# Simple pendulum in an electric field

## Homework Statement

A simple pendulum of length (1.0m) and mass (5.0*10^-3 kg) is placed in a uniform electric field that is directed vertically upward. The bob has a charge (-8*10^-6 C). The period of the pendulum is (1.2 s). What are the magnitude and direction of the electric field?

T=2*Pi*sqrt(L/g)

F=q*E

Maybe F=ma

## The Attempt at a Solution

I'm assuming the question was just being redundant since it provided the direction. Lacking a great deal of knowledge about pendulums, I at first assumed that g in the period equation could be replaced by a generic acceleration, then using the fact that the net vertical force (ignoring tension since if g were the net acceleration under regular circumstances, it would also ignore tension) is equal to the sum of gravity and coulomb force, go through a bunch of algebra to solve for the magnitude of E. I don't know if that's correct...

Otherwise, I'd imagine writing out some kind of DE would make it very complex. I could just use a few hints as to what I should do, or maybe some kind of primer on pendulums in general. Thank you very much.

kuruman
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I am not sure why you are asked to find the direction of the electric when you are told that it is directed "vertically upward". Setting that aside, yes you can calculate the effective acceleration of gravity, i.e. the vector sum of 9.81 m/s2 down and the acceleration due to the electric field (qE/m in what direction?) and from that deduce the magnitude of the electric field.

I am not sure why you are asked to find the direction of the electric when you are told that it is directed "vertically upward". Setting that aside, yes you can calculate the effective acceleration of gravity, i.e. the vector sum of 9.81 m/s2 down and the acceleration due to the electric field (qE/m in what direction?) and from that deduce the magnitude of the electric field.

So it's really as simple as the algebraic method I did at first? g in the period equation is just "effective gravity?"

I had come up with something on the order of 104 N/C, which seemed like a fairly reasonable strength electric field. I appreciate your response, since I was about ready to resign myself to not getting a response. heh

kuruman