Presentation on theme: "Liceo Scientifico Isaac Newton Physics course"— Presentation transcript:
1Liceo Scientifico Isaac Newton Physics course Potential Energy and mechanical energy conservationProfessorSerenella IacinoRead byCinzia Cetraro
2Potential energyGravitational Potential energyElastic potential energy
3Gravitational potential energy represents the work done by gravity m→P→→hW = P ∙ s = P ∙ h ∙ cos 0° = mghThe Potential energy is indicated by the symbol U or only ( E P ).fig.1Am→hBPW = m g h - m g h = U - UAABABBhfig.2
4m g = = 625 N (this is the weight). Let’s make an example:Am→Ph=40mBW = U - Um g h - m g h = U - Um g 40 – 0 = from whichm g = = 625 N (this is the weight).fig.3ABABABAB2500040
5Gravitational potential energy depends only on the height h →sthe vertical route ABh→→→→θW = P s= P AB = P h cos0°=mgh∙∙BABCA→fig.4sthe route ACBh→→→→W = W + W = P AC + P CB =∙∙s→θACBACCBBC= P AC cos(90°- )+ P CBcos90°=θfig.5h= mg = mghsenθsenθ
6Conservative force → s → s → → → → v < - 1 2 m v W = < 0 P→N→P→fig.6vif<-12m vW =< 0from whichvif>-12m vW => 0from which
7s → s → → → → → 1 2 v 1 m g h = m m g h = m v 2 - 1 2 m v = 0 W = 0 N ABP→P→12vA21m g h =m2fig.7m g h =mvB2-12m vfi= 0W= 0P→
8Elastic potential energy of a compressed spring U =12K xwhich represents the work done by the elastic force to pull the spring back towards its original length.We can observe that the work depends only on the compression x and so on the initial and final positions of the spring, therefore the elastic force is a conservative force.However not all forces are conservative.
9Non conservative forces: Friction →→Fa→FaABs→s→fig.8→FaDC→Fas→W = W + W + W + W = =- Fas- Fas- Fas- Fas- 4 FasABBCCDDA
10E = U + K E E = Mechanical Energy It is conserved only in systems where conservative forces are involved.1212m vf2-m vi2the work – energy theorem:W==K - Ksumfithe difference in potential energy:W=U - Uifconservative forceK - Kfi=U - Uiffrom which we haveU + K=U + KfiiE=Einitialfinal
11highest point - highest gravitational potential energy If there is no friction, the Roller Coaster is a demonstration of Energy Conservation.highest point - highest gravitational potential energyfig.9Mechanical energy remains constant.
12Spring and energy conservation →When the object compresses the spring, its kinetic energy decreases and is transformed into elastic potential energy.mfig.10v→When the motion is reversed, the potential energy decreases while the kinetic energy increases and when the object leaves the spring, the kinetic energy returns to its initial value.mfig.11
13The pinball machine: → → s→To fire the ball of mass m, suppose we compresse the spring, having a constant equal to K, by length x.Ignoring friction, we want to know what is the launch velocity of the ball.P→fig.12121222U + Kfi=K x+ 0 = 0 +mvf2K xv=m sfm
14two children, two slides, no friction, same height h, Water Park:two children, two slides, no friction, same height h,hhv1v2U + Kfi=121222m g h+ 0 = 0 +mvm g h+ 0 = 0 +mv12from whichv=2 g handv=2 g h12
15Law of energy conservation is no longer valid. Conservative and non conservative forces:W=Wcons+Wnon conssumWconsWnon cons=K - Kfi+W=K - KfisumWU - UifU - UifWnon cons+=K - Kficons=Wnon cons=U + Kf-U + KiWnon cons=Efinal-EinitialLaw of energy conservation is no longer valid.