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Physics for Engineers & Scientists I

by: Elmira Macejkovic

Physics for Engineers & Scientists I PHY 2048

Marketplace > University of Central Florida > Physics 2 > PHY 2048 > Physics for Engineers Scientists I
Elmira Macejkovic
University of Central Florida
GPA 3.56


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Class Notes
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This 13 page Class Notes was uploaded by Elmira Macejkovic on Thursday October 22, 2015. The Class Notes belongs to PHY 2048 at University of Central Florida taught by Staff in Fall. Since its upload, it has received 19 views. For similar materials see /class/227627/phy-2048-university-of-central-florida in Physics 2 at 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


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