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

In summary: I was starting to think I was doing something wrong. In summary, 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.
  • #1
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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?
 

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  • #2
spsch said:
Hi, so I was able to solve this problem by just equating the forces (Tension, mg, and EQ).
That is the correct approach.

spsch said:
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.)
 
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  • #3
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!
 
  • #4
spsch said:
Why would the charge swing past the equilibrium point?
Just because the net force is zero doesn't mean it stops.
spsch said:
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.)
 
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  • #5
Doc Al said:
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!
 

1. How does an electric field affect a mass hanging from a pendulum?

When a mass is suspended from a pendulum in an electric field, it experiences a force due to the electric field. This force causes the pendulum to swing in a different direction than it normally would, and thus affects the motion of the pendulum.

2. What factors determine the charge of a mass hanging from a pendulum in an electric field?

The charge of a mass hanging from a pendulum in an electric field is determined by the strength of the electric field, the mass of the object, and the length of the pendulum. These factors all play a role in the force experienced by the mass and the resulting charge.

3. Can the charge of the mass hanging from a pendulum in an electric field be changed?

Yes, the charge of the mass can be changed by altering the strength of the electric field or by adjusting the length of the pendulum. It is also possible to change the mass of the object, which would also affect the charge.

4. How can the charge of a mass hanging from a pendulum in an electric field be measured?

The charge of a mass hanging from a pendulum in an electric field can be measured by using a device called an electroscope. This instrument detects the presence and magnitude of electric charge by using the principles of attraction and repulsion between charged objects.

5. What are the real-world applications of studying the charge of a mass hanging from a pendulum in an electric field?

The study of the charge of a mass hanging from a pendulum in an electric field has several real-world applications, including in the fields of physics, engineering, and telecommunications. It can help us understand the behavior of charged particles in electric fields and can be used in the design and development of electrical devices and systems.

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