Physics for Engineers & Scientists I
Physics for Engineers & Scientists I PHY 2048
University of Central Florida
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Date Created: 10/22/15
Uta n Work emery theorem We Work by a eon terse 1 DAnays is 3DAn aly sis WorkKinetic Energy Theorem scalar uantit associated with a state or condition of one or more objects T AM From gt W Fx max 2 2 12 v0 2d v2v 2axd gtax F ma lmv2 v2lemadlmv2 v2 x x 2 0 X 0 1 Z 2 Work done by the force Energy aimw V390KfKi de gt39 transfer due to the force To calculate the work done on an object by a force during a displacement we use only the force component aon t force comoonentiperpte neliwlanttorth WorkKinetic Energy Theorem Kf Ki W 74 Change in the kinetic energy of the particle Net work done on the particle t by a comiettamt force W F cl mgd coup 75 maaergmm Momma gt F Object Fg IV Work by va ifiadb e if 1 Block attached to spring x positive x negative 3 Ni F negative f AAA F positive W4 u V E F W e wee e d pr mg beygs H klt U r o between the bum de if e E mk g pe ea kea nt di39izcae I 2 Fx39 me within each short AX segment WS ZFijzgt Ate gt0 gtWs jfFdxjf kx dx WS 2 kLf x dx kx xi2 9The39Work done by 7 rquot block IS the negative of the work done by the spring force AszF Ax Jaan W ZAW 2F Ax Lavg better approximation 3 more Ax Ax gt 0 gtW an F Ax WfFxdx lim Ax gt0 Geometrical W d rk iS quotthe area b ej39twe39en39 the curve and The Xaxis FFjijsz FXFx FyFy FZFz d7dx dy jdz1 1 X1 Y z dWFddexFydydezs W de IFdeIFydyszdz E 9 X it X X WjFxdxjma ix madxm ix gt m vdxmvdv dt dx i i v dt dxdz dx v v 1 21 2 WImv dvmjv dv3mvf5mvl KfiKlAK V V V Power Time rate at which the applied force does work amount of work done in an amount of time At by a force 712 dwtioswdxi dr 7 7 p Watt1 W 1Js 1 kilowatthour 1 kWh 0 x 10 J 36 MJ W FEFcos0d W AK 05mv v3 11 v0 0 gt AK 205mv 2Ncos0 054kgv gtVf Vcos ms b 10 1ms a AK 05 va 05 4kg1ms2 6 v0 1ms aAK 05mv12c 2 2N cos a 054kgv 2 2N cos 9 054kgv 2 gmm wFJmms NLJaWzo Only ng Fax do work a W WFax WFgX 0 Wm Fm d Fm 2 Fax ng 2000530 mg sin30 Wm 1732N 147N05m 2131 b KOZOAWZAKZKJC W 2131 05mvj Avf 093ms Motion a concave downward parabola 1 t10 t x10 Fctema2kg 02ms2 04N b IZSSAVfZO WFx 04Nt 01t2 a t1s vf 08ms C K 05 2k 08 2064J f gx ms W0 064 064J a W 2 Area under carve W 115sqaares05m1N 5751 I W jidx 9i3 9l 1 6 1X2 X 1 3 mm 4500kg 1800kg 6300kg a 17 m Em 6gt Fa Fg 0gt PFv 6174kN38mS P 23461kW Fa mg 6300kg98ms2 6174kN W ZAKsz Ko mquotv ABVBgtVAWgt0 BCAVC VB CD gtvDltvC aWlt0 DEAvElt0 VDWgt0 quot 39E 39L39 i a WFg ng mgd 025kg98ms2012m 029J i iuiiiiil I I IIIIHII 19 Ws 6de 05 250Nm012m2 18J 6 Wm AK 05mv12c 05mvl2 vf 0 gt Kf 0 gt AK 2 K 05mvl2 WFg Ws 0291 18J 05 025kgvi2 gt vi 347ms d If V19 695ms gt Maximum spring compression vf 0 Wnet 390 5kd392 05mvi392 d39 023m a Pulley 1 V cte F net 0 gt2T mg 0 gtT98N Hand cord T F0eF98N b To rise m 002m two segments of the cord must be shorten by that amount Thus the amount of the string pulled down at the left end is 004m 6 WF 2 F d 98N004m 392 d WFg mgd 002m20kg98ms2 392 WFWFgO There is no change in kinetic energy Recap Work done by a constant force W F Ar cos 6 Scaler product or dot product of two vetors A B A B cos 6 x Work done by a varying force W I f dex xi Kinetic Energy is the energy of a particle K 12 mv2 WorkKinetic Energy Principle 2W Kf K Potential Energy Potential energy is the energy associated with the configuration of a system of objects that exert forces on each other There are many forms of potential energy including Gravitational Electromagnetic Chemical Nuclear This system consists of Earth and a book Do work on the system by lifting the book through Ay A y mg A r 5 y w M WF app W Highm ya W mgyb mgya Ar 23 m g a Potential Energy The quantity mgy is identified as the gravitational potential energy U9 U9 mgy Units are joules J Is a scalar Work may change the gravitational potential energy of the system Wnet c There is no change in kinetic energy since the book starts and ends at rest Elastic Potential Energy Elastic Potential Energy is associated with a spring The force the spring exerts on a block for example is FS kx The work done by an external applied force on a springblock system is W 12 kxf2 12 kx2 l 100 ThlS expreSSIon IS the elastic a potential energy US 12 kx2 The elastic potential energy rm can be thought of as the m energy stored in the deformed quot viii spring The stored potential energy it can be converted into kinetic a aaaaaaaaaaaaaaaaaaaaa m energy Elastic Potential Energy The elastic potential energy stored in a spring is zero whenever the spring is not deformed U 0 when X 0 The energy is stored in the spring only when the spring a 53E l netir Prlrlllldl Tomi IS stretched or compressed HM The elastic potential energy IS a i i 1 maXimum when the spring has ltbgt my 7 Kg 0M reached its maximum extension 70 or compression 39i i s 0 C in 1 0 171 The elastic potential energy IS i fluff all always positive a uuuuuuuuuuuuuuuuuuuuu m X2 will always be positive 38 A 400 N child is in a swing that is attached to ropes 200 m long Find the gravitational potential energy of the child Earth system relative to the child39s lowest position when a the ropes are horizontal b the ropes make a 300 angle with the vertical and c the child is at the bottom of the circular arc Internal Energy The energy associated with an object s temperature is called its internal energy Eint In this example the surface is the system 0 The friction does work Kinetic Internal Total and increases the internal energy mm energy energyc fthe c 50 0 Kinetic Internal Total energy energy energy uuuuuuuuuuuuuuuuuuuuu an Summary Gravitational potential energy Ug mgy Elastic potential energy Us 1z kx2 Mechanical energy of a system is Emech K Ug Conservative Forces Wab 1 Wab 2 l 2 Nonconservative Forces Wab 1 7E Wab 2