lec09_Work and kinetic energy

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1、Physics I    Class 09Work and Kine6c Energy Newton’ssecondlaw⇒Work-EnergyTheoremin1and3dimensions.1.dim:WorkandforceConstantforce:xVariableforce,1D:W=∫fF(x)dxxi1Work and Kine6c Energy Star6ng from Newton’s Second Law in 1D we can  integrate to discover a new principle of physics.   Th

2、e special case of a constant force, Since F and aare constants, we know that if  v=002WorkandKineticEnergy(continued)Usingvectorstodoall3D(threedimensions),Workisequaltothechangeinkineticenergy!UnitofenergyandworkisJouleorJ.3Work for Constant Force ⇒Dot product Work-Energy:W=ΔK4Review

3、: Dot Product Ifyouknowlengthsandangle:W=Fdcos(φ)Ifyouknowcomponents:W=Fd+Fd+FdxxyyzzIfinthesamedirection:W=FdIfinoppositedirections:W=−FdIfatrightangles:W=05Work for Variable Force (1‐D) Integra6on  xW=∫fF(x)dxxiThis is easy to calculate when you know F(x).  Also, no6ce that 6m

4、e does not appear anywhere! 6Work‐Kine6c Energy Theorem 7Work-K.E.TheoremProofxxxxffffdvW=∫Fdx=∫madx=m∫adx=m∫dxnetnetxxxxdtiiiiUsingcalculusrules:dvdvdxdvdv1d2==v=v=(v)dtdxdtdxdx2dxInsertintotheintegral:x1fd1222Wnet=m∫(v)dx=m(vf−vi)=Kf−Ki2xdx2i08-8Take‐Away Concepts 91.Twobodiesofuneq

5、ualmass,placedatrestonafrictionlesssurface,areactedonbyequalhorizontalforcesoverequaldistances.Aseachmasscrossesthe“finishline”(notnecessarilyatthesametime),thebodyofgreatermasswillhave:(pick2answers)a)Smallerkineticenergythanthelesserbody.b)Thesamekineticenergyasthelesserbody.c)Great

6、erkineticenergythanthelesserbody.d)Smallermagnitudeofvelocitythanthelesserbody.e)Thesamemagnitudeofvelocityasthelesserbody.f)Greatermagnitudeofvelocitythanthelesserbody.08-10Solu6on of Problem of the Day Theanswersarebandd.Thework-kineticenergytheoremsaysthatthechangeinkineticenergyis

7、equaltothenetworkdone.Thenetworkdoneisthesameforbothobjects(forcedotdisplacement).Thereforebothobjectshavethesamekineticenergywhentheycrossthefinishline.Thechangeinkineticenergy=½mv2.Thegreatermasswillhavetheslowervelocity.11Ac6vity Goal:Toverifywork-kinetictheoremin1DW=K–KnetfiAppara

8、tus:T