Give me a lever and I will move the world
This is the bold statement that the Greek Archimedes is said to have made when explaining the operating principle of one of the simplest and most widely used machines in the history of humanity: the lever.
The lever and achievement are so closely associated in the human psyche that we say leverage when we want to express the intention of arranging things in such a way as to move something, change something, or make something happen. We also ask “What lever do we need to pull?” when we want to know what we have to do to achieve something that initially seems impossible.
And it’s no wonder! The lever has a very close relationship with a concept that interests us greatly: work, because the lever is a machine that essentially allows the same work to be done but in a much smarter way and with less human effort.
Work
In Physics, Work is the amount of energy involved in producing a certain physical change. For example, to lift a huge spherical stone weighing a ton, i.e., 1000 kilograms, by rolling it uphill on a ramp to a height of just one meter, a certain amount of energy is required. We can calculate this by *multiplying the weight by the height difference, measured in units of force multiplied by units of length.
If we measure the height in meters and the weight in kilograms, the work is expressed in kilogram-meters or “kgm.”
In Physics and Engineering, the Newton is often used as a unit of force. A newton is the force needed to accelerate a 1-kilogram object by one meter per second squared. For example, to accelerate a car to overtake another, its wheels need to exert 1 newton per kilogram of the car’s mass on the pavement for every meter per second increase in speed per second.
If we measure force in newtons and distance in meters, the result is expressed in a unit widely used to measure work and energy: the Joule.
What Goes Up Must Come Down
How much work would we have to do if we now wanted to let our massive 1000-kilogram stone roll downhill on the ramp from its height of one meter back to ground level?
The answer to that question is already implied in the phrase “let it roll.”
Indeed, we don’t have to do much physical work, except to decide to do it (which, as we’ll see later, while small, is not zero in energy terms). We just need to 1) decide to release it and 2) let it roll downhill. Moreover, when it reaches ground level, our heavy stone will have gained a speed that could undoubtedly cause a painful physical change in any unfortunate mortal standing in its path. And we already said that the ability to cause a physical change is called “energy.” How much energy does our one-ton rolling stone have when it reaches the ground? The answer: almost exactly the same amount of energy that was required to lift it to the height from which we let it fall.
To raise the one-ton ball (i.e., 1000kg) by one meter on the ramp, we had to do work that we can calculate:
1000 kilograms is 9800 newtons
9800 Newtons multiplied by 1 meter of height equals 9800 joules of work or energy.
If we were to measure the rolling ball’s speed as it returns to ground level, we would also find that multiplying half its mass in kilograms by its speed squared would yield almost exactly the same result: 9800 joules of kinetic energy, or energy in motion.
Who Can Lift a Ton One Meter Off the Ground with Their Arms?
You can!!! But, first, you’ll need the materials, tools, time, knowledge, and freedom to use those resources to build a 100-meter-long ramp!!
If you do, you can lift a ton one meter off the ground with your arms by simply pushing the ball uphill, overcoming a resistance of approximately 10 kilograms of force over the 100 meters of the ramp…
10 kilograms of force is 98 newtons
98 Newtons multiplied by 100 meters uphill on the inclined plane makes the 9800 Joules of work needed to lift a ton by one meter.
The Potential Lies in the Field
No, we’re not talking about corn or soybean biofuels! (at least not yet).
We are referring to the Earth’s gravitational field!!… those 9800 joules, whether by ramp, ladder, or lift, are used to move a one-ton weight one meter away from the center of the Earth…
Where did all that energy go while the ball remains stationary one meter high? We know that although the ball is completely still, that energy is conserved or stored somewhere, as it will reappear almost entirely if we let the ball roll downhill again!
The conclusion follows that the energy needed to move the ball away from the Earth was stored in some potential form within the gravitational interaction field and is released again when the ball is allowed to descend, gain speed, and that potential energy is transformed into kinetic energy.
Later, we will see that something very similar happens with energy when a charged particle, like an electron, moves within an electric field or changes levels within the atom it is part of.
Thinking Requires Work, but It’s Worth It
The brain’s functioning, including thinking, making a choice, or making a decision, involves material energy exchanges (by the way, energy is one of the manifestations of matter).
If we wanted to consider the total amount of work required to lift the one-ton ball up the ramp, we should also consider the work needed not only to build the ramp but also to design it… If we did, we would find that the use of intelligence and the ramp consumes slightly more work but definitely less human effort, better results, and in less time. Achieving better results with less human effort and in less time dramatically increases productivity.
Increasing Power
As we mentioned earlier, energy is the ability to do work, but we didn’t specify in how much time. Surely, traversing the entire ramp by pushing the one-ton sphere will take much longer than if we had the strength to lift it on the spot. The ability to do work in a given time is called power, and if we measure work in joules and time in seconds, we measure power in joules/second, a unit that goes by a much more recognizable name: the watt. So if it took us 980 seconds (a little over 16 minutes) to push the one-ton rock across 100 meters of ramp to raise its height by 1 meter, requiring 9800 joules of work, we worked during that time with the power needed to light a 10-watt light bulb!!
9800 joules / 980 seconds = 10 watts
If instead of the ramp, we used a crane or motorized lift, the achievement would require even more physical work, meaning more energy at play, but this time not through muscular force; most of the work would be done by intelligently channeling the energy and power that comes from fuels, hydroelectric dams, nuclear power plants, or solar energy, etc. Therefore, the human effort and time required would be dramatically lower, and the results obtained dramatically better.
The incalculable Value of Modernity
In Herodotus’s description of the construction of the Great Pyramid, interpreted in an 1820 engraving by Antoine-Yves Goguet, we can see Egyptian builders using levers as cranes.
The Great Pyramid was built with over two million stone blocks, each weighing slightly more than two tons. The blocks were lifted using two levers, one at each end, to raise them one step at a time. In the engraving, each step is just under one meter high… As each of the two crane/levers lifts half the block’s weight, or slightly more than one ton, to a height of just under one meter… the work done by each group of men seen in the image, pulling down on the ropes to raise each block just one step, is approximately the same as it takes to lift our spherical rock up the ramp, or about 9800 joules, which as we saw, mutatis mutando, is also approximately the energy consumed by a 10-watt lamp for 16 minutes.
In 2011, the average price of electricity in the United States was 10 cents per kilowatt-hour, which is the energy consumed by a 1000-watt device for one hour, or 60 minutes. This data allows us to calculate how much it would have cost us in 2011 to have the same energy required to raise one step on each crane/lever each of the 2,300,000 blocks of the Great Pyramid.
If 1000 watts for one hour, or 60 minutes, costs 10 cents of a dollar
10 watts for 16 minutes costs: (10 cents/60 minutes) x 16 minutes = 2.66 cents
Do you begin to understand the value of modernity? Assuming it took an hour to lift each block one step:
For the same task, the hourly work of six men in Ancient Egypt essentially gave the same useful result as the intelligent use of about 3 cents of electricity in the 21st century!
And let’s not even try to imagine what the value would be if the Egyptians hadn’t also used a machine: the lever!!
Conclusion
The previous analysis could be applied to any activity that involves bringing something to a form, a place, or a time according to our needs and desires.
Since wealth is the abundance of those goods we desire or need, in the form, place, and time we need them, we can see that intelligence and the freedom to exercise it are the primary source of wealth and abundance, and technology, the art of intelligently using matter and energy, is its instrument.