Should I use the arc tan of (ay/ax) or of (Fy/Fx) and why?

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SUMMARY

The discussion centers on calculating the angle of an asteroid's acceleration using either the arc tangent of acceleration components (ay/ax) or force components (Fy/Fx). Given the forces F1 = 28 N, F2 = 57 N, F3 = 38 N, and angles θ1 = 30° and θ3 = 60°, the calculated acceleration is a = 0.797 m/s². The user initially struggled with obtaining consistent angle values, ultimately finding that both methods yield similar results, around 10.7 degrees, but faced issues with significant figures when submitting answers on WileyPLUS.

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Ella1777
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Thread moved from the technical forums, so no Homework Template is shown
given: 128kg F1 = 28 N, F2 = 57 N, F3 = 38 N, θ1 = 30°, and θ3 = 60°.They are asking for the angle (measured relative to the positive direction of the x axis in the range of (-180°, 180°]) of the asteroid's acceleration?

The problem is displayed on quadrant I and IV
for vector notation I got Fx=(100.2N)i + Fy=18.91 j
So far I've got the acceleration part correct
$ a= \sqrt (0.783)^2 + (0.148)^2 a=0.797 m/s^2 $
BUT I'm trying to solve for the angle and the significant figures by 3rd sigfig
several other sites been doing tan^-1 (ay/ax) or tan^-1 (Fx/Fy) and i tried both but I am getting it wrong somehow.
should I do the arc tan by ay/ax or Fy/Fx and why should I ?
Thank you!
 
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It should not matter if you use the force components or acceleration components to deduce the direction since the force and acceleration are parallel (with the force being directly proportional to the acceleration according to Newton's second law ##\vec F = m\vec a##).
 
Orodruin said:
It should not matter if you use the force components or acceleration components to deduce the direction since the force and acceleration are parallel (with the force being directly proportional to the acceleration according to Newton's second law ##\vec F = m\vec a##).
Oh I see I tried it out and they got right around the same answer Thank you so much I understand now
when I used forces got : 10.687 degrees
when I used acceleration I got: 10.704 degrees
I typed this in several times into wileyplus as 10.7 degrees but I keep on getting it wrong. Why am I getting this wrong?
Thank you!
 
Ella1777 said:
when I used forces got : 10.687 degrees
when I used acceleration I got: 10.704 degrees
The difference can easily be attributed to rounding errors in your middle steps. You are giving too many significant digits here.

Ella1777 said:
Why am I getting this wrong?
This is unclear. Assuming your force components are correct (which they probably are if you get the correct magnitude of acceleration), I get the same angle.
 

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