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Energy is measured in Joules (J)A sense for size:Energy used to move a car 1 mile: 600 kJEnergy to lift a plate to cupboard: about 1 JEnergy needed to lift me to the next floor:about 1600 J
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WorkWork: force takingplace over distance.W = F * dWork is only donewhen an objectmoves against aforce.No move, no work.No force, no work.
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Example ProblemHow much work do you do when youpush a crate with a force of 150 N twometers?Work = Force * distance so...150 N * 2 m = 300 J
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More WorkThe force and thedisplacement in workmust be in the samedirection.If not we consider only thecomponent ofdisplacement aligned withthe force.No matter how it reaches2 meters from the floor,the 1 N box has the samework done on it due togravity.
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Potential EnergyEnergy in a stored state:Objects suspended above the surface ofearthstretched springschemical energy within gasoline
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Gravitational Potential EnergyPE = m*g*hm = massg = 10 m/s2h = distance abovesurfaceDouble m double PEDouble h double PE
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Example Potential Energy ProblemTwo cars, one twice as heavy as theother, are lifted to the same elevation in aservice station. How do their potentialenergies compare?Potential energies are directlyproportional to mass; so a car of twice themass would have twice the potentialenergy.
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Kinetic Energy• Energy of motion –– KE = ½*m*v2– So the more massive the moreenergy– but more dramatic, the morevelocity the MORE energy.Potential Energy and KineticEnergy freely interconvert:dropped objects, the releaseof a bow, etc.
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Example Kinetic Energy Problem• Which has more kinetic energy – a car traveling at 30km/hr or a car half the mass traveling at 60 km/hr?• A little more complicated: KE depends directly onmass so halving the mass would have the kineticenergy BUT it depends on the square of the velocityso twice the velocity would be 4 times the KE. Theresult is that the lighter car at 60 km/hr has twice thekinetic energy of the heavier, slower car.
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Conversion of Energy from one form toanother• At the top you have highpotential energy.• As you fall, the amountof potential energy falls,but kinetic energyincreases.• At the bottom all theenergy is converted tokinetic energy.
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So a pendulum is kinda interesting...• All potential energy at either end.• All kinetic at the lowest point.• Knowing how far the bob falls you can calculateexactly how quickly it will be going at the bottom.
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Work-Energy Theorem• When work is done on something it gainskinetic energy.• W = ΔKE• If an object’s energy changes we know workhas been done on it.
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Conservation of energy• In the absence of external work input or output,the energy of a system remains unchanged.Energy cannot be created or destroyed.
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Demo: Bowling Ball• Energy is conserved so:– Initial potential energy just enough to reach me– Kinetic energy at bottom of path will approximatelyequal that potential energy.– Since energy can only be lost (air resistance) itshouldn’t touch my face.
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Discovery of GravityPeople have long known thatmost thing fall to earth. Sowhat was the ‘discovery’?• The ancients believed thateverything had a naturalplace and sought to return toit.• Newton, however, was thefirst to think of falling objectsas being under the influenceof a force.
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Orbits of heavenly bodiesThe real breakthrough was in thinking of heavenlybodies (the moon, planets, etc.) as being under theinfluence of the same force as the apple.
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Review: Projectile Motion221gtd =• Imagine you throw theobject in a straight line(no gravity).• Due to gravity the objectwill be found below thisline – by exactly thesame distance as if ithad been dropped.
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The Moon “Falls” Around the Earth• Newton imagined the moonwould travel in a straight line– unless pulled downward byEarth.• Ultimately, he proved that,just as the projectile fallsunder its ideal path, so doesthe moon.• The force that makes anapple fall and the moon orbitare the same.
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Gravitational Force• The gravitational force isalways attractive.• Proportional to each massinvolved (doubling m1 OR m2doubles the force).• Inversely proportional tosquare of the distancebetween masses (double d,¼ force).221dm*m*GF =
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Inverse Square LawAs distance from source increases, the area of a shell around the sourceincreases as the square of distance.This results in the coverage (thickness) of the paint decreasing with the area.9 161/9 1/16
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Gravitational strength falls rapidly withdistance• Sun weights 333,000times more than earth.• Sun is 24,000 timesfurther away (than thecenter of the earth).• Acceleration due to thesun at earth’s surface:0.006 m/s2
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Example ProblemImagine an impossibleladder that extends intothe sky.• A girl, weighing 600 N,stands at the bottom. Shethen climbs to four timesthe earth’s radius.– What is her weight now?Distance goes from 1*earth radius to 4*earth radius (ladder adds 3x earth radius).Distance therefore increases 4 times.Distance squared will go up 16 times.Force depends on the inverse of distance squared so it will go down 16 times:600/16= 37.5 N
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Possible Test Problem• Consider a 1-N apple in atree.– If the tree were twice as tall,would the weight of the applebe ¼ as much?– Why or why not?– The problem is one of “whereis our reference point?” Similarto the problem withtemperature – We need tocount from the ‘right’ zero.The right zero is the center of the earth, some 6000 Km (6,000,000 meters)Increasing the height by 2 meters is negligible (6 million vs. 6 million and 2 meters).
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Weight• Weight only matchesgravitational force whenyou are not accelerating.• What you are actuallysensing is the normalforce supporting you.Nm*gm*am*g
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• When you fall you accelerate.• If your acceleration matchesgravitational acceleration (10m/s2) you will feel weightless.• This does not mean gravityis no longer acting on you.– If gravity were no longer acting onyou then you would notaccelerate.m*am*g
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Weight and Gravity not necessarilyequal:What do you feel inside anelevator?• Going up, as you accelerateyou feel heavy.• Going down, as youaccelerate, you feel light.• When you stop you feelnormal weight.• (If the elevator were to breakand you were to drop youwould feel brieflyweightless).
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Weightlessness• If you accelerate freelyyou have no weight.• Freefall, no matterwhere it occurs, resultsin ‘no weight’.• You may still beundergoing agravitationalacceleration, such as anastronaut in orbit.
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Connection: Newton’s 2ndLaw• Fnet = m*a• When standing on earth Fnet = 0N – m*g = 0• When falling Fnet = m*gm*g = m*g• When accelerating upward Fnet > 0N – m*g > 0 (so N > m*g)• When accelerating downward Fnet < 0N – m*g < 0 (so N < m*g)
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Artificial Gravity• When orbiting earth you feel weightless, this hasseveral consequences:– The body begins to lose muscle mass as it does not need toexert as much force to move.– Some organs lose capacity.• To combat this, several methods of producing gravityhave been proposed:– For long-distance travel, have the spacecraft accelerateslightly the whole trip.– For orbital stations, take advantage of rotation.• centripetal acceleration: a = v2/r
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Summing Up• Gravitational force:– double m1 or m2, double force• What if you double both?– double d, ¼ force.• Weightlessness:– Weight depends upon having a support force.• If everything falls together, as on the space shuttle, no support forceneeded.– When undergoing an acceleration the support force may belarger or smaller than gravitational force.221dm*m*GF =
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