Another day older, and deeper in debt… Or so the song goes, but is that realistic?
Man, loading 16 tons of coal in a day sounds like a lot of work… But is it as much work as it seems?
Fortunately, physics gives us a way to calculate the amount of work done. In this case, we will assume that the only work done is to lift the coal against the force of gravity. As the direction of motion is parallel to the direction of the force, the formula for work done is simple:
Work = Force x Distance
Where the force is the weight of the coal. So we have 16 tons, and let’s assume that you have to lift the coal to about waist height, or about 3 feet.
Now, the units here can get a little bit messy, but let me introduce you to a very useful tool in this case: Google. Google has a calculator that will also take care of all your units, and convert them to whatever units you want at the end of the calculation. So we simply type in:
16 tons * 3 feet *9.8 m/s^2
(About the extra factor of 9.8 m/s^2: Google apparently treats pounds and tons as units of mass rather than units of force. This is a somewhat subtle distinction: if you move a certain object from the earth to the moon, its mass will not change, but the gravitational force will change, as the acceleration due to gravity will change. In order to take care of this, we insert the factor of the gravitational acceleration while close to earth.)
This gives us a result of about 130 kilojoules. Okay, but what does this mean? Let’s just ask google to convert this to calories. This gives us over 31,000 calories. That sounds like a lot, but we must remember that the “calorie” used by dieticians is actually 1,000 regular calories. So this means we burn the equivalent of 31 dietary calories in lifting the coal.
So this means we only need to eat a granola bar, and then we have enough energy to lift 16 tons of coal all day? Well, not really. The energy expended by a human is much more complicated than this. There is the basal metabolic rate, or what you burn when you do absolutely nothing else, and the energy needed to contract the muscle fibers, etc.
Hmmm… that doesn’t seem to help much. Let’s look at the power expended. Power is the work done per unit time. If we assume 16 tons is shoveled during an 8 hour shift, turning to Google again, we find that we produce about 4.5 watts. This is less than a tenth of a horsepower. I know as a rule of thumb that a human is good for about a third of a horsepower. This implies that lifting 16 tons would be a trivial amount of work, which doesn’t seem likely.
This is one of those cases where we apply some basic physics to an everyday situation, but it doesn’t seem to help us much. But it does point out another valuable tool in the physicist’s arsenal: common sense. It’s amazing how much this can help, and on the flip side, how rarely beginning physics students use this tool. They crank through the calculations and then pronounce that the Mississippi River is 2 inches long, or that an ant runs 200 miles an hour, or something else that they would never say if they thought about it for a second or two.
So all this tells us is that we’re missing something crucial. Maybe instead of doing more physics, it might be better to ask an old coal miner. Anybody know one?