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.

www.PITHOCRATES.com

Share

Tags: , , , , , , , , , , , , , , , , , , , ,

Trucks, Trains, Ships and Planes

Posted by PITHOCRATES - August 21st, 2013

Technology 101

Big Over-the-Road Tractor Trailer Trucks have Big Wheels so they can have Big Brakes

If you buy a big boat chances are you have a truck or a big SUV to pull it.  For rarely do you see a small car pulling a large boat.  Have you ever wondered why?  A small car can easily pull a large boat on a level (or a near level) surface.  That’s not the problem.  The problem is stopping once it gets moving.  For that is a lot of mass.  Creating a lot of kinetic energy (one half of the mass times velocity squared).  Which is dissipated as heat as brake shoes or pads rub against the wheels.  This is why you need a big truck or SUV to pull a boat.  So you can stop it once it gets moving.

Big trucks and big SUVs have big wheels and big brakes.  Large areas where brake pads/shoes press against a rotating wheel.  All of which is heavy duty equipment.  That can grab onto to those wheels and slow them down.  Converting that kinetic energy into heat.  This is why the big over-the-road tractor trailer trucks have big wheels.  So they can have big enough brakes to stop that huge mass once it gets moving.  Without the brakes turning white hot and melting.  Properly equipped trucks can carry great loads.  Moving freight safely across our highways and byways.  But there is a limit to what they can carry.  Too much weight spread between too few axles will pound the road apart.  Which is why the state police weighs our trucks.  To make sure they have enough axles supporting the load they’re carrying.  So they don’t break up our roads.  And that they can safely stop.

It’s a little different with trains.  All train cars have a fixed number of axles.  But you will notice the size of the cars differ.  Big oversized boxcars carry a lot of freight.  But it’s more big than heavy.  Heavy freight, on the other hand, like coal, you will see in smaller cars.  So the weight they carry doesn’t exceed the permissible weight/axle.  If you ever sat at a railroad crossing as a train passed you’ve probably noticed that the rail moves as the train travels across.  Watch a section of rail the next time you’re stopped by a train.  And you will see the rail sink a little beneath the axle as it passes over.

If a Ship is Watertight and Properly Balanced it can be covered in Green Water and Rise back to the Surface

So the various sizes of train cars (i.e., rolling stock) keeps each car from being overloaded.  Unlike a truck.  Steel haulers and gravel trains (i.e., dump trucks) have numerous axles beneath the load they’re carrying.  But these axles are retractable.  For the more wheels in contact with the road the more fuel is needed to overcome the friction between the tires and the road.  And the more tires in contact with the road the more tire wear there is.  Tires and fuel are expensive.  So truckers like to have as few tires in contact with the road as possible.  When they’re running empty they will have as many of these wheels retracted up as possible.  Something you can’t do with a train.

That said, a train’s weight is critical for the safe operation of a train.  In particular, stopping a train.  The longer a train is the more distance it takes to stop.  It is hard to overload a particular car in the string of cars (i.e., consist) but the total weight tells engineers how fast they can go.  How much they must slow down for curves.  How much distance they need to bring a train to a stop.  And how many handbrakes to set to keep the train from rolling away after the pressure bleeds out of the train line (i.e., the air brakes).  You do this right and it’s safe sailing over the rails.  Ships, on the other hand, have other concerns when it comes to weight.

Ships float.  Because of buoyancy.  The weight of the load presses down on the water while the surface of the water presses back against the ship.  But where you place that weight in a ship makes a big difference.  For a ship needs to maintain a certain amount of freeboard.  The distance between the surface of the water and the deck.  Waves toss ships up and down.  At best you just want water spray splashing onto your deck.  At worst you get solid water (i.e., green water).  If a ship is watertight and properly balanced it can be covered in green water and rise back to the surface.  But if a ship is loaded improperly and lists to one side or is low in the bow it reduces freeboard.  Increases green water.  And makes it less likely to be able to safely weather bad seas.  The SS Edmund Fitzgerald sank in 1975 while crossing Lake Superior in one of the worst storms ever.  She was taking on water.  Increasing her weight and lowering her into the water.  Losing freeboard.  Had increasing amounts of green water across her deck.  To the point that a couple of monster waves crashed over her and submerged her and she never returned to the surface.  It happened so fast that the crew was unable to give out a distress signal.  And as she disappeared below the surface her engine was still turning the propeller.  Driving her into the bottom of the lake.  Breaking the ship in two.  And the torque of the spinning propeller twisting the stern upside down.

Airplanes are the only Mode of Transportation that has two Systems to Carry their Load

One of the worst maritime disasters on the Great Lakes was the sinking of the SS Eastland.  Resulting in the largest loss of life in a shipwreck on the Great Lakes.  In total 844 passengers and crew died.  Was this in a storm like the SS Edmund Fitzgerald?  No.  The SS Eastland was tied to the dock on the Chicago River.  The passengers all went over to one side of the ship.  And the mass of people on one side of the ship caused the ship to capsize.  While tied to the dock.  On the Chicago River.  Because of this shift in weight.  Which can have catastrophic results.  As it can on airplanes.  There’s a sad YouTube video of a cargo 747 taking off.  You then see the nose go up and the plane fall out of the sky.  Probably because the weight slid backwards in the plane.  Shifting the center of gravity.  Causing the nose of the plane to pitch up.  Which disrupted the airflow over the wings.  Causing them to stall.  And with no lift the plane just fell out of the sky.

Airplanes are unique in one way.  They are the only mode of transportation that has two systems to carry their weight.  On the ground the landing gear carries the load.  In the air the wings carry the load.  Which makes taking off and landing the most dangerous parts of flying.  Because a plane has to accelerate rapidly down the runway so the wings begin producing lift.  Once they do the weight of the aircraft begins to transfer from the landing gear to the wings.  Allowing greater speeds.  However, if something goes wrong that interferes with the wings producing lift the wings will be unable to carry the weight of the plane.  And it will fall out of the sky.  Back onto the landing gear.  But once the plane leaves the runway there is nothing the landing gear can gently settle on.  And with no altitude to turn or to glide back to a runway the plane will fall out of the sky wherever it is.  Often with catastrophic results.

A plane has a lot of mass.  And a lot of velocity.  Giving it great kinetic energy.  It takes long runways to travel fast enough to transfer the weight of the aircraft from the landing gear to the wings.  And it takes a long, shallow approach to land an airplane.  So the wheels touch down gently while slowly picking up the weight of the aircraft as the wings lose lift.  And it takes a long runway to slow the plane down to a stop.  Using reverse thrusters to convert that kinetic energy into heat.  Sometimes even running out of runway before bringing the plane to a stop.  No other mode of transportation has this additional complication of travelling.  Transferring the weight from one system to another.  The most dangerous part of flying.  Yet despite this very dangerous transformation flying is the safest mode of traveling.  Because the majority of flying is up in the air in miles of emptiness.  Where if something happens a skilled pilot has time to regain control of the aircraft.  And bring it down safely.

www.PITHOCRATES.com

Share

Tags: , , , , , , , , , , , , , , , , , , , , , ,

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.

www.PITHOCRATES.com

Share

Tags: , , , , , , , , , , , , , , , , , , , ,

Looking for the Higgs Boson, the so-called ‘God Particle’, is Real Science unlike Man-Made Global Warming

Posted by PITHOCRATES - December 17th, 2011

Week in Review

Fascinating stuff.  Theoretical physics taking us back to God?  Perhaps (see The search for the God particle goes beyond mere physics by Michael Gerson posted 12/15/2011 on The Washington Post).

The God particle — really the Higgs boson — still resists confirmation, though scientists at the Large Hadron Collider recently reported “tantalizing hints” of its existence. They also reject the notion that their search has anything to do with God, which is only technically true.

Modern physics can explain just about everything, except why anything has mass. The Standard Model of physics, which emerged four decades ago, employs an elegant mathematical formula to account for most of the elemental forces in the universe. It correctly predicted the discovery of various leptons and quarks in the laboratory.

But the equation doesn’t explain gravity. So the Standard Model requires the existence of some other force that seized the massless particles produced by the Big Bang and sucked them into physicality. The detection of Higgs bosons would confirm this theory — which is why scientists are smashing protons into one another in a 17-mile round particle accelerator and picking through the subatomic wreckage.

The Standard Model of Physics emerged 4 decades ago.  That’s 40 years.  And still they’re testing it.  Trying to find something that should be there.  But may not.  The Higgs boson.  The so-called ‘God particle’.  Which would really tie everything together.  They haven’t found it yet.  But, the good scientists they are, these physicists are still trying.  After 40 years.  Using real scientific inquiry.  And always being skeptical.

This is tough science.  Science held to a much higher standard than man-made global warming ‘science’.  Where they simply skip the experimental.  And announce their theory as fact.  You have to admit it saves a lot of time.  And lets government get down to business.  Taxing and regulating industry based on scientifically unfounded man-made global warming to replenish empty state treasuries.

Interesting stuff.  Be sure to read full Washington post article.  And follow the link to the Standard Model of physics.  Just because it’s so fascinating.  And really makes you think of the bigger picture.  And the tinier one, too.

www.PITHOCRATES.com

Share

Tags: , , , , , , , , ,