Gravitational EnergyGravitational WorkEnergy of PositionUsing Friction and EnergyFriction and HeightNo AbsoluteUniversal Gravitational WorkUniversal Gravitational PotentialKinetic Energy in OrbitEscape VelocityGravitational EnergyGravitational EnergyGravitational WorkGravitational WorkThe work done by the force of gravity only depends The work done by the force of gravity only depends on the vertical distance.on the vertical distance.•The path taken doesn’t matterThe path taken doesn’t matter•It’s a conservative forceIt’s a conservative force•There is a potential energyThere is a potential energydF = mghmghdmgdFW )sin(hmghyymgrdFW )(21y2y1Energy of PositionEnergy of PositionRaise a blockRaise a block•The state of the block The state of the block changeschanges•Work is stored in a new Work is stored in a new positionpositionEnergy due to position is Energy due to position is called called potential energy potential energy ((UU).).•An object has the potential An object has the potential to do workto do work•The potential energy of The potential energy of gravity: gravity: UU = = mgymgyymgyymgW )(12y1yy2ymgyymgU )(12Using Friction and EnergyUsing Friction and EnergyThe hill is 2.5 km long with a The hill is 2.5 km long with a drop of 800 m.drop of 800 m.The skier is 75 kg.The skier is 75 kg.The speed at the finish is The speed at the finish is 120 km/h.120 km/h.How much energy was How much energy was dissipated by friction?dissipated by friction?Friction and HeightFriction and HeightFind the total change in Find the total change in kinetic energy.kinetic energy.Find the total change in Find the total change in potential energy.potential energy.The difference is due to The difference is due to friction and drag.friction and drag.KK = ½ = ½ mvmv22 - 0 - 0= ½(75 kg)(130 m/s)= ½(75 kg)(130 m/s)22= 5.4 x 10= 5.4 x 1055 J JUU = = mghmgh= (75 kg)(9.8 m/s= (75 kg)(9.8 m/s22)(-800 m))(-800 m)= -5.9 x 10= -5.9 x 1055 J JWWnon non = = KK + + UU = -0.5 x 10= -0.5 x 1055 J JNo AbsoluteNo AbsolutePotential energy reflects the Potential energy reflects the work that may be done.work that may be done.•The point The point UU = 0 is arbitrary = 0 is arbitraryAt the top of a table of height At the top of a table of height hh::•UU = = mgmg((yy++hh))The same experiment is The same experiment is shifted by a constant shifted by a constant potential potential mghmgh::•UU = = mgymgy + + mghmgh = = mgymgy + + CCy1hy2yUniversal Gravitational Universal Gravitational WorkWorkGravity on the surface of the Earth is a local Gravity on the surface of the Earth is a local consequence of universal gravitation.consequence of universal gravitation.How much work can an object falling from very far How much work can an object falling from very far from the Earth do when it hits the surface?from the Earth do when it hits the surface?2rGmMF rREERrRrGmMWrrGmMWrFWE112Universal Gravitational Universal Gravitational PotentialPotentialThe work doesn’t depend on the path.The work doesn’t depend on the path.•Universal gravity is a conservative forceUniversal gravity is a conservative forceThe potential is set with The potential is set with UU = 0 at an infinite distance. = 0 at an infinite distance.•Gravity acts at all rangesGravity acts at all ranges•Gravity is weakest far from the sourceGravity is weakest far from the sourcerGmMU Kinetic Energy in OrbitKinetic Energy in OrbitThe kinetic energy for a The kinetic energy for a circular orbit is related to the circular orbit is related to the potential energy.potential energy.The total energy in a circular The total energy in a circular orbit can be described in orbit can be described in terms of either the kinetic or terms of either the kinetic or the potential energy.the potential energy.2/221222UKrGmMmvrGmMrmvKUEUUEUKE2/)2/(Escape VelocityEscape VelocityNegative total energy can be Negative total energy can be viewed as being captured by viewed as being captured by the force of gravity.the force of gravity.To get away from the To get away from the influence of gravity requires influence of gravity requires zero or positive energy.zero or positive energy.The minimum velocity is The minimum velocity is called the escape velocity. called the escape velocity. nextrGMvrGmMmvUKEesc202102On earth, vesc = 11.2
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