Work, Power and Machines AMA and IMA

Work, Power and Machines AMA and IMA

I can understand work, input, output and simple machines.

Background on Simple Machines:

A machine is a device that does work. Most machines consist of a number of elements, such as gears and ball bearings, that work together in a complex way. Nonetheless, no matter how complex they are, all machines are based in some way on six types of simple machines.

Fill in the Blank

A machine is a device that does ________.

The 6 simple machines are:

the inclinded plane

the lever

the screw

the wedge

the wheel and axle

the pulley

Principles of Simple Machines:

*Machines simply transmit mechanical work from one part of a device to another part. 

*A machine produces force and controls the direction and the motion of force, but it cannot create energy.

*A machine's ability to do work is measured by two factors. These are (1) mechanical advantage and (2) efficiency.

Mechanical Advantage

A measure of the ratio of output force to input force in a system, used to analyze the forces in simple machines like levers and pulleys. Despite changing the forces that are applied the conservation of energy is still true and the output energy is still equal to the input energy. Typically the mechanical advantage is expressed in ideal terms, where there is no losses in energy between the input and output times, also known as 100% efficient systems. No machine can never do more mechanical work than the mechanical work put into it.

Multiple Choice

Machanical Advantage is the ratio of ________ to _______ in machines.

• starting time to ending time

• height to length

• input force to output force

• potential force to kinetic force

Efficiency

*The efficiency of a machine is the ratio between the work it supplies and the work put into it.

*The efficiency of a machine is the ratio between the work it supplies and the work put into it.

*A lever has a high efficiency due to the fact that it has low internal resistance. The work it puts out is almost equal to the work it receives, because energy used up by friction is quite small. 

*On the other hand, an a pulley might be relatively inefficient due to a considerably greater amount of internal friction.

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No simple machine can be 100% efficient because of ______________.

Inclined Plane

 The inclined plane is a simple device that hardly looks like a machine at all. The mechanical advantage increases as the slope of the incline decreases. But the load will then have to be moved a greater distance.

Inclined Plane

The ideal mechanical advantage (IMA) of an inclined plane is the length of the incline divided by the vertical rise, the so-called run-to-rise ratio. The mechanical advantage increases as the slope of the incline decreases, but then the load will have to be moved a greater distance. L = Length of the incline and h = distance of resistance.

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What is the IMA of this ramp? Remember: IMA = Distance effort (L) / Distance resistance (h)

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What is the IMA of this ramp? Remember: IMA = distance effort (L) / Distance resistance (h)

AMA of an Inclined Plane

Actual Mechanical Advantage AMA

• Actual machines have friction.
• They do not have as high of a mechanical advantage as ideal machines because some of the effort is lost in overcoming friction.
• AMA = actual measured resistance force actual measured effort force 

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Calculate the AMA of the ramp below. Remember: AMA = Force resistance/Force effort

Efficiency

Efficiency. The efficiency of a machine is the ratio between the work it supplies and the work put into it. 

Efficiency = AMA/IMA x 100

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Determine the efficiency based on the following diagram.

MA of Levers

A lever is a bar resting on a pivot. Force (effort) applied at one point is transmitted across the pivot (fulcrum) to another point which moves an object (load).

IMA of Levers

The ideal mechanical advantage (IMA) - ignoring internal friction - of a lever depends on the ratio of the length of the lever arm where the force is applied divided by the length of the lever are that lifts the load. The IMA of a lever can be less than or greater than 1 depending on the class of the lever. There are three classes of levers, depending on the relative positions of the effort is applied, load, and fulcrum.

Calculating the IMA of a lever

*Determine the effort distance from the fulcrum

*Determine the resistance distance from the fulcrum

*Divide the Effort distance by the Resistance distance\

*IMA = dE/dR

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Determine the IMA for the following lever.

Remember IMA= dE/dR.

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Determine the IMA for the following lever.

Remember: IMA = dE / dR

AMA of levers

The differences between the three types of levers, is the location of the fulcrum to the input force and output force. Regardless of the type of lever, they all use the same equations to find AMA and IMA. The general formula for the actual mechanical advantage (AMA) of levers: AMAlever = Fo(output force) Fi (input force)  also written as AMA = resistant force (weight of object) / effort force

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Find the AMA of the following lever.

Remember: Resistance force (weight of the object) / effort force

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Find the AMA of the following lever:

Remember: AMA= resistance force (weight of the object) / effort force

Finding the efficiency of a lever

Efficiency = AMA/IMA x 100

Efficiency of Levers

Find the AMA = Fo / Fi = 45N/57.7N= 0.78

Find the IMA = dE / dR = 5.8m/6.3m= 0.92

Efficiency = AMA/IMA x 100 = .078/0.92 x 100 =

Multiple Choice

Find the AMA = Fo / Fi = 45N/57.7N= 0.78

Find the IMA = dE / dR = 5.8m/6.3m= 0.92

Efficiency = AMA/IMA x 100 = .078/0.92 x 100 =

• 80%

• 84.8%

• 92%

• 78.3%

Mechanical Advantage of Pulleys

In a pulley, the ideal mechanical advantage is equal to the number of rope segments pulling up on the object. The more rope segments that are helping to do the lifting work, the less force that is needed for the job.

Mechanical Advantage of Pulleys

In a pulley, to find the amount of force each rope holds, divide the total force by the total number of support ropes.

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Determine the IMA of the following pulley.

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Determine the IMA of the following pulley.

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Determine the IMA of the following pulley.

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Determine the IMA of the following pulleys.

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Determine the amount of force on each rope. Remember the last rope over the top is not a supporting rope.

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Determine the amount of force on each rope. Remember the last rope over the top is not a supporting rope.

Wheel and Axle

Radius = 1/2 the length of the inside of the circle

Diameter = the whole length of the inside of the circle.

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What is the IMA of the wheel and axle? The Radius of the axle is 1.5. The radius of the wheel will be 1/2 of the diameter given.

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What is the IMA of the wheel and axle.

More Simple Machines tomorrow!