Apr. 15, 2011

Science Dad on the Meaning of Work

by Vince Harriman

Click to enlarge images

Calibrating our scale

Last week I had the naive hope that explaining weight, mass, and density would answer most of Beckett's questions on the topic. Of course our discussion only led to more questions and questions that were more difficult to answer. So we came up with some simple demonstrations to show the relationship between mass, weight, and work.

The questions started again with the bike. Beckett was helping me get one of my bikes ready for riding again and noticed it did not have a kickstand. "Why not?" he asked.

"Because I don't want to carry the weight up a hill," was my answer, although we live at sea level and the highest 'hill' around here is the 80 foot high bridge over the Severn River.

"You don't have to carry it up the hill, it's on the bike," was his answer. So when we finally got my bike ready for a ride I had Beckett do two things: first, ride up the street which is slightly uphill; second, ride back down the exact same stretch, which was now slightly down hill.

"Which one was harder?" I asked him.

"Uphill," he said.


Marking our units on the strain guage

Later we decided to build our first scientific instrument, this one to measure work. The traditional definition of work is to move a mass over a vertical distance. We built a simple strain gauge that could measure joules. A joule is the unit that describes the energy used or work needed to apply a force of one newton a distance of one meter. A newton is a measure of force -- the amount of force needed to move one kilogram one meter/second squared. To create our strain gauge, we took two bamboo barbecue skewers and inserted them firmly into a block of wood that would serve as a handle. We glued a piece of paper to the top skewer and made sure that, at rest, the two skewers were straight and touched each other (our 'zero' point). Next we searched the kitchen for a weight of a known quantity and were lucky enough to find a chocolate bar of 100 grams. This was especially lucky for several reasons. First, we found a yummy treat for after the project. Second, the 100 gram bar plus the 2 grams or so for the paper wrapper and foil would give 102 grams. We then found several other objects (ok, we have a variety of chocolate bars in various weights -- an eighty gram bar, a two ounce bar (that we called 60 grams -- for the sake of this instrument it would be close enough) and a 140 gram bar.

Moving 100 grams laterally requires much less work than moving it vertically

Since the force of gravity (on average) is 9.81 meters per second per second, moving an object that weighs 102 grams (or 1/9.81 kilograms) one meter equals one joule. We marked the gauge and put it to work.

We would use our strain gauge to 'move' some objects, thereby accomplishing some measurable work and see what happened. Since our strain gauge would easily allow us to see what a joule looked like by moving the chocolate bar one meter up, we then placed the bar on the table to see how much work (energy) is needed to move the chocolate bar one meter horizontally and found that it required much less energy. Moving the chocolate bar up an incline would take more energy and down an incline would take less energy, just like riding a bike up or down hill.

Now that Beckett could 'see' how much energy or work was needed to move an object, it was immediately obvious why my 'racing' bike didn't have a kickstand. And using the simple formula for work we could easily calculate how much energy is required to perform simple tasks -- like for Beckett to walk up the stairs to his room. To do this, we measured a stair (in metric), counted the number of stairs, and weighed Beckett. We converted his weight to Newtons (one pound = 4.5 N). The formula for work is often simplified as

W = F times D or Work = Force times (vertical) Distance. So,

Work = Force (Beckett's weight in Newtons which is 270N) times Distance (3.56 meters)

W=270N x 3.56 m or W = 963 Nm

An obvious question is if work is defined as force over a vertical distance, does that mean that while moving on flat ground, such as running or riding a bike on a flat road, no work is being performed? The answer is no -- the method that humans use for locomotion is to lift one leg and put it in front of the other. To do this we are doing a small amount of work with every step, even if we are not moving our bodies continuously up in a vertical manner.

Now it is time for me to move my weight (which we will not calculate here, in pounds, kilograms, or Newtons) up the stairs (which are still 3.56 meters high) and go to bed. Next time you watch sports, think of of the work and energy required to move an object, whether it is kicking a football through a goal post or riding a bike up a mountain in France. Or, try to calculate the energy needed to get an airplane into the air. And if you decide to make your own strain gauge, don't forget to add the skull and cross bones. All good strain gauges have them!

About Vince Harriman

Science Dad, AKA Vince Harriman, is a freelance writer living in Annapolis. His two sons, Beckett-6 and Rowan-2 1/2 ask him 'why' approximately 6,542 times a day.

The views expressed are those of the author and are not necessarily those of Science Friday.

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