Find the charge of a mass hanging from a pendulum in an electric field

[spsch]

Homework Statement

A charge with mass 1 gram hanging from a pendulum is at equilibrium 12 cm above the lowest vertical position. E= 9500. l the length of the pendulum is 55 cm.

Relevant Equations

QEd = mgh?

Hi, so I was able to solve this problem by just equating the forces (Tension, mg, and EQ).

But I thought I could also solve this problem with Conservation of Energy.
However, I calculated it several times, and I never get the right answer this way.
Doesn't the Electric Field do the work to put this charge at its new Gravitational Potential Energy position 12cm higher?
Or the -difference in Electric Potential is the Gravitational Potential gained?

$Q*E*d = m*g*x$ and therefore $\frac {mgx}{Ed} = Q$ ?
Or is there another Energy term I am missing?

 

[Doc Al]

Hi, so I was able to solve this problem by just equating the forces (Tension, mg, and EQ).

That is the correct approach.

But I thought I could also solve this problem with Conservation of Energy.

No, this is a force problem, not a conservation of energy problem. (If you released the charge from rest at the bottom position, it would swing up past the equilibrium point.)

 

[spsch]

Hello @Doc Al , Thank you very much for answering!
The correct approach has been the most obvious. I'm trying to do old problems in several ways now to practice.

I'm sorry I don't understand yet. Why would the charge swing past the equilibrium point?

Maybe I'm picturing it wrong.
I imagined the charge being released in the middle and the electric field pushed it up to the current position.
Until the forces cancel each other.
x (12cm) above the original position and a distance d along the electric field.
The electric field accelerates the charge but is losing magnitude ($cos(θ)$) gravity (increasing in magnitude with ($sin(θ)$)) is decelerating the charge until it comes to rest?

I'm sorry I'm sure I'm being super difficult!

 

[Doc Al]

Why would the charge swing past the equilibrium point?

Just because the net force is zero doesn't mean it stops.

I imagined the charge being released in the middle and the electric field pushed it up to the current position.
Until the forces cancel each other.

At that point, it's still moving. So it will keep going until it runs out of kinetic energy.

Here's another example: Say you had a spring. You attach a mass and let it drop. The mass drops, but it keeps moving past the equilibrium point. It doesn't just stop at that point. (In the case of the spring, it oscillates.)

 

[spsch]

Just because the net force is zero doesn't mean it stops.

At that point, it's still moving. So it will keep going until it runs out of kinetic energy.

Here's another example: Say you had a spring. You attach a mass and let it drop. The mass drops, but it keeps moving past the equilibrium point. It doesn't just stop at that point. (In the case of the spring, it oscillates.)

@Doc Al Thank you. The spring did it for me!