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Simple MachinesSimple Machines

Ancient people invented simple Ancient people invented simple machines that would help them overcome machines that would help them overcome resistive forces and allow them to do the resistive forces and allow them to do the desired work against those forces. desired work against those forces.

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Simple MachinesSimple Machines

The six simple machines are:The six simple machines are: Lever Lever Wheel and Axle Wheel and Axle Pulley Pulley Inclined Plane Inclined Plane Wedge Wedge Screw Screw

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Simple MachinesSimple Machines

A machine is a device that helps A machine is a device that helps make work easier to perform by make work easier to perform by accomplishing one or more of the accomplishing one or more of the following functions: following functions: transferring a force from one place to transferring a force from one place to

another, another, changing the direction of a force, changing the direction of a force, increasing the magnitude of a force, or increasing the magnitude of a force, or increasing the distance or speed of a increasing the distance or speed of a

force. force.

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Mechanical AdvantageMechanical Advantage

It is useful to think about a machine It is useful to think about a machine in terms of the in terms of the input forceinput force (the (the force you apply) and the force you apply) and the outputoutput forceforce (force which is applied to the (force which is applied to the task).task).

When a machine takes a small input When a machine takes a small input force and increases the magnitude of force and increases the magnitude of the output force, a the output force, a mechanical mechanical advantageadvantage has been produced. has been produced.

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Mechanical AdvantageMechanical Advantage Mechanical advantage is the ratio of output force Mechanical advantage is the ratio of output force

divided by input force. If the output force is divided by input force. If the output force is bigger than the input force, a machine has a bigger than the input force, a machine has a mechanical advantage greater than one.mechanical advantage greater than one.

If a machine increases an input force of 10 If a machine increases an input force of 10 pounds to an output force of 100 pounds, the pounds to an output force of 100 pounds, the machine has a mechanical advantage (MA) of 10. machine has a mechanical advantage (MA) of 10.

In machines that increase distance instead of In machines that increase distance instead of force, the MA is the ratio of the output distance force, the MA is the ratio of the output distance and input distance.and input distance.

MA = output/input MA = output/input

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No machine can increase No machine can increase bothboth the magnitude and the magnitude and the distance of a force at the distance of a force at the same time.the same time.

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The LeverThe Lever

A lever is a rigid bar A lever is a rigid bar that rotates around a that rotates around a fixed point called the fixed point called the fulcrum.fulcrum.

The bar may be either The bar may be either straight or curved.straight or curved.

In use, a lever has In use, a lever has both an effort (or both an effort (or applied) force and a applied) force and a load (resistant force). load (resistant force).

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The 3 Classes of LeversThe 3 Classes of Levers

The class of a lever The class of a lever is determined by is determined by the location of the the location of the effort force and the effort force and the load relative to the load relative to the fulcrum. fulcrum.

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To find the MA of a lever, divide the output force by the input force, or divide the length of the resistance arm by the length of the effort arm.

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First Class LeverFirst Class Lever

In a first-class lever the fulcrum is In a first-class lever the fulcrum is located at some point between the located at some point between the effort and resistance forces.effort and resistance forces. Common examples of first-class levers Common examples of first-class levers

include crowbars, scissors, pliers, tin include crowbars, scissors, pliers, tin snips and seesaws. snips and seesaws.

A first-class lever always changes the A first-class lever always changes the direction of force (I.e. a downward effort direction of force (I.e. a downward effort force on the lever results in an upward force on the lever results in an upward movement of the resistance force). movement of the resistance force).

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Fulcrum is between EF (effort) and RF (load)Fulcrum is between EF (effort) and RF (load)Effort moves farther than Resistance.Effort moves farther than Resistance. Multiplies EF and changes its direction Multiplies EF and changes its direction

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Second Class LeverSecond Class Lever

With a second-class lever, the load is With a second-class lever, the load is located between the fulcrum and the effort located between the fulcrum and the effort force.force.

Common examples of second-class levers Common examples of second-class levers include nut crackers, wheel barrows, include nut crackers, wheel barrows, doors, and bottle openers.doors, and bottle openers.

A second-class lever does not change the A second-class lever does not change the direction of force. When the fulcrum is direction of force. When the fulcrum is located closer to the load than to the effort located closer to the load than to the effort force, an increase in force (mechanical force, an increase in force (mechanical advantage) results. advantage) results.

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RF (load) is between fulcrum and EF RF (load) is between fulcrum and EF Effort moves farther than Resistance.Effort moves farther than Resistance.

Multiplies EF, but does not change its directionMultiplies EF, but does not change its direction

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Third Class LeverThird Class Lever

With a third-class lever, the effort With a third-class lever, the effort force is applied between the fulcrum force is applied between the fulcrum and the resistance force.and the resistance force. Examples of third-class levers include Examples of third-class levers include

tweezers, hammers, and shovels.tweezers, hammers, and shovels. A third-class lever does not change the A third-class lever does not change the

direction of force; third-class levers direction of force; third-class levers always produce a gain in speed and always produce a gain in speed and distance and a corresponding decrease distance and a corresponding decrease in force. in force.

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EF is between fulcrum and RF (load) EF is between fulcrum and RF (load) Does not multiply force Does not multiply force

Resistance moves farther than Effort.Resistance moves farther than Effort.

Multiplies the distance the effort force travelsMultiplies the distance the effort force travels

Law of leversLaw of levers

The law of levers states that te length of The law of levers states that te length of the effort arm times the weight/force of the the effort arm times the weight/force of the effort arm must equal the length of the effort arm must equal the length of the resistance arm times the weight/force of resistance arm times the weight/force of the resistance arm.the resistance arm. lleeFFee = l = lrrFFrr

• Or Or

lle/e/llr =r = F Frr/F/Fee

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Law of Levers CalculationsLaw of Levers Calculations

lleeFFee = l = lrrFFrr

You need to move a 2450 N rock and decide to use a spud bar to pry You need to move a 2450 N rock and decide to use a spud bar to pry it free. The total length of the spud bar is 2 m. You place a brick 0.15 it free. The total length of the spud bar is 2 m. You place a brick 0.15 m from the base of the rock to act as the fulcrum, how much effort m from the base of the rock to act as the fulcrum, how much effort must you apply to move the rock?must you apply to move the rock?

llee = 2 m- 0.15 m= 1.85 m = 2 m- 0.15 m= 1.85 m

llrr= 0.15 m= 0.15 m

FFee = ? = ?

FFrr = 2450 N = 2450 N

FFee = l = lrrFFr r /l/lee FFee = (0.15 m x2450 N)/1.85 N = (0.15 m x2450 N)/1.85 N

FFee = 198 N = 198 N

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MA: Lever CalculationsMA: Lever Calculations

AMA (actual mechanical advantage)=AMA (actual mechanical advantage)= AMA= resistance/effortAMA= resistance/effort AMA= FAMA= Frr/F/Fee

• What is the MA of the spud lever system with an What is the MA of the spud lever system with an effort force of 198 N and a resistance force of effort force of 198 N and a resistance force of 2450N?2450N?

2450N / 198N= 122450N / 198N= 12

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IMA Lever CalculationsIMA Lever Calculations

IMA= lIMA= lee/l/lrr

lle e = 1.85 m= 1.85 m

llr r = 0.15 m= 0.15 m

IMA= 1.85 m/0.15 mIMA= 1.85 m/0.15 m IMA= 12IMA= 12

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Wheel and AxleWheel and Axle The wheel and axle is The wheel and axle is

a simple machine a simple machine consisting of a large consisting of a large wheel rigidly secured wheel rigidly secured to a smaller wheel or to a smaller wheel or shaft, called an axle. shaft, called an axle.

When either the wheel When either the wheel or axle turns, the or axle turns, the other part also turns. other part also turns. One full revolution of One full revolution of either part causes one either part causes one full revolution of the full revolution of the other part. other part.

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PulleyPulley A pulley consists of a grooved wheel A pulley consists of a grooved wheel

that turns freely in a frame called a that turns freely in a frame called a block.block.

A pulley can be used to simply change A pulley can be used to simply change the direction of a force or to gain a the direction of a force or to gain a mechanical advantage, depending on mechanical advantage, depending on how the pulley is arranged. how the pulley is arranged.

A pulley is said to be a A pulley is said to be a fixed pulleyfixed pulley if it if it does not rise or fall with the load being does not rise or fall with the load being moved. A fixed pulley changes the moved. A fixed pulley changes the direction of a force; however, it does direction of a force; however, it does not create a mechanical advantage. not create a mechanical advantage.

A A moveable pulleymoveable pulley rises and falls with rises and falls with the load that is being moved. A single the load that is being moved. A single moveable pulley creates a mechanical moveable pulley creates a mechanical advantage; however, it does not advantage; however, it does not change the direction of a force. change the direction of a force.

The mechanical advantage of a The mechanical advantage of a moveable pulley is equal to the moveable pulley is equal to the number of ropes that support the number of ropes that support the moveable pulley. moveable pulley.

Mechanical Advantage of Mechanical Advantage of PulleysPulleys

IMA of a pulley system is equal IMA of a pulley system is equal to the number of ropes that is to the number of ropes that is supporting the weight/load. supporting the weight/load.

For a fixed pulley that is all of For a fixed pulley that is all of the ropes except for the one the ropes except for the one you are pulling down on (that you are pulling down on (that is you are pulling in the same is you are pulling in the same direction as the force of direction as the force of gravity).gravity).

For a movable pulley it is equal For a movable pulley it is equal to all ropesto all ropes

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Fixed Pulleys

Movable PulleyIMA=2

Pulleys Mechanical Advantage CalculationsPulleys Mechanical Advantage CalculationsIMA= wIMA= wrr/F/Fee

IMA= dIMA= dee/d/drr

You are lifting a cow with a weight of 1560 N who is stuck in the mud with a block and tackle pulley You are lifting a cow with a weight of 1560 N who is stuck in the mud with a block and tackle pulley system. This block and tackle has 3 fixed and 3 movable pulleys. What is the MA of the block system. This block and tackle has 3 fixed and 3 movable pulleys. What is the MA of the block and tackle?and tackle?

IMA= 6 there are 6 supporting ropesIMA= 6 there are 6 supporting ropes

What is the force required to lift the cow?What is the force required to lift the cow?

wwr r = 1560 N = 1560 N

FFe e = ?= ?

IMA=6IMA=6

FFe e = w= wrr/IMA/IMA

FFe e = 1560 N/6= 1560 N/6

FFe e = 260 N= 260 N

What is the amount of rope needed to lift the cow 1.3 m vertically?What is the amount of rope needed to lift the cow 1.3 m vertically?

IMA= dIMA= dee/d/drr

ddr r = 1.3 m = 1.3 m

IMA=6IMA=6

ddee = d = dr r (IMA) (IMA)

dd e e = 1.3 m(6) = 1.3 m(6)

ddee = 7.8 m = 7.8 m 2323

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Inclined PlaneInclined Plane

An inclined plane is An inclined plane is an even sloping an even sloping surface. The surface. The inclined plane inclined plane makes it easier to makes it easier to move a weight move a weight from a lower to from a lower to higher elevation.higher elevation.

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Inclined PlaneInclined Plane The mechanical The mechanical

advantage of an advantage of an inclined plane is equal inclined plane is equal to the length of the to the length of the slope divided by the slope divided by the height of the inclined height of the inclined plane. plane.

While the inclined While the inclined plane produces a plane produces a mechanical advantage, mechanical advantage, it does so by it does so by increasing the distance increasing the distance through which the through which the force must move. force must move.

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Although it takes less force for car A to get to the top of the ramp, Although it takes less force for car A to get to the top of the ramp, all the cars do the same amount of work.all the cars do the same amount of work.

A B C

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Inclined PlaneInclined Plane A wagon trail on a A wagon trail on a

steep hill will often steep hill will often traverse back and forth traverse back and forth to reduce the slope to reduce the slope experienced by a team experienced by a team pulling a heavily loaded pulling a heavily loaded wagon.wagon.

This same technique is This same technique is used today in modern used today in modern freeways which travel freeways which travel winding paths through winding paths through steep mountain passes. steep mountain passes.

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WedgeWedge The wedge is a The wedge is a

modification of the inclined modification of the inclined plane. Wedges are used as plane. Wedges are used as either separating or either separating or holding devices. holding devices.

A wedge can either be A wedge can either be composed of one or two composed of one or two inclined planes. A double inclined planes. A double wedge can be thought of wedge can be thought of as two inclined planes as two inclined planes joined together with their joined together with their sloping surfaces outward. sloping surfaces outward.

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ScrewScrew

The screw is also a The screw is also a modified version of modified version of the inclined plane. the inclined plane.

While this may be While this may be somewhat difficult somewhat difficult to visualize, it may to visualize, it may help to think of the help to think of the threads of the threads of the screw as a type of screw as a type of circular ramp (or circular ramp (or inclined plane). inclined plane).

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MA of an screw can be calculated by dividing the number of turns per inch.

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Practice QuestionsPractice Questions1. Explain who is doing more work and why: a bricklayer 1. Explain who is doing more work and why: a bricklayer carrying bricks and placing them on the wall of a building carrying bricks and placing them on the wall of a building being constructed, or a project supervisor observing and being constructed, or a project supervisor observing and recording the progress of the workers from an observation recording the progress of the workers from an observation booth. booth.

2. How much work is done in pushing an object 7.0 m across 2. How much work is done in pushing an object 7.0 m across a floor with a force of 50 N and then pushing it back to its a floor with a force of 50 N and then pushing it back to its original position? How much power is used if this work is original position? How much power is used if this work is done in 20 sec?done in 20 sec?

3. Using a single fixed pulley, how heavy a load could you 3. Using a single fixed pulley, how heavy a load could you liftlift??

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Practice QuestionsPractice Questions

4.4. Give an example of a machine in which friction is Give an example of a machine in which friction is both an advantage and a disadvantage.both an advantage and a disadvantage.

5. Why is it not possible to have a machine with 5. Why is it not possible to have a machine with 100% efficiency?100% efficiency?

6. What is effort force? What is work input? Explain 6. What is effort force? What is work input? Explain the relationship between effort force, effort the relationship between effort force, effort distance, and work input. distance, and work input.

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Practice QuestionsPractice Questions1. Explain who is doing more work and why: a bricklayer carrying 1. Explain who is doing more work and why: a bricklayer carrying bricks and placing them on the wall of a building being bricks and placing them on the wall of a building being constructed, or a project supervisor observing and recording the constructed, or a project supervisor observing and recording the progress of the workers from an observation booth. progress of the workers from an observation booth. Work is defined as a force applied to an object, moving that object a distance in the direction of the applied force. The bricklayer is doing more work.

2. How much work is done in pushing an object 7.0 m across a 2. How much work is done in pushing an object 7.0 m across a floor with a force of 50 N and then pushing it back to its original floor with a force of 50 N and then pushing it back to its original position? How much power is used if this work is done in 20 sec? position? How much power is used if this work is done in 20 sec? Work = 7 m X 50 N X 2 = 700 N-m or J; Power = 700 N-m/20 sec = 35 W

3. Using a single fixed pulley, how heavy a load could you lift?3. Using a single fixed pulley, how heavy a load could you lift?Since a fixed pulley has a mechanical advantage of one, it will only change the direction of the force applied to it. You would be able to lift a load equal to your own weight, minus the negative effects of friction.

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Practice QuestionsPractice Questions4. 4. Give an example of a machine in which friction is both an Give an example of a machine in which friction is both an

advantage and a disadvantage. advantage and a disadvantage. One answer might be the use of a car jack. Advantage of friction: It allows a car to be raised to a desired height without slipping. Disadvantage of friction: It reduces efficiency.

5. Why is it not possible to have a machine with 100% efficiency? 5. Why is it not possible to have a machine with 100% efficiency? Friction lowers the efficiency of a machine. Work output is always less than work input, so an actual machine cannot be 100% efficient.

6. What is effort force? What is work input? Explain the relationship 6. What is effort force? What is work input? Explain the relationship between effort force, effort distance, and work input. between effort force, effort distance, and work input. The effort force is the force applied to a machine. Work input is the work done on a machine. The work input of a machine is equal to the effort force times the distance over which the effort force is exerted.