[Electrical force] 2 balls hanging from ceiling

[sea333]

Homework Statement

A ball with mass 144g hangs from a celling on a thread. Second ball is attached to the first ball with 20 cm thread. They both are charged with the same electric charge. How big is a force that is functioning on a thread?

Relevant Equations

F=ma

 

[Delta2]

You have to tell us some additional things like:

If the balls have both the same mass and charge
If the system is in equilibrium
Which thread tension you wish to found.

 

[sea333]

If the balls have both the same mass and charge
They are both charged with the same charge as I already specified.
No information about if they are the same weight. Assume they are both the same weight.

Which thread tension you wish to found.
The combine force in the thread.

 

[jbriggs444]

Homework Statement:: A ball with mass 144g hangs from a celling on a thread. Second ball is attached to the first ball with 20 cm thread. They both are charged with the same electric charge. How big is a force that is functioning on a thread?
Relevant Equations:: F=ma

View attachment 286586

I suspect that either the problem statement is incomplete or that the suggested "correct" answer is not correct.

We are told the mass of the two balls. We are told that they are hanging from the ceiling in a daisy-chain arrangement with threads. We are given some information about a repulsive electrostatic force between the two balls. But we are not given enough information to determine the magnitude of this electrostatic force.

We are asked for the magnitude of a force acting on a thread. Not a specific thread. Just a thread. Not a specific force. Just a force.

If we take the question literally, we might consider the electrostatic force acting on the top thread. Zero.

Or we could consider the contact force of the top ball on the top thread as you have done. Up to a possible sign error (you were asked for magnitude, not direction) your result is correct. The electrostatic force is an internal force and cannot change the net weight of a closed system. The weight of the system is the sum of the weights of the two balls, i.e. $F_\text{g1}+F_\text{g2}$, just as you say.

You have clarified somewhat that you want to know:

The combine force in the thread.

The combined force on which thread? Oh, I get it. Either one.

What is the net force on the thread connecting the two balls? That is, what is the sum of the force of the top ball on that thread and the force of the bottom ball on that same thread.

You can determine that result quite simply.

 

[sea333]

What is the net force on the thread connecting the two balls? That is, what is the sum of the force of the top ball on that thread and the force of the bottom ball on that same thread.

I mean all the forces working on the thread combined. A sum of all the forces working on that thread.
Which are only force of gravity and electrical force. And the sum of all those forces working on a thread should be 0.

I suspect that either the problem statement is incomplete or that the suggested "correct" answer is not correct.

I have provided all the information from the book. I have translated the exercises from the book and it is in my native language.

 

[jbriggs444]

I mean all the forces working on the thread combined. A sum of all the forces working on that thread.
And the correct result should be 0.

Good. Now show us a calculation of that sum.

Alternately, consider what Newton's second law says that sum must be.

 

[sea333]

Something like that?
Fthread = Fg1 + Fg2 + Fe1 + Fe2

 

[Delta2]

Your work in the picture is towards finding the tension of the thread that is hanging from the ceiling. However here you tell us that you wish to find the combined forced on the thread which is a different thing. Which forces are acting on the thread and from which bodies?

 

[sea333]

Your work in the picture is towards finding the tension of the thread that is hanging from the ceiling. However here you tell us that you wish to find the combined forced on the thread which is a different thing. Which forces are acting on the thread and from which bodies?

As I understand the exercise there are 2 forces acting on these thread, gravitational and electrical. And the sum of both is suppose to be 0.

 

[jbriggs444]

Something like that?
Fthread = Fg1 + Fg2 + Fe1 + Fe2

Something like that, yes. But pay attention to signs. That formula is littered with sign errors. Please show your work.

Also, please give Newton's second law some thought.

 

[sea333]

I think that this is correct?
Fthread = -Fg1 - Fg2 - Fe1 + Fe2

 

[jbriggs444]

I think that this is correct?
Fthread = Fg1 + Fg2 - Fe1 + Fe2

Nope. You're just guessing now.

What is the force of the bottom ball on the thread?
What is the force of the top ball on the thread

Show your work.

 

[haruspex]

As I understand the exercise there are 2 forces acting on these thread, gravitational and electrical. And the sum of both is suppose to be 0.

No, the threads are not charged, so no electrical force, and if they are taken to be massless then no gravitational force.
What two forces do act on each thread?

 

[Delta2]

As far as I can understand, if the thread is massless or the system is in equilibrium, the sum of forces on the thread is zero, simple as that.

 

[sea333]

I would say this is correct:
Fthread = -Fg1 - Fg2 - Fe1 + Fe2

so 2 gravitational forces point down and 1 electrical force is pointing up

 

[sea333]

What two forces do act on each thread?

gravitational and electrical force

 

[Delta2]

gravitational and electrical force

Nope that's wrong, on the thread that is hanging from the ceiling acts a contact force from the ceiling and a contact force from the body of mass m1=144. IF the system is in equilibrium (and hence the thread is in equilibrium) what is the sum of these two forces?

The gravitational and electrical forces act on the two bodies, not on the two threads.

 

[haruspex]

gravitational and electrical force

Did you not read the rest of post #13? gravitational and electrical force act on the balls.

 

[sea333]

As you said there are 2 threads :
Fthread1 = Fg - Fe //upper thread
Fthread2 = - Fg - Fe

 

[Delta2]

Yes there are two threads, but I am afraid you do not understand what the question is asking that's why you giving wrong answers.

 

[sea333]

Yes there are two threads, but I am afraid you do not understand what the question is asking that's why you giving wrong answers.

what is it asking ?

 

[sea333]

The gravitational and electrical forces act on the two bodies, not on the two threads.

yes but we need to know the sum of all forces on all threads

 

[Delta2]

what is it asking ?

Take the thread as a separate body, name it body A. What forces are acting on this body A?

 

[sea333]

Take the thread as a separate body, name it body A. What forces are acting on this body A?

2 Electrical forces and 2 gravitational forces

 

[Delta2]

The electrical and gravitational forces act on the two bodies of mass m1 (and charge q) and mass m2 (and charge q), not on the threads.

 

[sea333]

The electrical and gravitational forces act on the two bodies of mass m1 (and charge q) and mass m2 (and charge q), not on the threads.

aha I understand that, but what is then acting on the threads?

 

[Delta2]

aha I understand that, but what is then acting on the threads?

read again post #17 please.

 

[sea333]

Nope that's wrong, on the thread that is hanging from the ceiling acts a contact force from the ceiling and a contact force from the body of mass m1=144. IF the system is in equilibrium (and hence the thread is in equilibrium) what is the sum of these two forces?

You mean like that?
Fthread = Fceiling + Fbody = 0

 

[Delta2]

You mean like that?
Fthread = Fceiling + Fbody = 0

Yes! simple as that since the thread is not moving the sum of forces on it is zero.

 

[sea333]

Yes! simple as that since the thread is not moving the sum of forces on it is zero.

but where is the electrical force and what about all the rest of information (mass, charge, distance)

 

[Delta2]

but where is the electrical force and what about all the rest of information (mass, charge, distance)

Well this question is some sort of trap like question it gives a lot of irrelevant information but the only piece of information you need to answer it , is that the system is in equilibrium.

However if you want to determine Fbody or Fceiling the rest information will come into play.

 

[sea333]

However if you want to determine Fbody or Fceiling the rest information will come into play.

Do I need to determine it to solve this exercise?

 

[Delta2]

Do I need to determine it to solve this exercise?

Nope.

 

[sea333]

That is a very strange exercise with a lot of redundant information it seems

 

[jbriggs444]

but where is the electrical force and what about all the rest of information (mass, charge, distance)

The electrostatic force from the bottom ball acts on the top ball.
The electrostatic force from the top ball acts on the bottom ball.

The force of gravity on the top ball acts on the top ball
The force of gravity on the bottom ball acts on the bottom ball.

The force of the ceiling on the top string acts on the top string.
The force of the top string on the ceiling acts on the ceiling

The force of the string on the top ball acts on the top ball.
The force of the top ball on the top string acts on the top string.

The force of the top ball on the bottom string acts on the bottom string.
The force of the bottom string on the top ball acts on the top ball.

The force of the bottom string on the bottom ball acts on the bottom ball.
The force of the bottom ball on the bottom string acts on the bottom string.

We ignore gravity and electrostatic forces acting on both strings because the strings are uncharged and are negligibly massive.

If you want to know the net force on the top string, you add up the forces on the top string.

You can do this the hard way -- solve a bunch of simultaneous equations and find that everything cancels.
Or you can do it the easy way -- Newton's second law. $\sum F=ma$ and a = 0.

 

[sea333]

I am satisfied with easier route for this exercise.

 

[haruspex]

I do object to the wording of the question. Despite specifying "force", it is natural to assume the question is asking about tension. It should specify "net force".

 

[kuruman]

I do object to the wording of the question. Despite specifying "force", it is natural to assume the question is asking about tension. It should specify "net force".

Yes, the wording is vague but the intent of the author may have been lost in translation. "How big is a force that is functioning on a thread?" is looking for a tension, but in which thread? There are two of them.

 

[sea333]

I can paste the text in my native language but I don't know if it would help

 

[jbriggs444]

Yes, the wording is vague but the intent of the author may have been lost in translation. "How big is a force that is functioning on a thread?" is looking for a tension, but in which thread? There are two of them.

The net force on both is identical. It is not tension that is being asked for.

 

[kuruman]

The net force on both is identical. It is not tension that is being asked for.

I am not convinced that "How big a force that is functioning on a thread" is equivalent to "What is the net force on a thread", but OK. I will not pursue this any further.