velocitychanges.• Aerodynamics – The way the shape of an
objectaffectstheflowofairover,underoraroundit.
• Electrical energy – Energy derived fromelectricity.
• Frame of reference – The coordinatesystemforspecifyingthepreciselocationofan object, or the point or frame to whichmotioniscompared.
• Horsepower – A unit for measuring thepowerofenginesandmotorsbasedontheaverage rate at which a horse can do acertainamountofwork;1hp(horsepower)isequalto746wattsofpower.
• Joule – The unit of measurement forenergy; 1 joule = 1 kilogram •meter2/second2.
• Kinetic energy – Energy ofmotion; kineticenergy=½massxvelocity2,or𝐾𝐸 = !
!𝑚𝑣!
• Momentum – The combined mass andvelocityof anobject.Momentum=mass xvelocity,or𝜌 = 𝑚𝑣.
• Potential energy – Energy due to position;storedenergy,ortheabilitytodowork.
• Power – Rate of doing work, or workdividedbythetime.
• Relative motion – The comparison of themovement of one object with themovementofanotherobject.
• Work – The force on an object times thedistancethroughwhichtheobjectmovesasthe work is converted to either potentialenergy or kinetic energy; work = force xdistance,or𝑊 = 𝐹𝑑.
WorkandKineticEnergyIn previous lessons we have learned that inorder to move an object such as a race car,something or someone must apply a forcethrough a distance, so that work isaccomplished. The energy an object possessesby virtue of being in motion is called kineticenergy.Ingokartracingthisenergycomesfromthe work done by the electric motor andtransformed into energy of motion, or kineticenergy.
TransformingEnergyRemember that energy cannot be created ordestroyed. Energy can only be changed fromonetypeintoanother.Ifapersondoesworkbyprovidingaforceonacar,suchasapush,thentheenergyofwork comes from the calories inthefoodthepersonhaseaten. Inthiscasethefood energy is transformed into work energyand then into kinetic energy, or energy ofmotion as the person pushes the car, and thecargainskineticenergyasitmoves.Thekineticenergyofthecarwillthenbetransformedintoheat energy, or thermal energy, in the frictionofthebrakesorthetiresagainsttheroad.
Thesameistrueforgokartracing.Theenergystored in the battery pack is transformed intowork energy and then into kinetic energy, orenergy of motion as electric current passesthrough themotor causing themotor shaft tospin. Themotor shaft is connected to the rearaxle by a chain and sprockets. The rotation ofthe axle “pushes” the go kart, and the go kartgains kinetic energy as it moves. The kineticenergyof thegokartwill thenbe transformedinto heat energy, or thermal energy, in thefriction of the brakes or the tires against thetrack.
PerformingWorkOne way of doing work to provide kineticenergyisbysimplypushinganobjectsuchasacar.InbothNASCARandIndy-styleraces,whenthe cars are in the pit or the shop area, forsafetyreasonstheyneedtobepushedbyhandsince these areas are crowded both withspectatorsandwithpeopleworkingonthecars.
Howmuchworkdoesittaketopusharacecarthrough the shop area? Look at the image ofthepitcrewpushingaracecarofftheTrackatIndianapolisMotorSpeedway,inthe1920’s.Ifaforce of 2,000 Newtons is provided for adistanceof20meters,howmuchworkisdone?
𝑊 = 𝐹×𝑑 = 2,000𝑁×20𝑚 = 40,000𝐽
This work will be transferred to the kineticenergy of motion, KE = ½ mv2. In theory, thekinetic energy will be a measure of the workdone. Thus, 40,000 joules of work = 40,000joulesofkineticenergy.
Whenthekineticenergyisknown,thisformulacanberearrangedtodetermine thevelocityatwhich the pit crew push the race car. Let’sassumethatthemassofthecaris3,400pounds=1,545kilograms.
40,000𝐽 𝑤𝑜𝑟𝑘 = 40,000𝑘𝑔∙𝑚! 𝑠! 𝑘𝑖𝑛𝑒𝑡𝑖𝑐 𝑒𝑛𝑒𝑟𝑔𝑦
𝐾𝐸 =12𝑚𝑣!
𝑣 =𝐾𝐸12𝑚
=40,000𝑘𝑔 ∙𝑚! 𝑠!
12×1,545𝑘𝑔
= 7.2𝑚 𝑠
Even though in theory thework could provideas much kinetic energy as 40,000 joules, inrealitymuchoftheenergyfrompushingwillbelostduetofriction.Therealnumbersforkineticenergyandvelocitywillbealotlower.
4. What is themass of an object traveling at30m/sifithas33,750jofenergy?
ConvertingEnergiesGo karts that are actually racing go throughseveralenergychangesandaresubjecttomanydifferent forces. Their energy begins aschemical energy in the battery pack. Thebatterypackconverts thechemicalenergy intoelectricalenergy thatpasses to themotor.Themotor converts the electrical energy into themechanicalenergyofthemotorshaftrotating.
The mechanical energy of the motor shaftrotation is converted to mechanical energy ofthe axle rotating and then the mechanicalenergyistransferredtothewheels,whichmovethegokart,givingitkineticenergy.
Successful go kart engineering beginswith thebatteryandmotor.Themoreefficientlyenergycanbeconvertedfromchemicaltoelectricaltomechanicaltokinetic,thefasterthegokartcanmove.
AnalyzingWorkandEnergyAs a go kart comes out of a corner, the driveraccelerates rapidly over a short distance, withthegokart’smotorproviding the force.As themotor force pushes the go kart through thedistance,thegokartgainskineticenergy.
If a go kart comes out of the corner andincreasesitsspeedfrom15mphto45mphovera distanceof 150meters, howmuchworkwillbedoneby themotorandwhatwillbe thegokart’sgain inkineticenergy?Thegokarthasaweight (or mass) of 400 pounds, and 400pounds x 1 kilogram/2.2 pounds = 182kilograms.Notethatinordertocalculatekineticenergy,massmustbeinkilogramsandvelocitymustbeinmeters/second.
For the go kart exiting the corner at 15 mph,first calculate its initial kinetic energy then itsfinalkineticenergy,and then itsgain inkineticenergy. Note that 1 mile/hour = 0.447meters/second,orm/s.
TheoreticalSituationsvs.RealSituationsIn a real situation, there is a great amount offriction, so the actual numbers would besubstantially different from the results oftheoreticalcalculations.However, forageneralunderstanding, we can ignore the friction andstillgainanunderstandingof theconceptsandnecessarycalculations.
its speed from 35 mph to 15 mph over adistanceof10meters,howmuchworkwillbedonebythebreaksandwhatwillbethegokart’slossinkineticenergy?
6. Ifthegokartthencomesoutofthecornerand increases its speed from15mphto25mph over a distance of 15 meters, howmuchworkwill bedoneby themotor andwhat will be the go kart’s gain in kineticenergy?
7. Ifthegokartweretogointothecornerbydecreasing its speed from 35 mph to 20mphoveradistanceof10metersandthenexitthecornerandincreaseitsspeedto25over a distance of 15 meters, how muchworkwillbedonebythebreaksandmotorcomparetoquestions5and6?Howwouldthe change in kinetic energy compare toquestions5and6?
HorsepowerandWattsWork is defined as a force applied through adistance. Power, on theother hand, is definedasworkpertimeorenergypertimeandcanbecalculatedusingtheformula
𝑃 =𝑊𝑡
Another way to think of power is how rapidlyworkiscompleted.Powerismeasuredinwatts.Onewattisequalto1joule/second.
Inautomobilesingeneral,andingokartracing,the amount of work a motor can exert ismeasured in horsepower (hp). The concept ofhorsepower was developed by James Watt(1736-1819). Watt was looking for a way tomeasure power, so he devised a method ofhaving a horse lift a weight (of 33,000 lbs)through a height (1 ft) in a period of time (1min). He called the rate of 33,000 foot-pounds/minute1horsepower.Onehorsepoweris equivalent to 746 watts, or 746 joules/second.
racing. This is the principle behind the energyefficiency scoring during the AcademicChallenge portion of evGrand Prix WorldChampionships. The energy consumed by thego kart is compared between the competitorsand the team with the best energy efficiencyranked#1.Herepower isequal to theamountofenergyusedpergivenamountoftime(race).Thisiscalculatedbytheequation
𝑃 =∆𝐸𝑡
PracticeProblems8. A motor does 5,000 joules of work in 20
seconds.Whatisthepowerofthemotor?
9. Agokart ispushed to tech inspectionat aspeed of 4.5 m/s by a crew memberexerting an 1,800 N force. What is thepowerofthiscrewmember?
10. Agokartuses200wattsofpowermovesuptothestartline,adistanceof15meters,in15seconds.Find the forceneededand theworkdonebythismachine.
11. Agokartusesaforceof200Ntodo20,000joules of work in 20 seconds. Find thedistance thegokartmovedand thepoweroftherequiredbythegokart.(Hint:AjouleisthesameasaNewton-meter.)
