Work done by external force on a system

[cgiustini]

Hi,

I'm trying to formulate some general ideas on how systems convert energy imparted by external forces. Could anyone please read the following and see if any of the statements and examples are correct? I really like the idea of thinking of isolated systems as "machines" through which energy flows: there is input energy in one form and output energy in other form. Here is what I have:

Statement 1: Work done by external force on a system is equal to the change in total energy of the system (mechanical + thermal + any other form of energy)

Statement 2: Work by done an external force on a system is always a transfer of energy in the form of kinetic energy, but the system may be instantaneously converting it to some other form of energy.

Example 1: you pick up a ball

1. When you lift the ball, your force is doing positive work to lift the ball up
2. The ball/earth system is instantaneously converting the kinetic energy you provide to the ball by lifting it into potential energy of the system via gravity's negative work
3. In sum, your biochemical energy that was used to impart kinetic energy to the ball has all been converted into potential energy of the earth/ball system
4. Since originally the kinetic+potential energy of the earth/ball system was 0 and since you have increased the potential energy by lifting the ball, you have increased the mechanical energy of the system

Example 2: you throw the ball upward

1. When you throw the ball upwards, you instantaneously impart it with some kinetic energy
2. This example is the same as example 1 except that your force is applied for only a brief moment: this means that once your force is done imparting kinetic energy, the earth/ball system starts converting all the newly added kinetic energy to potential energy while the ball is moving upwards.
3. Once all the kinetic energy associated with upwards movement has been converted to potential energy, the system then converts the potential energy to kinetic energy associated with downwards movement as the ball falls towards the ground

Statement 3: From example 1) and 2), could we generalize the isolated earth/ball system (or any other system where the conservative force is gravitational force between a large object and a small object) as a system that:

1. continuously converts any kinetic energy associated with upwards motion to potential energy
2. once potential energy is maximal (kinetic energy associated with any motion is depleted), begins converting all potential energy into kinetic energy associated with downwards motion

Example 3: you push a block along a horizontal floor with friction:

1. As you push the block, your force is doing work on the block/floor system to impart kinetic energy to the block
2. Because of the kinetic frictional force between the block and the floor (which is a constant force for a given mass), the floor is continuously doing negative work on the block to convert a fixed amount the kinetic energy that your work imparts to the block. This negative work represents the kinetic energy you provide to the block being converted into thermal energy of the block/floor system
3. In order to accelerate the block, you need to do work that exceeds the fixed amount of energy that is being converted to thermal energy by the frictional force
4. The block/floor system is a system that converts a fixed amount of the kinetic energy imparted to the block into thermal energy of the block/floor.

 

[Doc Al]

Statement 1: Work done by external force on a system is equal to the change in total energy of the system (mechanical + thermal + any other form of energy)

This statement makes sense.

Statement 2: Work by done an external force on a system is always a transfer of energy in the form of kinetic energy, but the system may be instantaneously converting it to some other form of energy.

This statement does not make sense. In your example of lifting the ball, no kinetic energy was created (assuming you lifted at constant speed). You are complicating things with this assumption.

 

[cgiustini]

Thanks for the response. Statement 2 doesn't mean that any kinetic energy gets created while the ball gets lifted up. In statement 2, I mean that the earth/ball system is siphoning the kinetic energy from the ball and turning it in potential energy during the movement.

Through every incremental distance that the ball moves, the lifting force alone is providing some amount of kinetic energy. If there was no gravitational force, the ball would simply keep moving with the kinetic energy it was given. However, in this case the earth/ball system is instantaneously siphoning the kinetic energy that was added and converting it to potential energy via the gravitational force. What I'm trying to get at is that an external force can changes a system's total energy but it can only directly affect the kinetic energy of the system: any change in other energies of the system are due to an internal mechanism in the system that converts the kinetic energy into some other form.

If my way of thinking about this is valid, I think it may mean something about how two systems interact: there must always be a force between them in order for them to affect each other's energy levels. I'm not really sure where this goes, but I'm just trying to get a fundamental understanding of forces and energy relate. It goes something like: work is the only way to generate changes in the total energy of a system, which mean that somewhere, somehow, kinetic energy must be imparted to something even if it gets taken away instantaneously. I can't see how the lifting force could directly change the potential energy of the earth/ball system without first providing kinetic energy that the gravitational instantly takes away.

 

[Doc Al]

Statement 2 doesn't mean that any kinetic energy gets created while the ball gets lifted up. In statement 2, I mean that the earth/ball system is siphoning the kinetic energy from the ball and turning it in potential energy during the movement.

You are trying to justify your thought that work can only directly affect a system by giving it kinetic energy. Why in the world do you think that?

Through every incremental distance that the ball moves, the lifting force alone is providing some amount of kinetic energy.

But it's not. The speed is constant.

What I'm trying to get at is that an external force can changes a system's total energy but it can only directly affect the kinetic energy of the system: any change in other energies of the system are due to an internal mechanism in the system that converts the kinetic energy into some other form.

Why can't the internal mechanisms convert the mechanical work directly into some other form of energy, not just kinetic energy?

It goes something like: work is the only way to generate changes in the total energy of a system, which mean that somewhere, somehow, kinetic energy must be imparted to something even if it gets taken away instantaneously.

Only because you think that kinetic energy is created as some intermediate step and then instantly transformed to something else. But that's not an accurate or useful way to think.

 

[cgiustini]

Yea, it doesn't make sense to think that the potential energy is converted from kinetic energy that is created in some intermediate step.

While the ball moves up, the increase in kinetic energy of the system is equal to the net work on the ball. The net work on the ball is the sum of the lifting force's work (positive) and the gravitational force's work (negative). The negative of the work of the gravitational force's is the increase in the potential energy. In total, the change in total energy is equal to work done by the lifting force. This would be the case even if there weren't a gravitational force. When the gravitational force is present and the ball moves up over a fixed distance(either at constant speed or accelerated), some of that change in total energy gets converted to potential energy, which represents the fixed amount of energy that was required for the external force to overcome gravity.