Beam, Fulcrum, Torque, Law of the Lever and Mechanical Advantage

Posted by PITHOCRATES - April 30th, 2014

Technology 101

(Originally published May 1st, 2013)

A Lever is a Rigid Beam on a Fulcrum

Archimedes said, “Give me a place to stand, and I shall move the Earth with it.”  At least we think he did.  Archimedes of Syracuse was a Greek genius.  Mathematician.  Physicist.  Engineer.  Inventor.  And astronomer.  One of many of the ancient Greeks who advanced modern civilization.  By using math and science.  He did a lot.  And explained why things worked the way they did using math.  Like the Law of the Lever.

In the days before the twist-off bottle cap we used bottle openers.  Because try as we might we could not pry a bottle cap off with our hands.  Most grown men just didn’t have the strength to do that.  But a child could open a bottle if that child used a bottle opener.  For that bottle opener is a lever.  Giving the child leverage.  The ability to use a little bit of force to do a lot of work.

A lever is a rigid beam on a fulcrum.  Like a seesaw.  A common playground fixture.  If two kids of equal weight are on either end of the seesaw and the fulcrum is in the center these kids can effortless push up and down.  But if a grown adult sits on one end and a child is on the other the weight of the adult will drop his side of the seesaw down.  Leaving the child up in the air on the other side.

As the Lever increases in Length the more it will Amplify the Input Force we Apply

Now that’s no fun.  Having the seesaw permanently tipped in one direction.  However, even two people of different weights can enjoy playing on the seesaw.  All they have to do is move the fulcrum towards the heavier person until the seesaw balances.  So that there is a short length of seesaw between the fulcrum and the heavy person.  And longer length of seesaw between the fulcrum and the lighter person.  This creates the same amount of torque on both side of the fulcrum.

Torque is the turning force created by a force acting about a fulcrum.  The force in this case is the weight of the people on the seesaw.  Which we calculate by multiplying their mass by the force of gravity.  With the force of gravity being constant the greater the mass the greater the weight.  This weight pressing down on the beam creates torque.   And the further away from the fulcrum the greater the turning force.  Such that a lighter weight at a greater distance from the fulcrum can balance a greater weight at a shorter distance from the fulcrum.  Allowing a child to play on a seesaw with someone of far greater mass.  Because the lever amplified the smaller force of the child.  Allowing the child to move a heavier weight.  To illustrate this consider the following table.

Lever

This is just a visual aid.  The numbers don’t represent anything.  It just shows a relationship between force and the length of the lever.  In this example we need 1000 units of force to move something.  If we use a lever that is 10 units from the fulcrum we need to apply 100 units of force.  If we have a lever that is 40 units from the fulcrum we only need to apply 25 units of force.  If we have a lever that is 80 units from the fulcrum we only need to apply 12.5 units of force.  As the lever increases in length the more it will amplify the input force we apply.  Which is why a child can open a bottle with a bottle opener.

A Wheelbarrel combines the Lever with the Wheel and Axle

A lever gives us mechanical advantage.  The amplification of a small input force into a larger output force.  Such as a hand-held bottle opener.  But what about the kind that used to be fastened to pop machines?  When you bought a glass bottle of pop out of a vending machine?  The fulcrum is the fixed bottle opener.  And the lever is the bottle.  A can opener was often on the other end of a bottle opener.  Instead of a grip to latch onto a bottle cap this end had a triangular knife.  When we lifted up on the lever it pressed down and pierced a hole in a can.

A wheelbarrel allows us to move heavy loads.  This device combines two simple machines.  A wheel and axle.  And a lever.  The wheel and axle is the fulcrum.  The lever runs from the fulcrum to the handles of the wheelbarrel.  We place the load on the lever just before the axle.  When we lift the far end of the lever we can tilt up the load and balance it over the axle.  The lever amplifies the force we apply.  And the wheel and axle reduce the friction between this load and the ground.  Allowing us to move a heavy load with little effort.

Today’s pop bottles have screw-top caps.  Some people still use a lever to help open them, though.  A pair of pliers.  We use the pliers because we don’t have the strength to grip the cap tight enough to twist it open.  The pliers are actually two levers connected together at the fulcrum.  The pliers amplify our hand strand-strength to get a very secure grip on the bottle cap.  While our hands compress the two levers together getting a firm grip on the cap we can then use our arm to apply a force on the handles of the pliers.  Providing a torque to turn the bottle cap.  Very simple machines that make everyday life easier.  Thanks to the knowledge Archimedes handed down to us.

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Energy Storage

Posted by PITHOCRATES - September 18th, 2013

Technology 101

Our First Energy Storage Devices helped us Kill each other in Battle

There’s something very important to today’s generation.  Stored energy.  It’s utmost on their minds.  As they are literally obsessed with it.  And get downright furious when they have none.  Because without stored energy their smartphones, tablets and laptop computers will not work.  And when they don’t they will disconnect them from the Internet.  And social media.  A fate so horrible that they carry spare batteries with them.  Or a power cord to plug into an electrical outlet or cigarette lighter in a car.

Energy storage devices go back millennia.  Of course, back then there was no Internet or social media.  People just talked to each other in person. Something unimaginable to today’s generation.  For it was a simpler time then.  We ate.  We procreated.  Sometimes talked.  And we killed each other.  Which is where that energy storage comes in.

An early use of energy storage was to make killing each other easier.  Early humans used rocks thrown by slings and spears thrown by hand in hunting and war.  But you had to get pretty close to your prey/enemy to use these things.  As the human body doesn’t have the strength to throw these things very far or hard.  But thanks to our ingenuity we could use our tools and make machines that could.  Such as the bow and arrow.

The Bow and Arrow and the Crossbow use Tension and Compression to Store Energy

We made early bows from wood.  They had a handgrip and two limbs, one above and one below the handgrip.  Attached to these limbs was a bowstring.  The limbs were flexible and could bend.  And because they could they could store energy.  The archer would draw back the bowstring, bending the two limbs towards him.  This took a lot of strength to bend this wood.  The farther the archer pulled back the bowstring the more strength it took.  Because it was not the natural state for those limbs.  They wanted to remain unbent.  And were ready to snap back to that unbent position in a fraction of a second.  Much quicker than the archer pulled back the bowstring.

As the limbs bent the inside of the limb (towards the archer) was under compression.  The outside of the limb (facing away from the archer) was under tension.  The compression side was storing energy.  And the tension side was storing energy.  Think of two springs.  One that you stretch out in tension that will snap back to an un-stretched position when released.  And one that you push down in compression that will push back to an uncompressed position when released.  These are the two forces acting on the inside and the outside of the bending limbs of a bow.  Storing energy in the bow.  When the archer releases the bowstring this releases that stored energy.  Snapping those limbs back to an unbent position in a fraction of a second.  Bringing the bowstring with it.  Very quickly.  Launching the arrow into a fast flight toward the archer’s prey/enemy.

The stronger the bow the more energy it will store.  And the more lethal will be the projectile it launches.  Iron is much harder to bend than wood.  So it will store a lot more energy.  But a human cannot draw back a bowstring on an iron bow.  He just doesn’t have the strength to bend iron like he can bend wood.  So they added a couple of simple machines—levers to turn a wheel—at the end of a large wooden beam to draw back the bowstring.  At the other end of this beam was the iron bow.  What we call a crossbow.  With the wheel increasing the force the archer applied to the hand-crank the iron bow slowly but surely bent back.  Storing enormous amounts of energy.  And when released it could send a heavy projectile fast enough to penetrate the armor of a knight.

The Mangonel uses Twisted Rope to Store Energy while a Trebuchet uses a Counterpoise

Most children did this little trick in elementary school.  The old rattlesnake in the envelope trick.  You open up a large paperclip and stretch a small rubber band across it.  Then you slide a smaller paperclip across the taut rubber band.  And then you turn that small paperclip over and over until you twist the rubber band up into a tight twist.  Storing energy in that twist.  Slip it into the envelope.  And let some unsuspecting person open the envelope.  Allowing that rubber band to untwist quickly.  With the paperclip spinning around in the envelope making a rattlesnake sound.

We call this type of energy storage torsion.  An object that in its normal state is untwisted.  When you twist it the object wants to untwist back to its normal state.  On the battlefield we used this type of energy storage in a catapult.  The mangonel.  Which used a few simple machines.  We used a lever inserted into a tight rope braid.  In its normal state the lever stood upright.  A lever turned a wheel a cog at a time to pull the large lever down parallel to the ground.  Twisting the rope.  Putting it under torsion.  Storing a lot of energy.  When they released the holding mechanism the rope rapidly untwisted sending the large lever back upright at great speed.  Sending the object on it hurling towards the enemy.

The problem with the mangonel is that it took a long time to crank that rope into torsion.  Another catapult did away with this problem.  The trebuchet.  Perhaps the king of catapults.  This was a large lever with a small length on one side of the pivot and a large length on the other side of the pivot.  Think of a railroad crossing arm.  A long arm blocking the road with a counterweight at the other end.  We balance this so well that we need very little energy to raise or lower it.  The trebuchet, on the other hand, is not perfectly balanced.  It has a very heavy counterweight—a counterpoise—that in its normal state is hanging down with the long end of the lever pointing skyward.  They pull the long end of the lever down close to the ground.  Pulling up the counterweight.  Attached to the far end of the lever is a rope.  At the end of the rope is a rope pouch to hold the projectile.  When released the counterweight swings back down.  Sending the long end of the lever up quickly.  With the far end traveling very quickly.  Pulling the rope with it.  Because the length of the rope adds additional distance to the lever the projectile travels even faster than the end of the lever.  Which is why the stored energy in the hanging counterweight can launch a very heavy projectile great distances.

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Beam, Fulcrum, Torque, Law of the Lever and Mechanical Advantage

Posted by PITHOCRATES - May 1st, 2013

Technology 101

A Lever is a Rigid Beam on a Fulcrum

Archimedes said, “Give me a place to stand, and I shall move the Earth with it.”  At least we think he did.  Archimedes of Syracuse was a Greek genius.  Mathematician.  Physicist.  Engineer.  Inventor.  And astronomer.  One of many of the ancient Greeks who advanced modern civilization.  By using math and science.  He did a lot.  And explained why things worked the way they did using math.  Like the Law of the Lever.

In the days before the twist-off bottle cap we used bottle openers.  Because try as we might we could not pry a bottle cap off with our hands.  Most grown men just didn’t have the strength to do that.  But a child could open a bottle if that child used a bottle opener.  For that bottle opener is a lever.  Giving the child leverage.  The ability to use a little bit of force to do a lot of work.

A lever is a rigid beam on a fulcrum.  Like a seesaw.  A common playground fixture.  If two kids of equal weight are on either end of the seesaw and the fulcrum is in the center these kids can effortless push up and down.  But if a grown adult sits on one end and a child is on the other the weight of the adult will drop his side of the seesaw down.  Leaving the child up in the air on the other side.

As the Lever increases in Length the more it will Amplify the Input Force we Apply

Now that’s no fun.  Having the seesaw permanently tipped in one direction.  However, even two people of different weights can enjoy playing on the seesaw.  All they have to do is move the fulcrum towards the heavier person until the seesaw balances.  So that there is a short length of seesaw between the fulcrum and the heavy person.  And longer length of seesaw between the fulcrum and the lighter person.  This creates the same amount of torque on both side of the fulcrum.

Torque is the turning force created by a force acting about a fulcrum.  The force in this case is the weight of the people on the seesaw.  Which we calculate by multiplying their mass by the force of gravity.  With the force of gravity being constant the greater the mass the greater the weight.  This weight pressing down on the beam creates torque.   And the further away from the fulcrum the greater the turning force.  Such that a lighter weight at a greater distance from the fulcrum can balance a greater weight at a shorter distance from the fulcrum.  Allowing a child to play on a seesaw with someone of far greater mass.  Because the lever amplified the smaller force of the child.  Allowing the child to move a heavier weight.  To illustrate this consider the following table.

Lever

This is just a visual aid.  The numbers don’t represent anything.  It just shows a relationship between force and the length of the lever.  In this example we need 1000 units of force to move something.  If we use a lever that is 10 units from the fulcrum we need to apply 100 units of force.  If we have a lever that is 40 units from the fulcrum we only need to apply 25 units of force.  If we have a lever that is 80 units from the fulcrum we only need to apply 12.5 units of force.  As the lever increases in length the more it will amplify the input force we apply.  Which is why a child can open a bottle with a bottle opener.

A Wheelbarrel combines the Lever with the Wheel and Axle

A lever gives us mechanical advantage.  The amplification of a small input force into a larger output force.  Such as a hand-held bottle opener.  But what about the kind that used to be fastened to pop machines?  When you bought a glass bottle of pop out of a vending machine?  The fulcrum is the fixed bottle opener.  And the lever is the bottle.  A can opener was often on the other end of a bottle opener.  Instead of a grip to latch onto a bottle cap this end had a triangular knife.  When we lifted up on the lever it pressed down and pierced a hole in a can.

A wheelbarrel allows us to move heavy loads.  This device combines two simple machines.  A wheel and axle.  And a lever.  The wheel and axle is the fulcrum.  The lever runs from the fulcrum to the handles of the wheelbarrel.  We place the load on the lever just before the axle.  When we lift the far end of the lever we can tilt up the load and balance it over the axle.  The lever amplifies the force we apply.  And the wheel and axle reduce the friction between this load and the ground.  Allowing us to move a heavy load with little effort.

Today’s pop bottles have screw-top caps.  Some people still use a lever to help open them, though.  A pair of pliers.  We use the pliers because we don’t have the strength to grip the cap tight enough to twist it open.  The pliers are actually two levers connected together at the fulcrum.  The pliers amplify our hand strand-strength to get a very secure grip on the bottle cap.  While our hands compress the two levers together getting a firm grip on the cap we can then use our arm to apply a force on the handles of the pliers.  Providing a torque to turn the bottle cap.  Very simple machines that make everyday life easier.  Thanks to the knowledge Archimedes handed down to us.

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Flint Tools, Levers, Wheels, Animal Power, Water Power, Wind Power, Steam Power, Electrical Power, Nuclear Power and Solar Power

Posted by PITHOCRATES - February 22nd, 2012

Technology 101

Man harnessed the Energy in Moving Water with a Water Wheel

When prehistoric man first chipped a piece of flint to make a sharp edge he learned something.  It made work easier.  And his life better.  This tool concentrated his energy into that sharp edge.  Increasing the amount of energy he could put to work.  Allowing him to skin an animal quickly and efficiently like never before.  Making better hides to protect him from the elements.  Yes, he said, this tool is good.  But in a somewhat less sophisticated manner of speech.

From that moment forward it has been man’s singular desire to improve on this first tool.  To find ways to concentrate energy and put it to work.  Levers allowed him to move heavier things.  Wheels allowed him to move heavier loads.  The block and tackle allowed him to lift or pull heavier weights.  Harnessing animals allowed him to do all of these things even better.  And we would use animal power for millennia.  Even today they still provide the primary source of power for some less developed countries.

But animals have their limitations.  They’re big, they eat, drink, pee and poop.  Which doesn’t make them an ideal source of power to turn a mill wheel.  A big wheel that grinds grain into flour.  It’s heavy.  But it doesn’t have to spin fast.  Just for long periods of time.  Then man had another moment like he did when he chipped a piece of flint.  He noticed in his environment that things moved.  The wind.  And the water in a river.  The wind could blow fast or slow.  Or not at all.  But the water flow was steady.  And reliable.  So man harnessed the energy in the moving water with a water wheel.  And connected it to his mill wheel via some belts and pulleys.  And where there was no water available he harnessed the less reliable wind.

The Steam Engine eliminated the Major Drawbacks of Water Power and Wind Power 

The water flowed day and night.  You didn’t have to feed it or clean up after it.  And a strong current had a lot of concentrated energy.  Which could do a lot of work.  Far more than a sharpened piece of flint.  Which was ideal for our first factories.  The water wheel shaft became a main drive shaft that drove other machines via belts and pulleys.  The main drive shaft ran the length of the factory.  Workers could operate machinery underneath it by engaging it to the main drive shaft through a belt and pulley.  Take a trip to the past and visit a working apple mill powered by a water wheel.  It’s fascinating.  And you’ll be able to enjoy some fresh donuts and hot cider.  During the harvest, of course.

While we built factories along rivers we used that other less reliable source of energy to cross oceans.  Wind power.  It wasn’t very reliable.  And it wasn’t very concentrated.  But it was the only way you could cross an ocean.  Which made it the best way to cross an ocean.  Sailors used everything on a sailing ship from the deck up to catch the wind and put it to work.  Masts, rigging and sails.  Which were costly.  Required a large crew.  And took up a lot of space and added a lot of weight.  Space and weight that displaced revenue-earning cargo.

The steam engine eliminated the major drawbacks of water power and wind power.  By replacing the water wheel with a steam engine we could build factories anywhere.  Not just on rivers.  And the steam engine let ships cross the oceans whenever they wanted to.  Even when the wind didn’t blow.  And more space was available for revenue-earning cargo.  When these ships reached land we transferred their cargoes to trains.  Pulled by steam locomotives.  That could carry this revenue-earning cargo across continents.   This was a huge step forward.  Boiling water by burning coal to make steam.  A highly concentrated energy source.  A little of it went a long way.  And did more work for us than ever.  Far more than a water wheel.  It increased the amount of work we could do so much that it kicked off the Industrial Revolution.

With Nuclear Power our Quest to find more Concentrated Forms of Energy came to an End 

We replaced coal with oil in our ships and locomotives.  Because it was easier to transport.  Store.  And didn’t need people to shovel it into a boiler.  Oil burners were more efficient.  We even used it to generate a new source of power.  Electrical power.  We used it to boil water at electrical generating plants to spin turbines that turned electrical generators.  We could run pipelines to feed these plants.  Making the electricity they generated even more efficient.  And reliable.  Soon diesel engines replaced the oil burners in ships and trains.  Allowed trucks and buses to run where the trains didn’t.  And gasoline allowed people to go anywhere the trains and buses didn’t go.

The modern economy ran on petroleum.  And electricity.  We even returned to the water wheel to generate electricity.  By building dams to build huge reservoirs of water at elevations.  Creating huge headwater forces.  Concentrating more energy in water.  Which we funneled down to the lower elevation.  Making it flow through high-speed water turbines connected to electrical generators.  That spun far faster than their water wheel ancestors.  Producing huge amounts of reliable electrical power.  We even came up with a more reliable means to create electrical power.  With an even more concentrated fuel.  Fissile material gave us nuclear power.  During the oil shocks of the Seventies the Japanese made a policy change to expand their use of nuclear power.  To insulate them from future oil supply shocks.  Which it did.  While in America the movie The China Syndrome came out around the time of the incident at Three Mile Island.  And killed nuclear power in America.  (But as a consolation prize we disproved the idea of Keynesian stimulus.  When the government created massive inflation with Keynesian policy.  Printing money.  Which raised prices without providing any new economic activity.  Causing instead high inflation and high unemployment.  What we call stagflation.  The Japanese got a big Keynesian lesson about a decade later.  When their massive asset bubble began to deflate giving them their Lost Decade.)

And with nuclear power that quest to find more ways to make better and more efficient use of concentrated energy from that first day we used a flint tool came to an end.  Global warming alarmists are killing sensible sources of energy that have given us the modern world.  Even animal rights activists are fighting against one of the cleanest sources of power we’ve ever used.  Water power.  Because damming rivers harms ecosystems in the rivers we dam.  Instead political pressures have turned the hands of time backwards by using less concentrated and less efficient sources of energy.  Wind power.  And solar power.  Requiring far greater infrastructure installations to capture far less amounts of energy from these sources.  Power plants using wind power and solar power will require acres of land for windmills and solar panels.  And it will take many of these power plants to produce what a single power plant using coal, oil, natural gas or fissile material can generate.  Making power more costly than it ever has been.  Despite wind and sunshine being free.  And when the great civilizations become bankrupt chasing bankrupt energy policies we will return to a simpler world.  A world where we don’t make and use power.  Or machinery.  Much like our flint-tool using ancestors.  Albeit with a more sophisticated way of expressing ourselves.

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