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ENERGY

Work

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Work Formula

• Work = Force x Distance

W=Fd• Factor one: there must be a force

applied

• Factor two: there must be movement in the direction of the force

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Types of Work

• 1. The work done to overcome a force (lifting something to overcome the force of gravity…)

• 2. Changing something’s velocity (working against its inertia to speed up or slow down).

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Units• Work – joules (J)

–a joule is a N•m or

• 1 J is the amount of work done by 1 N of force for 1 m of distance.–For large work values we use kJ

(kilojoules, or 1000 joules).

2

mkg m

s

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Power• When we look at time we use power.

• The unit for Power is the Watt (W)• 1 watt is the power expended when 1 Joule of work

is done in 1 second of time– One kW (kilowatt) is 1000 watts. One MW (megawatt) is

one million watts

Work donePower=

time interval

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Problems - 1Adam, a very large man of mass 130 kg, stands on a pogo stick. How much work is done as Adam compresses the spring of the pogo stick 0.50 m?

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Problem - 2After finishing her physics homework, Kayla pulls her 50.0 kg body out of the living room and climbs up the 5.0-m-high flight of stairs to her bedroom. How much work does Kayla do in ascending the stairs?

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Problem - 3In the previous example, Kayla slowly ascends the stairs, taking 10.0

seconds to go from bottom to top. The next evening, in a rush to catch her favorite TV show, she runs up the stairs in 3.0 seconds.

a) On which night does Kayla do more work?b) On which night does Kayla generate more power?

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PRACTICEPROBLEMS

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Energy• Energy enables work to be done• Mechanical energy is energy that comes from the

position of something or the movement of something and it can be either potential energy or kinetic energy

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Potential Energy• Potential energy is energy due to position• Chemical potential energy is found in food, fossil fuels, and electric

batteries.• Positional potential energy can be found in a compressed spring, a

the string on a bow ready to shoot an arrow, etc.– PE in this case equals the force times the distance used to store the

energy (how hard you pulled on the string times how far back you pulled it.

• Gravitational potential energy comes from an objects distance from the surface of the earth.– Gravitational potential energy can be found by GPE = mgh (mass times

acceleration due to gravity times height)

– Gravitational potential energy only depends on height not on path

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Potential Energy Problems - 1Legend has it that Isaac Newton “discovered” gravity when an apple fell from a tree and hit him on the head. If a 0.20-kg apple fell 7.0 m before hitting Newton, what was its change in PE during the fall?

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Potential Energy Problems - 2

Legend has it that Galileo dropped objects off the Leaning Tower of Pisa to determine whether heavy or light objects fall faster. If Galileo had dropped a 5.0-kg cannon ball to the ground from a height of 12 m, what would have been the change in PE of the cannon.

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Kinetic Energy• Kinetic energy is energy of motion. • KE = ½ mv² where m is mass and v is velocity or speed• Kinetic energy is also equal to the amount of work done

to give the object the velocity that it has • So…net force x distance = kinetic energy, which can also

be written as: Fd = ½ mv²• Note that the speed of the object is squared; this means that if you

double the objects speed you are quadrupling the kinetic energy. Also an object moving twice as fast takes four times as much work to stop.

• The work energy theorem states that whenever work is done energy changes. This can be represented by the following formula: Work = E

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A greyhound at a race track can run at a speed of 16.0 m/s. What is the KE of a 20.0-kg as it crosses the finish line?

Kinetic Energy Problem - 1

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The 2000 Belmont Stakes winner, Commendable, ran the horse race at an average speed of 15.98 m/s. If Commendable and jockey Pat Dayhad a combined mass of 550.0 kg, what was their KE as they crossed the finish line?

Kinetic Energy Problem - 2

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PRACTICEPROBLEMS

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Conservation of Energy

• The law of conservation of energy states: Energy cannot be created or destroyed. It can be transformed from one form into another, but the total amount of energy never changes.– In order to see this we will need to look at

entire systems, not single objects!– One of the classic PHYSICS examples of this

is the pendulum.

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Pendulum

• In this image you can see that when the pendulum is all the way up, it has large PE, when it has fallen it has small PE, and then when it rises back up it has large PE again

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More Pendulum

• Here you can see that when the pendulum is up it has 10 J of PE and 0 KE and when it is down it has 0 J of PE and 10 J of KE

• Disregarding friction,energy changes between the two types but is not lost.

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Roller Coaster

• The rollercoaster is a more complicated example, however you can see that at the top there is 40,000 J of PE and 0 KE, and at the bottom there is 0 PE and 40,000 J KE.

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The Energy Ramp

• In the energy ramp we can demonstrate the fact that the path an object takes does not determine its energy.

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Machines• A machine is a device used to multiply forces or

simply change the direction of forces. Some common simple machines are the:– Lever– Pulley– Inclined plane– Wedge– Screw– Wheel & axle

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The Lever– The lever – we work on one end of the lever the other

end works on the load.– Neglecting friction, work input equals work output. So

(force x distance) input = (force x distance) output.

• Fulcrum is middle point of lever• Mechanical Advantage is ratio of input force to output force

or input distance traveled to output distance traveled.

• http://www.cosi.org/files/Flash/simpMach/sm1.swf

( ) ( )input outputF d F d

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The Pulley– The Pulley – a pulley is a type of machine that

can be used to change the direction of a force.

– The mechanical advantage of a simple pulley system is the same as the number of strands of rope that support the load. Note: Not all strands on a pulley are necessarily supporting!!!

http://www.cosi.org/files/Flash/simpMach/sm1.swf

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The Ramp• The mechanical advantage of a ramp can

be found either by the ratio of input force to output force or by the ratio of distance traveled along the ramp to height risen.