a particle?

Friction can act in the opposite direction of the applied force, causing the particle to slow down or change direction. It can also act in the same direction as the applied force, aiding in the movement of the particle. The specific direction of movement will depend on the strength and direction of the applied force and the type of friction present.

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