Magnitude and direction of acceleration from two forces at 60°

[SherlockOhms]

Homework Statement

A particle of mass 2kg is moving under the action of two forces. They
are of magnitudes 12N and 8N, acting at an angle of 60 
to each other. Find
the magnitude of the acceleration of the particle and its direction relative to the
direction of the 12N force.

Homework Equations

F = ma.

The Attempt at a Solution

I know that this isn't actually a tricky problem but I can't seem to think it out properly.
Am I correct in decomposing both the 12N and 8N forces into vector form, i.e. 12cos60i = 12sin60j and 8cos60i + 8sin60j respectively. Then summing them and calculating both the magnitude and direction using tanθ = vj/vx. Is this correct? I'm sort of confused by the whole "relative to the 12N force" part. Thanks.

 

[SteamKing]

I think for this problem, assume the direction of the 12N force is a convenient reference, say F = (12, 0) N, so that this force acts in the positive x-direction. Then, the 8N force acts in a direction such that the angle with F is 60 degrees. Then, you can decompose into components and find the resultant before figuring the effect on the particle. In the OP, you had both force vectors heading in the same direction.

 

[Saxby]

I don't really know what you're doing with is vector thing. I believe the best way to solve this would be to find the total force in the direction along the 12N, and the total force perpendicular to it. Then use Pythagoras' theorem.

 

[SherlockOhms]

I think for this problem, assume the direction of the 12N force is a convenient reference, say F = (12, 0) N, so that this force acts in the positive x-direction. Then, the 8N force acts in a direction such that the angle with F is 60 degrees. Then, you can decompose into components and find the resultant before figuring the effect on the particle. In the OP, you had both force vectors heading in the same direction.

I understand what you're saying. Sounds correct to me like. Thanks.

 

[SherlockOhms]

I don't really know what you're doing with is vector thing. I believe the best way to solve this would be to find the total force in the direction along the 12N, and the total force perpendicular to it. Then use Pythagoras' theorem.

I'm not too sure what you have in mind. I can't think of anyway to solve this without the use of vectors. I'm struggling to visualise what you have in mind.