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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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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Thales of Miletus, Olive Oil, Tulip Mania of 1636 and the Chicago Board Options Exchange

Posted by PITHOCRATES - April 30th, 2013

History 101

Thales of Miletus was able to Predict a Bumper Crop of Olives

Italian restaurants will have a bottle of olive oil on the table.  The more authentic restaurants.  That give you a taste of old Italy.  Where they give you bread to munch on while you wait for your food.  We pour a little olive oil on a plate.  And dip our bread in it.  And enjoy that Mediterranean flavor.  Something that some of us may believe the Olive Garden brought to the dining experience.  But olive oil actually predates the Olive Garden.  We probably started eating olives for the first time around the 8th millennium BC.  When our Neolithic ancestors were still using stone tools.  Someplace in ancient Greece.

Olive trees grew all around the Mediterranean Sea.  And the Mediterranean people probably started using olive oil around the 4th millennium BC.   That’s 4000 BC.  Awhile ago.  We began to produce olive oil commercially somewhere around 2500 BC.  And began trading this luxury good.  We ate it.  Used it in religious rituals.  In medicines.  And fuel for oil lamps.  Among other uses.  As demand grew we planted more trees.  And brought in large harvests at the end of the growing season.  And took the olives to the olive presses.  And waited for our turn.  To pay the pressman to press our olives into oil.  And during a good growing season you could find yourself waiting quite awhile.

But who has time to wait?  If only we could figure out some way to avoid that long line.  Well, as it turned out, if you were smart you could.  As Thales of Miletus did.  A Greek astronomer, philosopher and mathematician.  As well as a pretty good weather forecaster.  For he was able to predict a bumper crop of olives one year because of favorable weather.  Which would make those olive presses busy at the harvest.  So he went to the olive press owners and reserved time on their presses for a nominal down payment.  So when the harvest came in he would be at the front of the line.  If he was wrong about his forecast he would give up his nominal deposit.  And walk away.  As the press owners didn’t care whose olives they were pressing they were glad to take his money for this right to buy press time later.  They had nothing to lose.  And when Thales prediction proved true and there was a bumper crop of olives those options to buy time on those presses became very valuable.  Those anxious to get their olives into the presses were glad to pay him for those options.  To buy his right to be first to buy press time.  Which he did.  Getting quite wealthy in the process.  As well as proving a point.  Rational thinking had real value.  They could use philosophy to make life better.

As Tulip Prices continued their Meteoric Rise the Speculators entered the Market to Get Rich Quick

And the option was born.  You can use them to speculate about the price of something in the future to make a lot of money.  And you can use them for hedging risk.  Such as farmers do.  They enter contracts with people to sell their crops at a set price.  Which protects the farmer if there is a bumper crop and prices fall.  Those who didn’t enter an options contract will only get the market price for their crops.  And have an unprofitable season.  While those with options contracts will be able to sell their crops above the market price.  And have a profitable season.  But if there are droughts that reduce the harvest prices will rise.  Which protects the buyer.  As he is able to buy below the market price.  At the price in the options contract.  While those buyers without options contracts will have to pay the higher market price.  Thus entering a contract hedges risk for both buyer and seller.  One party may do better than the other if there is a large swing in price.  But neither party will suffer a bad loss.  So whatever happens in that growing season they will be around for the following growing season.  But the speculators, on the other hand, can suffer great losses.

Tulips were big in the 17th century.  The affluent adorned their homes with these beautiful flowers.  And they soon became a sign of affluence.  Today people go to the affluent shops on Rodeo Drive and buy the latest in high fashion to show off their wealth.  In the 17th century they planted tulips.  People were impressed with what they saw.  And soon had to have these wonderful flowers themselves.  Causing a great surge in demand for tulips.  Which tulip growers rushed in to meet.  But the supply couldn’t keep up with the demand.  So tulip prices soared.  Soon, growers (sellers) and wholesalers (buyers) start entering options contracts to hedge their risks in the volatile tulip market.  As tulip prices continued their meteoric rise the speculators entered the market to get rich quick.  This speculation grew into such a frenzy that people would even mortgage their homes to raise money to buy tulip options.  Waiting for the big payday when they could exercise those options.  And buy tulips at one price.  Then resell them at a higher price.  A much higher price.  The demand for options grew so great that an options market opened.  And people bought and sold tulip options.

All good things must come to an end, though.  As must speculative bubbles.  And that happened in the Netherlands in 1637.  For there comes a time where buyers simply refuse to buy anymore tulips at those high prices.  And when they stopped buying people with vast amounts of tulips to sell began to panic.  And started lowering their price.  As other sellers started doing.  When interest in buying tulips fell supply began to exceed demand.  Sending the tulip price into a freefall.  With falling tulip prices no one was buying options contracts.  Because the market price was falling so fast that it would fall below the price in those options contracts.  And when they did ‘fall out of the money’ those options contracts became worthless.  And all that money the speculators poured into the options market was lost.  People lost everything.  Even their homes.  Sending the Dutch economy into a nasty recession.

With the Advent of the Internet it’s Never been Easier to Buy and Sell Options

Stock options were a way to get rich quick.  And what made them so attractive to speculators was leverage.  A small investment could turn into great riches.  But that leverage worked both ways.  And it could take that small investment and turn it into a great loss.  Should the price move in the wrong direction and fall when you have a contract obligating you to buy at a higher price.  And with the tulip mania of 1636 investors were getting a little gun-shy of options in general.  Causing the volume of options trading to fall in London.  Concerned of the speculative nature of options London made options trading illegal in 1733.  A ban that remained until 1860.

Russell Sage inaugurated options trading in the United States in 1872.  These were over the counter (OTC).  There was no central stock exchange.  Or standardized options format.  Which made the trading difficult to say the least.  Brokers placed ads in financial journals for their respective buyers and sellers.  And waited.  For someone to read the ad.  And call.  Then haggled over the price a bit.  Signed a contract.  And then waited until the expiration date of the option.  Or placed another ad in some financial journal.  To find someone else to buy the option.

Then things started changing in 1935.  The SEC granted a license to the Chicago Board of Trade (CBOT) as a national securities exchange.  And in 1968, CBOT finally did something with that license.  They created the Chicago Board Options Exchange (CBOE).  Which standardized and organized options trading.  One Nobel Prize later to Fischer Black and Myron Scholes for their “The Pricing of Options and Corporate Liabilities” we had a ‘scientific’ way for valuing stock options.  And with the advent of the Internet it’s never been easier to buy and sell options.  Allowing some to hedge risks easily.  While others live dangerously.  And speculate.  Trying to score big.  Before they lose everything trying to get rich quick.

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FUNDAMENTAL TRUTH #26: “If we need Big Government to protect us from ourselves, then our public schools can’t be the best place to learn.” -Old Pithy

Posted by PITHOCRATES - August 10th, 2010

IT’S A PARADOX.  You can’t have both.  Great public schools.  And a Big Government nanny state.  The public schools can’t be the best place to learn if we graduate hopelessly incapable of taking care of ourselves.  You cannot reconcile the two.  It is impossible.  The need of Big Government is an indictment on public education.  It sucks.  It sucks so bad that our only hope to survive is by a dependence on government.

The Founding Fathers did NOT want a Big Government nanny state.  So they tried to limit its money and power.  The nation’s capital ended up in a swamp because Thomas Jefferson wanted to keep it out of the big cities (such as New York and Philadelphia).  History has shown that wealth (the big cities) and power (sovereign authority) combine to make the worst of governments. 

And they believed in the importance of education.  A real education.  History.  Math.  Science.  Architecture.  Engineering.  Economics.  For they believed an educated constituency was the greatest protection against Big Government.  They knew it.  Just as well as the proponents of Big Government knew it.  Know it.

So is it a coincidence?  That the rise of Big Government corresponded with a fall in the quality of public education?  If we need Big Government to be our nanny, we obviously are not well educated.  Otherwise, we could take care of ourselves.  Like we did for the first century or so of our existence.  So, did our poor public school system give life to Big Government?  Or is it the other way around?  Did a growing Big Government protect itself from the danger of a well educated constituency?

STUDENTS GRADUATE TODAY without being able to do the most simple of tasks.  To point to Australia on a map.  To identify the three branches of government.  To name a current member of the U.S. Supreme court.  The current Speaker of the House.  To identify the allies during World War II.  Or even tell us who’s buried in Grant’s tomb.

Few can define compound interest.  Or calculate it.  Few can make important investment decisions for their retirement.  But they can tell you how Christopher Columbus raped the indigenous people in the New World.  How America ruthlessly expanded westward, stealing land from the North American Indians.  How we cruelly enslaved a race to build a nation predicated on liberty.  You’ll find these in the curriculum.  And in the schools’ libraries.  But you won’t learn much about how Martin Van Buren created the Democrat Party to prosper on political spoils and patronage.  Or that the Democratic Party was the party of slavery.  The party of the KKK.  The party of Jim Crowe laws (the legal segregation of blacks after the Republicans ended slavery).  That it was the Democrats who enacted Prohibition because they knew what was best for us.

No, instead, students today learn about the importance of being sensitive to other people’s feelings.  That we should be our brother’s keepers.  That Big Government is good.  Important.  And necessary.  We teach them that FDR’s New Deal programs ended the Great Depression.  That massive government spending on make-work government jobs restored the economy.  It didn’t.  They learn that LBJ’s Great Society ended racial discrimination and poverty.  It didn’t.  These programs failed.  As many Big Government programs of compassion do.  But that’s not in the curriculum. 

Worst, most students haven’t a clue about economics.  What makes economic activity.  What hinders it.  The consequences of monetary and fiscal policy.  So they haven’t a clue about how all those compassionate programs of Big Government often lead to unemployment and recession.  So when they are old enough to vote, they are compassionate.  They approve of expanding the nanny state without any idea of the economic impact.

WE SPEND A fortune on public education.  Per student expenditures are among the highest in the world.   But the money we spend is never enough.  They always ask for more.  For the children.  So, to help the children, they raise taxes (property, sales, etc.).  For the children, they get the poor to gamble away what little they have (the lotto).  More money than ever before is collected.  For the children.  But it’s still not enough.  Which begs the question, where is all that money going?  Clearly, it isn’t to the children.

And because the children are so precious, they’re good leverage.  There’s nothing like a good strike at the beginning of the school year to get a better contract.  Why, they even have our precious children carry picket signs.  Because it’s all about the children.  Of course, unions protect dues-paying members.  And the last I heard, children don’t pay union dues.

But the teachers are underpaid and overworked, aren’t they?  If they are, they are the only union workers that are.  It’s why you join a union.  For leverage.  For negotiating power to get better salary and benefit packages.  And they do.  Your typical public school teacher does better than your typical salaried worker.  And they work less to get it.  Oh, they talk about ‘non-compensated’ hours worked after school.  That means approximately anything more than an 8-hour day.  The real world typically pays a salaried worker for only a 40 hour week when they often work 50 hours or more.  And they often don’t get the Friday after Thanksgiving off.  Or a Christmas break.  Or a winter break.  Or an Easter break.  Or the 3 months of summer off.   When you factor in the actual time worked and the benefits, they do very well.  Far better than private school teachers.  And private school students outperform public school students.  Hell, some of the most stalwart defenders of public education send their kids to private school.  Because they can.  The poor do, too.  When they can.  When they have access to school vouchers.  Everyone, when given the choice, chooses private school over public school.  If that ain’t an indictment on the public school system, I don’t know what is.

So where does all that money go?  To the teachers.  Their unions.  And the public school bureaucracy.

WE SPEND MORE money on public education.  But private school students do better than public school students.  And private school teachers make less than public school teachers.  So when we pay more we get less.  A more poorly educated student.  So what conclusion can we draw?  We are spending more money than we need to on public education.  And if we’re spending too much right now, spending more money sure isn’t going to make anything better for the children.  The teachers, perhaps.  But not the children.  Because the truth is this.  It’s not about the children.

The public schools are not educating.  They’re indoctrinating.  They’re producing good liberal democrats.  Because Big Government knows that an educated constituency is the greatest threat against their power.  So they control education.  They take care of the union teachers who, in turn, teach the students to love Big Government.  It’s rather Orwellian, really.  Elites taking care of elites.  At the expense of the children.  And our future.

Conspiracy?  If it wasn’t so much in the open, perhaps.  But the Democratic Party hasn’t changed much since the days of Martin Van Buren.  It’s about getting power.  And keeping power.  And you do that with patronage.  And dependency.  Big Government has given us Social Security, Medicare, Medicaid, unemployment benefits and numerous welfare programs.  And now the holy grail of them all.  National health care.  The larger these programs, the greater the dependence.  The larger the dependency, the greater number of loyal Democrat voters. 

SO IS THERE a paradox?  It depends on your point of view.  From outside of the public school system, yes.  If you think it’s about the children, yes.  But from inside the public school system or from inside of Big Government, no.  Because, there, it is not about the children.  It’s about well paid teachers.  And an uninformed electorate.  And the systems in place work very well in achieving these goals.

So, no, our public schools are not the best place for children to learn.  But it’s a pretty good place to indoctrinate them into loving Big Government.

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