Need help with physics please!!

[doctorme555]

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I was wondering if anyone would be willing to help me with a problem I have in my physics class relating to electric fields. Here it goes:


A point charge (m=1.0 g) at the end of an insulating string of length 50 cm is observed to be in equilibrium in a known uniform horizontal electric field, E = 9200 N/C, when the pendulum has swung so it is 1.0 cm high. If the field points to the right, determine the magnitude and sign of the point charge.

Here's the answer: 2.2 X 10^-7, positive. I just don't know how to get to this answer. Any help is greatly appreciated.

 

[Rapid Decomposition]

This is kind of hard to explain without diagrams, but here goes. Ok, the string is 50 cm long, and the ball rises to a height of one cm. So if you were to draw a right triangle where the string is the hypotenuse, the vertical side would 49 cm, since the ball is 1 cm higher than where it started - the vertical component would be 50-1, which is 49. Then, to find the angle closest to the charge, you would just use arcsin 49/50, which gives you 78.5 degrees for that angle.

Alright, now make a force diagram - there are three forces on the charge, tension on the string (directed at 78.5 degrees from the horizontal), the electric field (horizontal), and gravity(vertical).

Gravity is easy - .001kg x 9.8 m/s2 = .0098 N downwards. So, because the charge is in equilibrium, the vertical component of the tension must equal .0098. So if you set up a right triangle where the vertical side is .0098 and the opposite angle is 78.5, you can use tangent to find the horizontal force, which is .0019938 N (number of decimal places is arbitrary), directed to the left (I'm assuming because of the answer that the electric field is going to the right, and the point charge is to the right side of vertical). So, the electric field exerts the same force to the right.

Use q = F/E to find q, which is 2.2x10^-7 C. The charge is positive because electric fields exert force on positive charges in the same direction as the field, while they exert forces in the opposite direction of the field for negative charges.

Let me know if you understand this. You can PM me if you have other questions!

 

[tryingagain]

Thank God I'm done with Physics.

 

[OnyxGaia]

Originally posted by tryingagain
Thank God I'm done with Physics.

I was all happy, ready to get a jump start on my Physics before the class begins (today). For some reason, I fall into the sweetest sleep while reading my textbook on the train. I have a feeling I need to review trig, because my eyes just glaze over when reading about vectors, sines and cosines.

🙁

Onyx