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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River Traffic, Road Traffic, Ferry Crossings, Vertical Lift Bridges and Bascule Bridges

Posted by PITHOCRATES - August 7th, 2013

Technology 101

(Originally published March 6th, 2013)

Bridges that rise High Enough for Shipping Traffic to Pass Underneath need Long Approaches

As civilizations expanded they followed rivers inland.  People traveled on the river and founded new cites on sites further upstream.  Which they could supply from cities downstream.  Including the materials to build a waterwheel and lumber mill.  They can go upstream to fell trees and float them downriver to the lumber mill.  They can use this lumber to expand the city.  Out away from the river.  On a growing network of roads.  On both sides the river.

As this city grows cross-river traffic increases.  A road on both sides of the river end at a dock.  Between these docks runs a ferry.  That can transport people, horses, carts, wagons, etc.  Allowing people and goods to travel anywhere within this city on the river.  Over time cross-river traffic increases causing backups at the ferry crossing.  Eventually cars replace horses.  Concrete replaces dirt roads.  And vehicular traffic increases.  While railroads connect our cities.  All of which has to cross the river.  While at the same time allowing boats to continue to navigate the river.

If you ever driven on a bridge over a navigable river with shipping traffic you probably noticed a couple of things.  First of all, when you crossed the navigable portion of the waterway you were pretty high in the air.  Second, there was a long approach to that portion of the bridge that allowed you to reach that height over a gradual incline.  And you started that incline about a mile or so away from the river.  Which is fine for an interstate that can rise above a city until it reaches a sufficient height to cross the river without impeding river traffic.  But it’s a bit of a problem for the roads at the river’s edge.  For it is just not practical to drive a mile or so away from the river, cross over on the bridge, and then drive a mile or so back to the river.  Not to mention the incredible cost of such a bridge that would provide only one river crossing.  It would be far more practical and less costly to build multiple bridge crossings at the current elevation of the roads at the river’s edge.  But that would, of course, block river traffic to most commercial shipping.

The Vertical Lift Bridge can lift Heavier Road Sections than Bascule Bridges with the same Size Counterweights

The solution is the moveable bridge.  A bridge at the elevation of the local roads so a car can cross from one shore to the other in the shortest possible distance.  And one that can move to create an opening in the roadway to allow a ship to navigate the river at the bridge crossing.  Because vehicular traffic is greater than river traffic vehicular bridges are normally in a position to allow vehicular traffic to cross.  In places where river traffic is greater than rail traffic rail bridges are normally in a position to allow river traffic to pass.  Which can be a problem for trains that ignore a red signal to stop.  For a train can drive right off the tracks and into a river.  And have.

Two of the most common moveable bridges are the vertical lift bridge.  And the bascule bridge.  Each has benefits.  Each has its faults.  The vertical lift bridge raises a portion of the roadway over the shipping channel.  At each end of the lifting section is a tower.  Inside these towers are counterweights.  The counterweights equal the weight of the section of the moveable roadway.  Because the roadway and the weights are balanced it doesn’t take much force to raise or lower the bridge.  Like an elevator in a building.

Older bridges had a bridge operator that rode up and down with the bridge.  As a ship approached traffic signals would stop traffic.  Once all traffic was off the bridge gates came down blocking further traffic from entering.  Once all vehicles and pedestrians were off the lift portion a signal sounded to warn people the bridge would begin to move.  Then it moved.  The section of roadway traveled up between the two towers.  Creating a safe passage for the ship below.  Most bridges today are automated and unmanned.  The big advantage of the lift bridge is the size of the counterweights.  They only have to equal the weight of the span. Allowing heavier road sections to be lifted.  Making them good for rail bridges.

The ‘Chicago’ Bascule Bridge is the most common Moveable Bridge in the World

The drawback to the vertical lift bridge is that there is still a maximum height of ship that can pass underneath.  Which isn’t a problem for most shipping.  But it can be an issue for some oversized loads or ships with tall masts.  Also, those tall towers can be unsightly.  Consider a city like Chicago.  Which has a lot of tall buildings right on the banks of the Chicago River.  Where a lot of bridge towers at all of those river crossings could really ugly up the Chicago skyline.  So in Chicago you won’t see vertical lift bridges spanning the Chicago River.  Instead you’ll see bascule bridges.

The typical bascule bridge you see in Chicago is a double-leaf bascule bridge.  Bascule is French for seesaw.  Think of a playground seesaw.  When one side goes up the other side goes down.  Each leaf of a bascule bridge is a seesaw.  A teeter-totter.  One side of the seesaw is a metal roadbed.  The other side is a counterweight.  When the bridge opens the counterweight teeters down below the road elevation while the other end teeters up above the road elevation.  Creating an opening over the river for ships to pass through.  To span a river two seesaws are connected together with their metal roadbeds pointing towards each other.  And their counterweights pointing away from the river.  Because the leaf is longer than the counterweight the counterweight has to be heavier than the bridge leaf.  To equal the torque between the leaf and the counterweight.  So it takes the same turning force to raise and lower the bridge leaf.  Keeping both sides of the seesaw balanced so it takes little power to operate a bascule bridge.  Just as it takes little power to raise and lower a vertical lift bridge.

The greater weight of the counterweights makes the bascule bridge more costly than the vertical lift bridge.  But in return for the added cost you get a cleaner bridge installation with no unsightly towers.  And when the bridge is opened there is no limit to how tall a ship can pass through the bridge crossing.  Because there is an open gap in the roadway.  Which creates one additional challenge for the bascule bridge over the vertical lift bridge.  When a lift bridge rises cables can rise with it like in an elevator.  Keeping both ends and the moveable roadway connected to each other electrically.  Both power and communication.  This is not possible in the bascule bridge.  With nothing going over the river crossing when the bridge is open there is only one option for electrically connecting the two ends of the bridge.  If cables can’t go over a ship they must go underneath a ship.  With a bascule bridge submarine power and communication cables interconnect the two bridge ends.  Requiring a diving crew to lay this cable.  Making both the bridge cost and maintenance more costly on a bascule bridge than a vertical lift bridge.  But in return you get a less unsightly installation.  And a shorter time to open and close the bridge.  Making the ‘Chicago’ bascule bridge the most common moveable bridge in the world.

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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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River Traffic, Road Traffic, Ferry Crossings, Vertical Lift Bridges and Bascule Bridges

Posted by PITHOCRATES - March 6th, 2013

Technology 101

Bridges that rise High Enough for Shipping Traffic to Pass Underneath need Long Approaches

As civilizations expanded they followed rivers inland.  People traveled on the river and founded new cites on sites further upstream.  Which they could supply from cities downstream.  Including the materials to build a waterwheel and lumber mill.  They can go upstream to fell trees and float them downriver to the lumber mill.  They can use this lumber to expand the city.  Out away from the river.  On a growing network of roads.  On both sides the river.

As this city grows cross-river traffic increases.  A road on both sides of the river end at a dock.  Between these docks runs a ferry.  That can transport people, horses, carts, wagons, etc.  Allowing people and goods to travel anywhere within this city on the river.  Over time cross-river traffic increases causing backups at the ferry crossing.  Eventually cars replace horses.  Concrete replaces dirt roads.  And vehicular traffic increases.  While railroads connect our cities.  All of which has to cross the river.  While at the same time allowing boats to continue to navigate the river.

If you ever driven on a bridge over a navigable river with shipping traffic you probably noticed a couple of things.  First of all, when you crossed the navigable portion of the waterway you were pretty high in the air.  Second, there was a long approach to that portion of the bridge that allowed you to reach that height over a gradual incline.  And you started that incline about a mile or so away from the river.  Which is fine for an interstate that can rise above a city until it reaches a sufficient height to cross the river without impeding river traffic.  But it’s a bit of a problem for the roads at the river’s edge.  For it is just not practical to drive a mile or so away from the river, cross over on the bridge, and then drive a mile or so back to the river.  Not to mention the incredible cost of such a bridge that would provide only one river crossing.  It would be far more practical and less costly to build multiple bridge crossings at the current elevation of the roads at the river’s edge.  But that would, of course, block river traffic to most commercial shipping.

The Vertical Lift Bridge can lift Heavier Road Sections than Bascule Bridges with the same Size Counterweights

The solution is the moveable bridge.  A bridge at the elevation of the local roads so a car can cross from one shore to the other in the shortest possible distance.  And one that can move to create an opening in the roadway to allow a ship to navigate the river at the bridge crossing.  Because vehicular traffic is greater than river traffic vehicular bridges are normally in a position to allow vehicular traffic to cross.  In places where river traffic is greater than rail traffic rail bridges are normally in a position to allow river traffic to pass.  Which can be a problem for trains that ignore a red signal to stop.  For a train can drive right off the tracks and into a river.  And have.

Two of the most common moveable bridges are the vertical lift bridge.  And the bascule bridge.  Each has benefits.  Each has its faults.  The vertical lift bridge raises a portion of the roadway over the shipping channel.  At each end of the lifting section is a tower.  Inside these towers are counterweights.  The counterweights equal the weight of the section of the moveable roadway.  Because the roadway and the weights are balanced it doesn’t take much force to raise or lower the bridge.  Like an elevator in a building.

Older bridges had a bridge operator that rode up and down with the bridge.  As a ship approached traffic signals would stop traffic.  Once all traffic was off the bridge gates came down blocking further traffic from entering.  Once all vehicles and pedestrians were off the lift portion a signal sounded to warn people the bridge would begin to move.  Then it moved.  The section of roadway traveled up between the two towers.  Creating a safe passage for the ship below.  Most bridges today are automated and unmanned.  The big advantage of the lift bridge is the size of the counterweights.  They only have to equal the weight of the span. Allowing heavier road sections to be lifted.  Making them good for rail bridges.

The ‘Chicago’ Bascule Bridge is the most common Moveable Bridge in the World

The drawback to the vertical lift bridge is that there is still a maximum height of ship that can pass underneath.  Which isn’t a problem for most shipping.  But it can be an issue for some oversized loads or ships with tall masts.  Also, those tall towers can be unsightly.  Consider a city like Chicago.  Which has a lot of tall buildings right on the banks of the Chicago River.  Where a lot of bridge towers at all of those river crossings could really ugly up the Chicago skyline.  So in Chicago you won’t see vertical lift bridges spanning the Chicago River.  Instead you’ll see bascule bridges.

The typical bascule bridge you see in Chicago is a double-leaf bascule bridge.  Bascule is French for seesaw.  Think of a playground seesaw.  When one side goes up the other side goes down.  Each leaf of a bascule bridge is a seesaw.  A teeter-totter.  One side of the seesaw is a metal roadbed.  The other side is a counterweight.  When the bridge opens the counterweight teeters down below the road elevation while the other end teeters up above the road elevation.  Creating an opening over the river for ships to pass through.  To span a river two seesaws are connected together with their metal roadbeds pointing towards each other.  And their counterweights pointing away from the river.  Because the leaf is longer than the counterweight the counterweight has to be heavier than the bridge leaf.  To equal the torque between the leaf and the counterweight.  So it takes the same turning force to raise and lower the bridge leaf.  Keeping both sides of the seesaw balanced so it takes little power to operate a bascule bridge.  Just as it takes little power to raise and lower a vertical lift bridge.

The greater weight of the counterweights makes the bascule bridge more costly than the vertical lift bridge.  But in return for the added cost you get a cleaner bridge installation with no unsightly towers.  And when the bridge is opened there is no limit to how tall a ship can pass through the bridge crossing.  Because there is an open gap in the roadway.  Which creates one additional challenge for the bascule bridge over the vertical lift bridge.  When a lift bridge rises cables can rise with it like in an elevator.  Keeping both ends and the moveable roadway connected to each other electrically.  Both power and communication.  This is not possible in the bascule bridge.  With nothing going over the river crossing when the bridge is open there is only one option for electrically connecting the two ends of the bridge.  If cables can’t go over a ship they must go underneath a ship.  With a bascule bridge submarine power and communication cables interconnect the two bridge ends.  Requiring a diving crew to lay this cable.  Making both the bridge cost and maintenance more costly on a bascule bridge than a vertical lift bridge.  But in return you get a less unsightly installation.  And a shorter time to open and close the bridge.  Making the ‘Chicago’ bascule bridge the most common moveable bridge in the world.

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