# Why isn’t work being done

According to my professor if you are lifting a book at a constant velocity , work is being done even though the net force is 0... ok

A car is traveling down the highway at a constant velocity, is work being done?
He says no because the net force is 0

Now the road is not frictionless . I asked. Just like the book was being lifted against gravity , the car is traveling against friction. Why is there no work?

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ZapperZ
Staff Emeritus
According to my professor if you are lifting a book at a constant velocity , work is being done even though the net force is 0... ok

A car is traveling down the highway at a constant velocity, is work being done?
He says no because the net force is 0

Now the road is not frictionless . I asked. Just like the book was being lifted against gravity , the car is traveling against friction. Why is there no work?
Let's look at the first case of lifting a book.

Your hand is applying a force upwards. While the net force ON THE BOOK is zero, your hand applies an upward force. So your hand, and you, are doing work, to move it with constant velocity.

Second case of a car traveling with constant velocity. Here, you need to specify if there is air friction or not.

(i) No air friction. The car is coasting. There are no external force being applied to cause it to move at a constant velocity. So no work is done.

(ii) Air friction isn't zero, or other friction comes into play. Then to keep the car moving at constant velocity, you need to have your foot on the gas peddle just a bit to maintain the speed. Otherwise, the car will slow down. In this case, even though the net force is zero, the car engine is exerting a force to keep it moving that way. So here, there IS work done by the car engine.

Zz.

russ_watters
russ_watters
Mentor
According to my professor if you are lifting a book at a constant velocity, work is being done even though the net force is 0... ok

A car is traveling down the highway at a constant velocity, is work being done?
He says no because the net force is 0

Now the road is not frictionless . I asked. Just like the book was being lifted against gravity , the car is traveling against friction. Why is there no work?
The entire difficulty here is that the scenarios are vague/ill-defined/inconsistent. You need to ask what is doing work against what and be consistent about it. Specifically: any force parallel to the direction of motion causes work to be done. 0 NET force means 0 NET work, but that's just an issue of subtraction....and usually the word "net" is only used to denote whether forces are balanced or not, and in all of these cases the forces are balanced.

So re-build those scenarios separating the net into to its parts and you'll get your answers.

....also, though, you are probably talking about two different scenarios with the car. He's probably neglecting friction.

Let's look at the first case of lifting a book.

Your hand is applying a force upwards. While the net force ON THE BOOK is zero, your hand applies an upward force. So your hand, and you, are doing work, to move it with constant velocity.
Right work is being done by your hand on the book
Second case of a car traveling with constant velocity. Here, you need to specify if there is air friction or not.

(i) No air friction. The car is coasting. There are no external force being applied to cause it to move at a constant velocity. So no work is done.

(ii) Air friction isn't zero, or other friction comes into play. Then to keep the car moving at constant velocity, you need to have your foot on the gas peddle just a bit to maintain the speed. Otherwise, the car will slow down. In this case, even though the net force is zero, the car engine is exerting a force to keep it moving that way. So here, there IS work done by the car engine.

Zz.
I asked if it was in a frictionless environment he said no. So I assume at the very least the road is producing friction. I’d say the air too

The entire difficulty here is that the scenarios are vague/ill-defined/inconsistent. You need to ask what is doing work against what and be consistent about it. Specifically: any force parallel to the direction of motion causes work to be done. 0 NET force means 0 NET work, but that's just an issue of subtraction....and usually the word "net" is only used to denote whether forces are balanced or not, and in all of these cases the forces are balanced.

So re-build those scenarios separating the net into to its parts and you'll get your answers.
That vagueness was the question. I can’t change the question.
But if I were to, I would say work is being done on the book, so is work being done on the car? By the engine/tires exerting the force against the road to push the car

ZapperZ
Staff Emeritus
I asked if it was in a frictionless environment he said no. So I assume at the very least the road is producing friction. I’d say the air too
You need to have him clarify that. Maybe he meant that there is friction between the wheel and the road, so that the vehicle will roll without slipping. If this is the ONLY source of friction, then the answer that the work done is zero is still valid.

Otherwise, normal experience is enough to show that when you let go of your gas peddle while driving, your vehicle slows down!

Zz.

You need to have him clarify that. Maybe he meant that there is friction between the wheel and the road, so that the vehicle will roll without slipping. If this is the ONLY source of friction, then the answer that the work done is zero is still valid.

Otherwise, normal experience is enough to show that when you let go of your gas peddle while driving, your vehicle slows down!

Zz.
The road will slow the car down. Unless you are assuming that the wheels don’t slip?
Friction within the car will cause it to slow

But if it encounters air resistance, you that’s work in that situation

ZapperZ
Staff Emeritus
The road will slow the car down. Unless you are assuming that the wheels don’t slip?
Friction within the car will cause it to slow

But if it encounters air resistance, you that’s work in that situation
Now it is you that I do not understand.

I said that if the ONLY friction involved is the friction between the wheel and the road to prevent slipping, then (insert what i said earlier). I didn't say anything about "friction within the car". So Pay Attention!

I have already explained the situation if you include other dissipative frictional forces that are involved in a vehicle motion. You are welcome to scroll up.

Zz.

Now it is you that I do not understand.

I said that if the ONLY friction involved is the friction between the wheel and the road to prevent slipping, then (insert what i said earlier). I didn't say anything about "friction within the car". So Pay Attention!

I have already explained the situation if you include other dissipative frictional forces that are involved in a vehicle motion. You are welcome to scroll up.

Zz.
I know that you didn’t say friction within the car. I did. No need to get upset. Your response was a bit vague I was just trying to restate it more directly to make sure I understand. Because what I got from your response is that the professor is wrong

russ_watters
Mentor
That vagueness was the question. I can’t change the question.
Unless this is a test question you can change it and even then you can ask the prof to clarify.

I can easily see how with clarifications, both of the prof's statements may be true.
But if I were to, I would say work is being done on the book...
Careful: I said break the "net" into parts. You only gave me one part.
so is work being done on the car? By the engine/tires exerting the force against the road to push the car
As I said, any force parallel to the motion does work. That's one force, yes.

Unless this is a test question you can change it and even then you can ask the prof to clarify.

Careful: I said break the "net" into parts. You only gave me one part.

As I said, any force parallel to the motion does work. That's one force, yes.
But only if the tires are slipping, right? If the tires don’t slip(in a perfect world), and there is no other friction as zapper says, then no work is done

ZapperZ
Staff Emeritus
I know that you didn’t say friction within the car. I did. No need to get upset. Your response was a bit vague I was just trying to restate it more directly to make sure I understand. Because what I got from your response is that the professor is wrong
And I said you need to clarify if the presence of friction in the car case is simply due to the wheel not slipping on the road!

This would have been simpler if you just have a block sliding on a horizontal surface! Take two cases: (i) block sliding on a frictionless surface at constant velocity and (ii) block sliding on a surface with friction at a constant velocity.

Which one is work done NOT zero?

Zz.

grandpa2390
And I said you need to clarify if the presence of friction in the car case is simply due to the wheel not slipping on the road!

This would have been simpler if you just have a block sliding on a horizontal surface! Take two cases: (i) block sliding on a frictionless surface at constant velocity and (ii) block sliding on a surface with friction at a constant velocity.

Which one is work done NOT zero?

Zz.
2nd one

russ_watters
Mentor
But only if the tires are slipping, right? If the tires don’t slip(in a perfect world), and there is no other friction as zapper says, then no work is done
If we assume there are no forces, then there is no work, yes. I think that should be obvious.

grandpa2390
ZapperZ
Staff Emeritus
2nd one

Zz.

grandpa2390 and russ_watters
sophiecentaur
Gold Member
The point has been made already that the question is too open for a proper answer. But, making some natural assumptions:
you are lifting a book
This is the old chestnut which confused Work Done On something with Work Done By something.
Energy is being transferred to the book because its gravitational potential energy is increasing. So, however the Energy is supplied, there is Work Done On the car.
traveling down the highway at a constant velocity,
The car is not gaining any energy (Kinetic or Potential) so no work is being done ON it. Work is being done on the air as it's pushed aside and also a few other things are gaining energy but the net force on the car itself is zero so Force X Speed is zero and No Work is Done On the car. The engine could be straining its little guts out, doing as much work as it is capable of.
Putting myself in the place of the teacher who thought up the question in an odd few minutes in the shower, too much was assumed in the wording of the question because of the intended audience. If the teacher had knows that PF would be dissecting it, then he/she would have made it tighter..

russ_watters
Mentor
The car is not gaining any energy (Kinetic or Potential) so no work is being done ON it.
NET work is zero, but work is being done (In the scenario where we consider friction). I think the entire issue here is loose use/definition of "net" between the scenarios.

sophiecentaur

Zz.
Thanks all. After questioning my professor, he agreed but explained that the car referred to an entire system that when broken apart he agreed work is being done. But as a whole work is not. I’m the book scenario, if we said the human book system, no work is being done. But we broke it into two pieces and analyzed those parts. This makes sense to me I think... maybe

russ_watters
Would A rocket traveling at a constant velocity. No work is being done unless we break it down and look at the individual components.

ZapperZ
Staff Emeritus
Would A rocket traveling at a constant velocity. No work is being done unless we break it down and look at the individual components.
Depends... is this within a gravitational field? If it is, then this is similar to lifting a book scenario in your first post, with the thrusters replacing your hand.

Notice how one has to be very careful and precise in describing the full scenario of a problem?

Zz.

russ_watters
Mentor
Thanks all. After questioning my professor, he agreed but explained that the car referred to an entire system that when broken apart he agreed work is being done. But as a whole work is not. I’m the book scenario, if we said the human book system, no work is being done. But we broke it into two pieces and analyzed those parts. This makes sense to me I think... maybe
No, it's not just a human-book system, it's a human-book-earth system. If you draw your system boundary around earth, then there are no external forces at all. When I talked about breaking the "net" into pieces, that was looking at individual pieces of a system.

You could do the same thing with the car: draw the system around the earth. Energy is still conserved, but internally you still have work being converted to heat.

Depends... is this within a gravitational field? If it is, then this is similar to lifting a book scenario in your first post, with the thrusters replacing your hand.

Notice how one has to be very careful and precise in describing the full scenario of a problem?

Zz.
Right. The rocket system there is no work. But if we break it down the thrusters are doing work on the rest of the rocket. If the entire rocket is accelerating, then there is work being done on the entire rocket system

No, it's not just a human-book system, it's a human-book-earth system. If you draw your system boundary around earth, then there are no external forces at all. When I talked about breaking the "net" into pieces, that was looking at individual pieces of a system.

You could do the same thing with the car: draw the system around the earth. Energy is still conserved, but internally you still have work being converted to heat.
So he was still wrong? Unless the problem defines the system as car and earth, a car at a constant velocity encountering air resistance is still has work being done on it? Even though the thing supplying the propulsion force is a part of the system defined as just the car
Because the “engine “ is like the hand

Stephen Tashi
Now the road is not frictionless . I asked. Just like the book was being lifted against gravity , the car is traveling against friction. Why is there no work?

To make the scenarios specific lets assume that "the" work done on something refers to the work done by all the forces acting on it. (Since free body diagrams are used to analyze situations in Newtonian mechanics, we can assume that there is no ambiguity in the concept of the "total" or "net" force on free body.)

What is the difficulty with saying that the total work done on the book is zero and the total work done on the car is zero?

The intuitive difficulty happens when we imagine the net force becoming non-zero in such a manner that the objects come to a halt. We imagine the book stopping at a height where its potential energy has increased. If we think of the car on a flat road, we imagine it stopping without obtaining added potential energy. However, we could also imagine that the car was traveling up or down an incline at a constant velocity. So after it stops, its potential energy could be increased or decreased.

The interesting aspect of the problem is to reconcile the concept of zero net work with the concept of conservation of energy. How can zero net work on an object change the potential energy of object?

In order to bring a moving object to a halt, there must be some time interval when a non-zero net force is applied to it. During that interval, non-zero total work is done on the object. That aspect must be considered, but, by itself, it doesn't resolve the issue with potential energy. The book stops with increased potential energy after work is done upon it to stop it moving. A car on a flat road stops with no increase in potential energy after work is done upon it to stop it moving.

In order to sort things out, perhaps we must think about conservative versus non-conservative force fields and the conversion of kinetic energy into heat.

russ_watters
Mentor
So he was still wrong?
I don't know that he was ever wrong, just that as stated here the scenarios are incomplete. Missing words could either be omitted in the telling or hearing of the scenarios.
Unless the problem defines the system as car and earth, a car at a constant velocityencountering air resistance is still has work being done on it? Even though the thing supplying the propulsion force is a part of the system defined as just the car
Because the “engine “ is like the hand
It's a bit of a trick: only external forces do work. If the system is the car, the work being done on the car comes from a force applied to the car by the road.