Why is Equal and Opposite Force Necessary for Work Against a Field?

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Discussion Overview

The discussion revolves around the necessity of applying an equal and opposite force when doing work against a field on an object. Participants explore the implications of force application when an object is at rest and the transition to motion, considering both potential and kinetic energy in the context of work done against a field.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants argue that to initiate motion from rest, a force greater than the field force is necessary initially, suggesting that the applied force must exceed the field force to overcome inertia.
  • Others contend that once the object is in motion, the applied force can be equal to the field force, indicating a transition from greater to equal force during the object's movement.
  • It is noted that the extra force required for acceleration contributes to kinetic energy, which is relevant when considering the work done against the field.
  • Some participants question the accuracy of expressing work done against the field as the product of force and displacement, particularly when considering the initial conditions of motion.
  • There is a discussion about the definitions of forces involved, with distinctions made between applied force and field force in the context of work calculations.

Areas of Agreement / Disagreement

Participants express differing views on whether the applied force must always be greater than the field force to initiate motion, leading to an unresolved debate on the conditions under which work is done against a field.

Contextual Notes

Participants highlight the importance of distinguishing between potential and kinetic energy in the context of work done against a field, but the discussion remains open regarding the precise definitions and implications of force application.

ViolentCorpse
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Hello everyone!

When we do work against a field on an object, why must the force we apply on it be equal and opposite to that of the field? If the object is initially at rest, then shouldn't we be applying a force greater and opposite to that of the field to first set it into motion? We could later make it equal after the object has been set into motion, but the first initial push should be greater.

Thank you! :)
 
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ViolentCorpse said:
Hello everyone!

When we do work against a field on an object, why must the force we apply on it be equal and opposite to that of the field? If the object is initially at rest, then shouldn't we be applying a force greater and opposite to that of the field to first set it into motion? We could later make it equal after the object has been set into motion, but the first initial push should be greater.

Thank you! :)
You are quite right. If the applied force was always equal and opposite, there would be no net force and, so, no acceleration. The applied force has to be just a tad greater initially in order to give the body some velocity and then it can be reduced to be equal in magnitude to the field force.

AM
 
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ViolentCorpse said:
When we do work against a field on an object, why must the force we apply on it be equal and opposite to that of the field? If the object is initially at rest, then shouldn't we be applying a force greater and opposite to that of the field to first set it into motion? We could later make it equal after the object has been set into motion, but the first initial push should be greater.
That extra force needed for acceleration goes into kinetic energy, which is released when the object stops again. For "work against a field" we usually consider just the potential energy part.
 
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ViolentCorpse said:
When we do work against a field on an object, why must the force we apply on it be equal and opposite to that of the field?

If we want to do work against the field,the force must not be equal to that of field. We need to apply a force greater than what the field exerts on the object

ViolentCorpse said:
If the object is initially at rest, then shouldn't we be applying a force greater and opposite to that of the field to first set it into motion? We could later make it equal after the object has been set into motion, but the first initial push should be greater.

True
 
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san203 said:
If we want to do work against the field,the force must not be equal to that of field. We need to apply a force greater than what the field exerts on the object
That applies only to an object initially at rest. In general, positive work is done on a body by an applied force against the field force if the direction of the applied force is opposite to the direction of the field force and if it is applied through some positive displacement. It doesn't necessarily have to be greater in magnitude than the field force.

AM
 
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A.T said:
That extra force needed for acceleration goes into kinetic energy, which is released when the object stops again. For "work against a field" we usually consider just the potential energy part.

Shouldn't the entire journey of that object against the field comprise of part potential and part kinetic energy?

Thank you so much each and everyone of you!
 
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ViolentCorpse said:
Shouldn't the entire journey of that object against the field comprise of part potential and part kinetic energy?

Thank you so much each and everyone of you!
If you meant that the work done by an external force, F, in moving the body from point a to point b: (\int_a^b \vec{F}\cdot d\vec{s}) must be equal to the sum of the change in kinetic energy + change in potential energy of the body from a to b, then the answer is: yes.

AM
 
Thank you for clearing that, though I know that much. I'm just trying to see how accurate it is to express work done against the field as F.ds, if that F was a little more than F for a very short period of time to get the object moving in the first place..
 
ViolentCorpse said:
I'm just trying to see how accurate it is to express work done against the field as F.ds, if that F was a little more than F for a very short period of time to get the object moving in the first place..
What is F here?

If F is the negated field-force then integral F.ds is the work done against the field.

If F is the net force, then integral F.ds is the net work done.
 
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  • #10
ViolentCorpse said:
Thank you for clearing that, though I know that much. I'm just trying to see how accurate it is to express work done against the field as F.ds, if that F was a little more than F for a very short period of time to get the object moving in the first place..

If Fa is the applied force and Ff is the field force, the work done by the applied force on the object in moving from a to b is: \int_a^b \vec{F_a}\cdot d\vec{s}, which consists of the change in potential energy + change in kinetic energy. The work done against the field is \int_a^b \vec{F_f}\cdot d\vec{s}, which is just the change in potential energy.

AM
 
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Oh, I think I get it now. I'm clearly not a very bright student.

Thank you, Andrew Mason and A.T for your continued help. I very much appreciate it.
 
  • #12
ViolentCorpse said:
Oh, I think I get it now. I'm clearly not a very bright student.
On the contrary. You asked a very good question. This is something that many physics texts gloss over. You learn by asking questions. The only kind of dumb question is one that should have been asked - but wasn't.

AM
 
  • #13
That's really very nice and encouraging of you, Mr. Andrew Mason. Thank you! :smile:
 

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