Citizen Science No. 14 by Jamie Zvirzdin

Calculating the Metaphysical and Physical Value of Work

This year in the “Citizen Science” column, we’re looking at what energy is…and isn’t. We’ll start by examining the most critical mechanism to give and get energy: work. Work is the way energy is transferred or transformed from one form to another, and we’ll be discussing those forms in the coming months. I find a great deal of value in contemplating both the physical and metaphysical—dare I say spiritual—forms of work, so we’ll have fun blending them here. However, we take great care in differentiating the two, particularly because the physics definition of work doesn’t always match our cultural idea of what it means to “do work.” My hope is that a close look at work will inspire you to do the thing you need to do, whether it be vacuuming or taxes or exercising or physics homework or extra patience with your loved ones, any form of work.

While visiting family in Richfield Springs, New York, my sister-in-law and I wandered into a local thrift store. The owner had a wry sense of humor and called herself “the junk lady.” The thrift store was a place of old dishes and ancient keys, the type of place a child might stumble into and find a mystical object, like in one of Bruce Coville’s “Magic Shop” series. Among the trinkets, I did indeed find a mystical treasure: a 1903 book called “Work” by Hugh Black, from Cambridge University Press.
I picked up the tattered book from the low bookshelf, using my body to lift the decently dense mass of the old hardcover so I could better examine it in the light from the shop window. This is the physics definition of work, to exert a force on something over a distance. If I pick up a book from a low shelf and move it up and away from my body, holding it toward the light, that’s work, since I’m applying a force to the book over a physical distance, moving it up and out. However, if I continue holding the book with my outstretched arms—not moving it, just holding it—until I start to shake and sweat, then it’s not technically work, in the strict physics sense, because I haven’t physically moved the book from one place to another. No displacement, no work, even if my whiny, weak muscles say otherwise.

I opened the dark green, gold-lettered cover in the light and saw Hugh Black’s meticulously screenprinted interior images. Like many mortals, I grumble a bit…a lot…at the neverending list of chores and less-than-enjoyable parts of work. But my attitude toward work softened when I read the following chain of quotations about the value of work:

The ultimate ambition in our minds is to be freed from the necessity of work, as if work and not idleness were the evil. We do not value work for its own sake, but think of it as a disagreeable necessity. (Black, 10–11)

Society among us seems to be carefully graded in inverse proportion according to the amount of leisure enjoyed…This is not just the ignorant contempt of a select class; it has permeated all classes, so that to climb the social ladder means getting rid of work.” (11)

A further instance of the prevalence of the false ideal is seen in the way it even colors religious thought. Many treat the work and service of life as a painful necessity in order to qualify for the Rest that remaineth, and look forward to a millennium of ease. (17)

Intrigued, I decided to buy the book. I “did work” on the book “Work” by walking it over to the counter (again exerting a force on the book over a distance) and sliding the book across the counter—my arm at an angle as I pushed it—toward the thrift store lady, who accepted only cash. If you picture energy like money, performing work on a system in physics is like putting money into that system—in this case, the system of the thrift store. Conversely, when a system does work against external forces (like the IRS or a landlord), energy is “spent” or transferred out, reducing its stored energy.

The angle at which something is pushed or pulled over a distance also matters in the calculation of work. If I’m pushing the book across the counter at an angle, part of the force I’m putting into pushing the book is directed down into the counter, which doesn’t actually make the book move across the counter. Some of my effort is lost, in other words, because the force I’m exerting isn’t in the direction of my goal. In my undergraduate copy of Serway and Jewett’s “Physics and Engineers with Modern Physics” (9th ed.), the section on work includes a delightful example called “Mr. Clean”:

A man cleaning a floor pulls a vacuum cleaner with a force of magnitude F = 50.0 N [Newtons, the unit of force] at an angle of 30.0 degrees with the horizontal. Calculate the work done by the force on the vacuum cleaner as the vacuum cleaner is displaced 3.00 m [meters, the unit of distance] to the right. (143)

Let’s put our brains to work and solve this. (I asked ChatGPT to generate an image of this situation with hilariously incorrect results, so we’ll just have to picture it ourselves.) Because the man is holding the long nozzle of the vacuum hose at an upward angle and moving to the right with it, pulling the old-school, bucket-like vacuum behind him across the floor, we want to find how much of his force is actually acting horizontally to pull the vacuum along the floor, which is why we multiply the force by the cosine of the angle. So even though Mr. Clean is exerting 50.0 Newtons of force at an angle, only 43.3 Newtons of that force is actually working to drag the vacuum across the floor.

Finally, we calculate the value of work by multiplying 43.3 Newtons of force by the vacuum’s displacement, 3.00 meters, and the result will be in units of Newton-meters, also known as Joules (physicists love to rename things, and they do it way too often). These are the units used for work and for energy, too. After all this brain work, we find that Mr. Clean is putting about 130 Joules of work into moving that old vacuum across the floor. If he reduced the angle of the vacuum hose to zero (since the cosine of zero degrees equals 1), he’d be a more efficient worker, getting 150 Joules of work done for the same amount of force.

This is only practical, of course, if Mr. Clean needs to vacuum under the couch on his hands and knees, but it shows that in physics, the angle with which we apply a force affects how much work we get done, an idea that has larger application for how efficiently (and with what attitude) we approach our daily tasks. Most of all, I think I appreciate seeing a man doing the vacuuming in a physics textbook (I’ll post the hilarious ChatGPT illustration attempts on Instagram, for the curious. My handle is @cosrayjamie).

I didn’t agree with everything Black had to say about work, but I’m glad I bought the book, and I appreciate the chance to reflect on how we approach work and the intriguing notion that doing work on a system transfers energy to or from that system. I leave you with the following additional quotes from great people who knew the value of work:

• All labor that uplifts humanity has dignity and importance and should be undertaken with painstaking excellence. —Martin Luther King Jr.
• Nothing will work unless you do. —Maya Angelou
• Opportunity is missed by most people because it is dressed in overalls and looks like work. —Thomas A. Edison
• It’s not that I’m so smart, it’s just that I stay with problems longer. —Albert Einstein

Work hard but smart this month, and I’ll see you next time for our discussion of kinetic energy, when things really get going.

Jamie Zvirzdin researches cosmic rays with the Telescope Array Project, teaches science writing at Johns Hopkins University and is the author of “Subatomic Writing.”