Posted by Meredith Mcneeds Help! on Monday, November 19, 2007 at 8:08pm.
Hey, ok so I am supposed to be helping my cousin this with this physics problem, and this is the only one that has ever stumped me! Neutral metal spheres A and B each of mass 0.2 kg hang from insulating wires that are 4.0 m long and are initially touching. An identical metal sphere C, with a charge of -6.0 x 10^-6C is brought into contact with both spheres simultaneously and then removed. Spheres A and B then repel. What is the angle between the wires? Note>> use small angle approximation Tan theta is approximately equal to sin theta. I think I the answer is 9.6 or 9.4 degrees, roughly, but please help me!! Thanks!
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Physics Repost - bobpursley, Monday, November 19, 2007 at 8:40pm
Sphere A and B each have 1/3 the original charge.
The electrostatic force separates them.
Electrostaticforce/mg= tanTheta
but sinTheta= d/2 / length where d is the sphere separation. Using the small angle approximation
Force/mg= d/2*4
K(1/3 q)^2/d^2 = d/8
solve for d. q is given as the initial charge.
When d is found, you can find theta.
Physics Repost - Meredith Mcneeds Help!, Monday, November 19, 2007 at 9:01pm
Ok good, I did something similar to you! I had slightly different values then the ones I gave in this question for certain purposes, but; I did this: tan theta =f horizontal (which is Electric force)/Fg , but Fg =mg
mgtantheta= Fhorizontal (tan theta = 1/2r over 4)
mg1/2r/4= Kq^2/r^2 >>>I have written down what 1/3 of the original charge is... so I have accounted for it)
and then finally r^3=4Kq^2/mg and then I solved and wound up getting the angle to one side, but because there are two small triangles in the big one, added the two small angles together to get a value near 17-18 degrees... before I added, the angle was roughly 9 degrees...
Does all of this sound correct? Thanks sooo much!
Based on the information provided, it seems like you have made some correct calculations. However, it would be helpful to see the exact calculations and values you used to confirm if everything is correct.
Here's a step-by-step breakdown of the solution for finding the angle between the wires:
1. Start with the equation: tan(theta) = sin(theta) = d/2L (using the small angle approximation)
2. Use the equation for the electrostatic force between the spheres in terms of the distance "d":
F = K(q1*q2)/d^2
Since the charge of C is divided equally between A and B, q1 and q2 are both (1/3)q, where q is the initial charge of C.
3. Equate the electrostatic force to the weight of the spheres:
(K((1/3)q)^2/d^2) / m = g
4. Rearrange the equation to solve for "d":
d^3 = (3Kq^2)/(mg)
5. Substitute the given values into the equation and solve for "d".
6. Once "d" is found, substitute it into the equation for tan(theta) = d/2L to find the angle "theta".
It is important to ensure that you are using consistent units and values throughout the calculations. Double-checking your calculations is always a good idea to avoid any mistakes.
It seems like you and the other person were on the right track with your approaches to solving the problem. The equation they provided, "K(1/3 q)^2/d^2 = d/8", is derived from Coulomb's law and the equation for gravitational force. By equating the force due to the electrostatic repulsion to the force due to gravity, you can solve for the distance "d" between the spheres.
You mentioned that you used the equation "mg1/2r/4= Kq^2/r^2" and then simplified it to "r^3=4Kq^2/mg". This equation seems incorrect based on what you described. The correct equation to use is "K(1/3 q)^2/d^2 = d/8".
To find the angle "theta", you can use the small angle approximation, which states that tan(theta) is approximately equal to sin(theta) for small angles. Once you have found the value of "d" using the equation above, you can use the equation "sin(theta) = d/2 / length" to calculate the angle "theta".
It seems like you obtained an angle of roughly 9 degrees using your calculations. However, you also mentioned adding two small angles together to get a value near 17-18 degrees. It's important to make sure that you're using the correct equations and not double-counting or adding angles incorrectly. Double-check your calculations to ensure accuracy.
Overall, it seems like you have the right approach to solving the problem. Just be careful with your calculations and make sure to use the correct equations.