Coulomb's Law Problem and net force

[Cisneros778]

Homework Statement

In a region of two-dimensional space, there are three fixed charges: +1 mC at (0, 0), -2 mC at (16 mm, -6 mm), and +3 mC at (-6 mm, 20 mm). What is the net force on the -2-mC charge?
-magnitude
-direction (° counterclockwise from the +x-axis)

Homework Equations

F = k*q1*q2 / d^2

The Attempt at a Solution

I got the magnitude correct. Fnetx: 8.77e07 N and Fnety: 5.71e07 N ; magnitude: 1.05e08 N. When I try to get the angle however my answer of 145 degrees is wrong. I don't understand why. I used arctan(Fnety/Fnetx).

 

[gneill]

Could be an accuracy issue. Your Fx and Fy values look okay, so try calculating your angle again. Show your work.

 

[Cisneros778]

@=theta
F12 = k*2mC*1mC/(17.1mm)^2 = 6.16e7
F32 = k*2mC*3mC/(34.1mm)^2 = 4.65e7

Fnetx = F12 cos(@) + F32cos(@)
Fnety = F12 sin(@) + F32sin(@)

Fnetx = 5.77e7 + 3e7 = 8.77e7
Fnety = 2.16e7 + 3.55e7 = 5.71e7

Answer for the magnitude of the force.
sqrt [ Fnetx^2 + Fnety^2 ] = 1.05e8 N
Answer for the angle of the force counterclockwise from the x-axis.
180 - arctan(Fnety/Fnetx) = 147 degrees

I've tried values of 33, 57, 123, 147, 145 and I still get the answer wrong (the reason why I tried 33, 57 etc. was to see if the computer was mistaken and wanted the angle from a different reference axis).

 

[gneill]

@=theta
F12 = k*2mC*1mC/(17.1mm)^2 = 6.16e7
F32 = k*2mC*3mC/(34.1mm)^2 = 4.65e7

Fnetx = F12 cos(@) + F32cos(@)
Fnety = F12 sin(@) + F32sin(@)

Fnetx = 5.77e7 + 3e7 = 8.77e7
Fnety = 2.16e7 + 3.55e7 = 5.71e7

Answer for the magnitude of the force.
sqrt [ Fnetx^2 + Fnety^2 ] = 1.05e8 N
Answer for the angle of the force counterclockwise from the x-axis.
180 - arctan(Fnety/Fnetx) = 147 degrees

I've tried values of 33, 57, 123, 147, 145 and I still get the answer wrong (the reason why I tried 33, 57 etc. was to see if the computer was mistaken and wanted the angle from a different reference axis).

Your work looks good. When I calculate the angle, keeping several extra decimal places for all intermediate results, the result is 146.933 degrees. So I think that your 147° answer should have been acceptable. I suggest that you contact your lecturer and present the issue.

 

[asteriatic]

I would first check to see if my calculations were correct. It is possible that there was a mistake in the calculation for the angle, which could result in an incorrect answer. I would also check to see if the values for the charges and their positions were entered correctly. If everything seems to be correct, I would then consider the possibility of using a different equation or method to calculate the angle.

Additionally, I would also consider the direction of the forces acting on the -2-mC charge. Since there are three charges present, there may be multiple forces acting on the charge from different directions. I would make sure to take into account all of the forces and their directions in order to accurately determine the net force and angle.

It is also important to note that Coulomb's Law only gives the magnitude of the force between two charges. It does not provide information about the direction of the force. Therefore, it is possible that the angle may need to be calculated using vector addition or trigonometric methods, rather than relying solely on the Coulomb's Law equation.

In conclusion, as a scientist, I would thoroughly check my calculations and consider other factors that may affect the determination of the angle in order to provide an accurate response to this problem.