# Why isn't work done when carrying a backpack with constant velocity?

Here's an excerpt from my textbook:

In the following situations, state whether work is being done, and why or why not.

A) A person carrying a backpack walking across a floor

B) A person shoveling snow across a driveway at a constant speed

The solutions are:

A) No work is being done on the bag because the direction of motion is perpendicular to the direction of force due to gravity

B) Work is being done on the shovel because the direction of motion and the direction of the applied force is the same

I have no issue with situation B, but situation A bothers me. Although I agree that no work is being done by the forces of gravity and the force applied to hold it up, is it not the case that the person is applying a force forward to the bag as they walk, and therefore work is being done by that force? To make things a bit more uniform (since walking is a jerky motion), presuming that the person wearing the bag is riding a bike at a constant speed, that means that they have to apply a force that balances wind resistance.

I might say that since there is no net force there is no work being done, but then situation B would have no work being done as well, since the shovel/snow are moving at a constant speed.

Where did I misread this?

• can you quote the scenarios exactly as written in your textbook? – Bob Jul 10 '18 at 14:08
• Yes, please see the edits – Michael Stachowsky Jul 10 '18 at 14:11
• As others have pointed out, the explanations are bad. Do yourself a favor and find an alternate or supplemental resource. The question itself stinks. The author of the question meant "... whether work is being done by gravity... ". So bad. How does stuff like that get published? I see it frequently. – garyp Jul 10 '18 at 14:49

In situation a), if the person is walking perfectly smoothly in a vacuum then no work is being done on the bag, if there is air resistance then both the person and the air do work on the bag, if there is jiggling then gravity does work too.

Situation b) is clearer, the snow is initially at rest and accelerated by the spade, so the force from the spade acts in the direction of motion and work is done.

Abd yes, you need a clearer textbook! :P

• I see. So is the following correct? For the bag, presuming that the person starts and ends at rest, there are three phases of the motion. During the acceleration phase, work is being done. During the "constant walk" phase the person does positive work, the air does negative work, so no net work is done. During the deceleration phase, the person does negative work, essentially un-doing what happened during acceleration. Sine we are interested in the scenario during the walk, no work is being done there for the reason stated above? – Michael Stachowsky Jul 10 '18 at 14:21
• That is correct – Eddy Jul 10 '18 at 14:47

This is a very common question, and a fair one. The point is that if you walk forward with constant average velocity, even if it's "jerky" as you say, the periods of positive work done on the backpack are balanced out by periods of negative work done, since the backpack's kinetic energy remains the same on average. If you really applied a forward force on the backpack the whole time, it should instead get faster and faster. (This is of course neglecting wind resistance.)

Another example: you do zero work on a backpack when you hike up and down a mountain with it, because the work done moving upward is balanced out by the work "undone" moving downward.

The reason that this is unintuitive is that people imagine work is synonymous with "physical effort" or "fuel expended". This isn't true for human beings because we're not perfect machines. You get hungry when you go up a mountain but you don't get that energy back by going down. For a lot more about this, see this question.

The explanations given by the textbook really aren't the clearest. I urge you to take control of your own learning, and go and get a better one! You might be afraid to do this because then it wouldn't be the "official" textbook, but all introductory physics textbooks are teaching the same things. (It's not like one textbook will say $F=ma$ and another will say $F=mv$.) Some explain much much better than others. Using a good book will be well worth it in the long run.

• I certainly appreciate that, but then why is there work being done on the shovel? It is not gaining or losing kinetic energy, so it should have no work done as well, shouldn't it? – Michael Stachowsky Jul 10 '18 at 14:14
• @MichaelStachowsky The snow does negative work on the shovel, and you do positive work on the shovel, so the shovel has constant kinetic energy. – knzhou Jul 10 '18 at 14:14
• I appreciate that, but the bag also has constant kinetic energy. As far as I can tell, either work is being done on both by the person and that work is exactly cancelled by other effects (wind resistance and snow resistance, respectively), and therefore no net work is done on either one, OR work is being done on both due to applied forces. – Michael Stachowsky Jul 10 '18 at 14:19
• @MichaelStachowsky In the bag case, if there were wind resistance, then your positive work on the backpack would be canceled out by negative work by wind resistance. If we're assuming there's nothing like that, then no net work is done. – knzhou Jul 10 '18 at 15:12

After reading your statements, I think you may also look at this from the point of view of the work-kinetic energy theorem ($W_{net}=\Delta KE$).

In the first scenario, the bag is moving as constant speed, then $\Delta KE = 0$ which implies no work done. From the point of view of forces acting on the bag, $\vec{a}=\vec{0} \Rightarrow \vec{F}_{net}=\vec{0} \Rightarrow W_{net}=0$

I don't like the solution given by the book because when determining total work done on an object, you should consider all the forces acting on that object, which includes the force of the person holding the backpack against gravity as well. If you want to determine work done by a single force, that's fine as well, but gravity is not the only force acting on the backpack. Sorry you have a poor textbook.

• Only true if there are no dissipation forces such as air resistance. – garyp Jul 10 '18 at 14:47
• True. I did say all forces, but I could have been more explicit on ignoring air resistance. – Bob Jul 10 '18 at 17:09