How Does Tension Affect Electric Charge Calculation?

[verd]

Hey,

I thought I did this correctly and my answer turned out incorrect. Here's the problem:

http://synthdriven.com/images/deletable/help.jpg"

This is what I did:

In order to use Coloumb's Law, I need r, the distance between the two charges.

$$\arcsin{4}=\frac{x}{0.24m}$$
$$x=0.24\arcsin{4}=0.098m$$
$$r=2x=0.196m$$

So that's r.

Then I need to pick one side of this thing apart and break it down into x and y-components.

With the weight, I have three forces acting on this thing. The tension in the rope, the weight, and the electrical force repelling each sphere.

My goal is to find the x-component of the electrical force so I can then plug it into Coulomb's law and find the charge.

For the weight,
Wx=0
Wy=-mg=-0.98

For the tension,
Tx=-Tsin4
Ty=Tcos4

For the electrical force,
Fx=Tsin4
Fy=0

To find T, all I did was:

FyNET=Wy+Ty+Fy=Tcos4-mg
(net force of y-component)

T=mg/cos4
Right??

So for T, I get 0.098239

Plugging that into Tx, I get 0.006853And then it goes into Coulomb's law. Which I have reformatted this way:

$$F=\frac{kq^2}{r^2}$$

...Because both charges are supposed to be equal... Moving that around, I get:
$$q=\sqrt{\frac{Fr^2}{k}}$$

Plugging in values, I got 1.711e-7What did I do wrong?

 

[Doc Al]

This is what I did:

In order to use Coloumb's Law, I need r, the distance between the two charges.

$$\arcsin{4}=\frac{x}{0.24m}$$
$$x=0.24\arcsin{4}=0.098m$$
$$r=2x=0.196m$$

So that's r.

That first equation should have sin(4), not arcsin(4).

 

[kyle8921]

Hi there,

First of all, it's great that you are trying to use Coulomb's Law to solve this problem. However, there are a few mistakes in your calculations that led to the incorrect answer.

1. In order to use Coulomb's Law, you need to find the distance between the two charges, not the angle. The equation you used to find r is incorrect. The correct equation is: r = 0.24m / sin(4°) = 5.99m. This is the distance between the two charges.

2. Your calculations for the y-components of the tension and electrical force are incorrect. For the tension, Ty should be Tsin4°, not Tcos4°. For the electrical force, Fy should be -Tsin4° (since the force is repelling the spheres). Therefore, your equation for T is also incorrect. The correct equation is: T = mg / sin4° = 14.47N.

3. The x-component of the electrical force is not equal to Tx. It should be -Fx = -Tsin4° = -0.98N.

4. Your equation for q is incorrect. The correct equation is: q = sqrt(Fx * r^2 / k) = 3.43e-7 C.

I hope this helps you understand where you went wrong in your calculations. Remember to always double check your equations and units to ensure accuracy. Keep up the good work!