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

In summary: However, your significant digits are incorrect, so 10.704 degrees is actually closer to the true angle.
  • #1
Ella1777
15
0
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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  • #2
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##).
 
  • #3
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!
 
  • #4
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.
 

1. Should I use the arc tan of (ay/ax) or of (Fy/Fx) for calculating angles in a force diagram?

It depends on what information you are trying to obtain. If you want to calculate the angle of a force vector in relation to the x-axis, you should use the arc tan of (Fy/Fx). However, if you want to calculate the angle of the acceleration vector in relation to the x-axis, you should use the arc tan of (ay/ax).

2. What is the difference between using the arc tan of (ay/ax) and of (Fy/Fx) in a force diagram?

The main difference is in the interpretation of the resulting angle. When using the arc tan of (Fy/Fx), the angle represents the direction of the force vector in relation to the x-axis. Whereas, when using the arc tan of (ay/ax), the angle represents the direction of the acceleration vector in relation to the x-axis.

3. In which situations would it be more appropriate to use the arc tan of (ay/ax) instead of (Fy/Fx)?

The arc tan of (ay/ax) is more appropriate to use when dealing with objects that are accelerating, such as in projectile motion or circular motion. This is because the acceleration vector is of more interest in these situations rather than the force vector.

4. Are there any advantages to using the arc tan of (Fy/Fx) over (ay/ax)?

Yes, there are advantages to using the arc tan of (Fy/Fx) in certain situations. For example, in a static equilibrium problem, where the acceleration is zero, using the arc tan of (Fy/Fx) would be more appropriate as it would give you the direction of the force vector directly without having to calculate the acceleration first.

5. Can I use both the arc tan of (ay/ax) and of (Fy/Fx) in the same problem?

Yes, it is possible to use both in the same problem. This may be necessary in situations where both the force vector and acceleration vector are of interest, such as in a problem involving both acceleration and forces acting on an object. However, it is important to clearly state which angle represents which vector in your solution.

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