[Physics] Why isn’t work done when carrying a backpack with constant velocity

homework-and-exerciseswork

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?

Best Answer

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.