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

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Homework Help Overview

The discussion revolves around determining the angle of an asteroid's acceleration based on given force components and their relationship to acceleration. The problem involves vector notation and the application of trigonometric functions to find the angle relative to the positive x-axis.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand whether to use the arctangent of acceleration components (ay/ax) or force components (Fy/Fx) to find the angle. Some participants suggest that it should not matter since force and acceleration are parallel according to Newton's second law. There is also a concern about discrepancies in the angle calculated from different methods.

Discussion Status

Participants have provided guidance on the relationship between force and acceleration, noting that both methods yield similar results. However, the original poster continues to seek clarity on why their final answer is being marked incorrect despite consistent calculations.

Contextual Notes

The original poster mentions a requirement for significant figures and expresses confusion over the accuracy of their input into a system, indicating potential issues with rounding or significant digit handling.

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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