Energy and the Environment Lecture 5 PHYS/ENVS 3070 Professor Dmitri Uzdensky Sept. 5, 2014 PHYS/ENVS 3070 1Announcements: • Read Chapter 1 of E&E textbook • CAPA Homework #1 due today at 11 PM • Pick up your paper copy of CAPA Homework #2, due next Friday. Sept. 5, 2014 PHYS/ENVS 3070 2!How!much!money!is!spent!in!the!USA!on!gas!for!cars!each!year?!!!This!is!relevant!for!gas!standards,!gas!tax,!…!!How!can!we!es?mate!this!without!detailed!informa?on?!!Perhaps!start!with!how!many!people!in!the!USA?!!!Es?mate!~!300!Million!(could!check!from!US!Census)!!How!many!cars!per!person?!!!Es?mate!~!1!car!/!person!!So!we!have!~!300!million!cars!in!the!USA.!!!Sept.!5,!2014! PHYS/ENVS!3070! 3!With!300!million!cars,!how!much!gas!do!they!use?!!What!is!the!mileage!driven!per!car!per!year?!!Es?mate!~!15,000!miles!per!year!!!!What!is!the!miles!per!gallon!(MPG)!on!the!average!car?!!Es?mate!~!20!MPG!( )Cars # Gallons =⎟⎠⎞⎜⎝⎛×CarDriven Miles⎟⎠⎞⎜⎝⎛×Driven Mile Gas of Gallons cars) 10 (3 Gallons8×=( )mil es/car105.14××⎟⎠⎞⎜⎝⎛×MPG 201 10 10 10 Gallons-148=××≈Gasoline of Gallons 10 11=100!billion!gallons!of!gasoline!each!year!!!Sept.!5,!2014! PHYS/ENVS!3070! 4!Es?mate!~!Roughly!$4.00!per!gallon!The!ques?on!was:!How!much!money!is!spent!in!the!USA!on!gas!for!cars!each!year?!So!for!these!1011!gallons!of!gas,!we!only!need!to!know!the!average!price!people!paid!per!gallon!of!gas.!One!can!look!up!the!real!numbers!at:!!US!Energy!Informa?on!Administra?on!!h^p://www.eia.gov/tools/faqs/faq.cfm?id=23&t=10!They!es?mate!US!uses!138.!6!billion!gallons!of!gas!per!year!for!2010!So#roughly#400#billion#dollars#are#spent#on#gasoline#per#year!#Sept.!5,!2014! PHYS/ENVS!3070! 5!People!use!an!enormous!amount!of!energy!each!year!~!400!QBtu!!People!in!the!USA!use!about!¼!of!the!total!~!100!QBtu!But!what!exactly!(in!physics!terms)!is!energy?!And!how!do!we!know!what!a!small!amount!versus!an!enormous!amount!of!energy!is?!Sept.!5,!2014! PHYS/ENVS!3070! 6!Sept.!5,!2014! PHYS/ENVS!3070! 7!WORK#AND#ENERGY#What#is#Energy?#All!kinds!of!things!come!to!mind…!Things!in!mo?on,!collisions,!electricity,!stored!energy!Sept.!5,!2014! PHYS/ENVS!3070! 8!• To!understand!energy,!its!interfconversion!to!different!forms,!and!its!conserva?on,!we!must!first!define!some!terms:!• Work; !!• Kine?c!Energy!(KE );!!!!• WorkfEnergy!Princip l e; !!!!• Poten?al!Energy!(PE)!What#is#Energy?#Sept.!5,!2014! PHYS/ENVS!3070! 9!ENERGY#AND#WORK#Defini?on:!!!!Energy#is#the#ability#to#do#Work#How!much!energy!you!have!tells!you!how!much!work!you!can!do.!Whenever!work!is!being!done,!energy!is!being!changed!from!one!form!to!another!or!being!transferred!from!one!body!to!another.!!The!amount!of!work!done!on!a!system!(or!by!a!system)!equals!the!change!in!energy!of!the!system.!!Sept.!5,!2014! PHYS/ENVS!3070! 10!Work#=#Force#x#Distance#dFW!!⋅=This!is!the!defini?on!in!terms!of!forces!as!specified!by!Isaac!Newton!(i.e.!Force!=!mass!x!accelera?on![F=ma]).!So!what!is!work?!Consider!a!moving!object!acted!upon!by!a!force!F%While!the!force!is!applied,!if!the!object!moves!a!distance!d!in!the!direc?on!of!the!force!vector,!then!the!work!done!is:!Force!|Δx|!=!d!ntDisplaceme Force W Work ×==Work!must!have!units!of!Newtons!x!meters!=!(kg!m/s2)!x!m!=!kg!m2/s2!We!also!call!this!Joules!–!the!SI!unit!for!work!and!also!energy!!WORK#Sept.!5,!2014! PHYS/ENVS!3070! 11!Clicker#QuesIon#Room!Frequency!DC!Atlas!holds!up!the!en?re!celes?al!sphere!for!20!centuries.!What!can!you!say!about!the!work!!done!by!Atlas?!A) !An!enormous!amount!of!work!!!!!!(many,!many!Joules)!B)!!20!Joules!C)!!None!There!is!no!displacement!of!the!celes?al!sphere.!!Thus,!despite!the!very!large!force!(Mg)!needed!to!hold!up!the!earth,!no!work!is!done.!Sept.!5,!2014! PHYS/ENVS!3070! 12!If!you!hold!a!weight!fixed,!there!is!no!change!in!posi?on!(d=0)!and!so!zero!work!is!done.!!The!same!if!you!push!against!a!wall.!!Counterintui?ve,!it!is!not!the!“English!language!usage”,!but!It!is!well!defined!in!physics!terms!and!very!useful.!!!istancedorceFWork!!⋅=Sept.!5,!2014! PHYS/ENVS!3070! 13!WORK#Force!|Δx|!=d!What!if!the!force!vector!is!at!some!angle!with!respect!to!the!displacement!vector?!Work = W = Fx ⋅ d = F cos(θ) d = F||dComponent!of!force!along!the!displacement!Sept.!5,!2014! PHYS/ENVS!3070! 14!Displacement!Note:!Work!is!a!scalar!(not!a!vector),!but!it!does!have!a!sign.!When!the!component!of!force!in!the!direc?on!of!displacement!points!along!the!displacement,!Work#is#posiIve.!When!the!force!is!perpendicular!to!the!displacement,!Work#is#zero.!When!the!component!of!force!in!the!direc?on!of!displacement!points!opposite!to!displacement,!Work#is#negaIve.!!Sept.!5,!2014! PHYS/ENVS!3070! 15!Energy!is!the!key!to!everything.!!However,!ouen!energy!in!different!forms!appears!very!different!to!us.!Energy!can!be!converted!from!one!form!to!another.!• !Kine?c!energy!(KE)!f!energy!of!mo?on!• !Thermal!energy!f!energy!of!atomic!vibra?ons!• !Poten?al!energy!(PE)!!f!energy!stored!in!configura?on!!f!gravita?onal!!!!f!electrosta?c!!f!elas?c!!f!chemical!!f!nuclear!• !Radiant!(e.g.,!solar)!energy!–!energy!of!light!• !Rest!Mass!energy!–!Einstein’s!E=mc2!FORMS#OF#ENERGY#Sept.!5,!2014! PHYS/ENVS!3070! 16!The!kineIc#energy#(KE)!of!an!object!of!mass#m!(in!kilograms)!moving!with!speed#v!(in!meters/second)!is: !!• !KE!is!the!energy!of!mo?on.!• !KE!is!always!posi?ve!(KE!>=!0).!• !KE!and!Work!are!related!by!the!“WorkfEnergy!Principle”!• !Units!of!KE:!KineIc#Energy#221KE mv=22]/][[21KE smkgmv ⇒=⎥⎦⎤⎢⎣⎡= mskgm2[ ]]Joules[== NmSept.!5,!2014! PHYS/ENVS!3070! 17!m!=!mass!of!the!object!(in!kilograms)!!!v!=!velocity!of!the!object!(in!meters/second).!The!work!done!by!the!net#force#on#a#single#object#is!equal!to!the!change!in!kine?c!energy!of!that!object:!Since!work!is!a!transfer!of!energy!via!a!force,!this!is!a!statement!of!conserva?on!of!energy.!!WORKRENERGY#PRINCIPLE#Wnet!!=!!WFnet!!=!!ΔKE!!=!!KEf!f!KEi!Sept.!5,!2014! PHYS/ENVS!3070! 18!This!person!pushes!the!curling!rock!of!mass!=!20!kg!and!releases!it!with!a!velocity!v!=!3!meters/second.!!What!is!the!kine?c!energy!of!the!rock?!!A)!!30!Joules!!! !!!B)!!60!Joules!C)!90!Joules!!!!!!D)!180!Joules!E)!320!Joules!!!22)3)(20(2121== mvKESept.!5,!2014! PHYS/ENVS!3070!
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