# Potential energy and work

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! :)

Andrew Mason
Homework Helper
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

1 person
A.T.
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.

1 person
san203
Gold Member
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

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

Last edited:
1 person
Andrew Mason
Homework Helper
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

1 person
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!

Last edited:
Andrew Mason
Homework Helper
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..

A.T.
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.

1 person
Andrew Mason
Homework Helper
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

Last edited:
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.

Andrew Mason