Phy 211 General Physics I Chapter 8 Potential Energy Conservation of Energy Lecture Notes Work Potential Energy Potential Energy U is the energy associated with the configuration of a system such as The position of an object The deformation of a spring Potential Energy is a calculated quantity that represents the stored energy within the system associated with a force that has the potential to perform work Forms of Potential Energy Gravitational PE Ugrav The potential for gravitational force to perform work due to an object s elevation defined as Ugrav mgy Elastic PE Uelastic The potential for elastic force to perform work due to a spring s deformation defined as Uelastic 12 kx2 1 Conservative vs Nonconservative Forces Conservative Forces 1 When the configuration of a system is altered a force performs work W 1 Reversing the configuration of the system results in the force performing work W 2 The force is conservative if W 1 W 2 2 A force that performs work independent of the path taken 3 A force in which the net work it performs around a closed path is always zero or W net 0 J for closed path Examples Gravitational force Fg Elastic force Fspring and Electric force FE Nonconservative Forces 1 2 The work performed by the force depends on the path taken When the configuration of a system is altered then reversed the net work performed by the force is not zero W net 0 J for closed path 3 Work performed results in energy transformed to thermal energy Examples Air Drag FDrag and Kinetic friction fkinetic Sliding on an Incline Example No friction conservative force A 1 kg object vo 5 m s travels up a 30o incline and back down 1 The W net performed by Fg up 2 2 Wup 12 1 kg 0 ms 5 ms 12 5 J 2 The W net performed by Fg down 2 2 Wdown 12 1 kg 5 ms 0 ms 12 5 J 3 The total W net performed Wnet by Fg 12 5 J 12 5 J 0 J Example With Kinetic Friction nonconservative force A 1 kg object vo 5 m s travels up a 30o incline and back down against a 1 7 N kinetic friction force Note Block will not travel up as far as previous example The W up performed by fk up Wf up fk r 1 70 N 1 89 m 3 21 J The W down performed by fk down Wf down fk r 1 70 N 1 89 m 3 21 J The total W net performed Wnet by f Wf up Wf down 3 21 J 3 21 J 6 42 J 2 Defining or Identifying a System A system is a defined object or group of objects that are considered distinct from the rest of its environment For a defined system 1 all forces associated strictly with objects within the defined system are deemed internal forces Internal forces do not transfer energy into out of the system when performing work within the system Example The attractive forces that hold the atoms of a ball together These forces are ignored when applying Newton s 2nd Law to the ball 2 all forces exerted from outside the defined system are deemed external forces External forces transfer energy into out of the system when performing work on a system Example The gravitational force that performs work on a falling object the system increases the ball system s kinetic energy Note When the ball and the earth are together defined as the system the work performed by the gravitational force on the ball does NOT transfer energy into the system The appropriate of a system determines when a force is considered internal or external can go a long way toward simplifying the analysis of a physics problem The total energy associated with a defined system Esystem U K Ethermal EInternal Conservation of Mechanical Energy In mechanical systems where only conservative internal forces are present the total mechanical energy of the system is conserved Wnc 0 Esystem U K constant Energy within the system may transform from one type of mechanical energy to another When this occurs E 0 J U K system Example 1 A simple pendulum y Utop yo 0 m Kbottom 2 An ideal spring Ktop Ubottom yo 0 m y 3 Interpreting a Potential Energy Graph A potential graph is plot of U vs r for a system The slope of the graph defined the force exerted along the graph slope dU i F dr U slope 0 mJ F 0 N r slope 5 mJ F 5N i r i r is in the direction of r U slope 5 mJ F 5N i r i r is in the direction of r r r dU J slope i r 5 m F 5N i r dr i r is in the direction of r Instantaneous U r Work Done on a System by External Forces For a defined system external forces are forces that are not defined within the system yet perform work upon the system External forces transfer energy into or out of a con NC system WExt WExt WExt Esystem WExt U K EInternal Ethermal Conservative external forces alter the U and K a k a the mechanical energy of a system con WExt Esystem U K Nonconservative external forces may alter the mechanical energy U K as well as the non mechanical energy Einternal and or Ethermal of a system NC WExt Esystem U K EInternal Ethermal 4 Conservation of Energy In general the total energy associated with a system of objects represents the complete state of the system ETot U K EInternal Ethermal Work represents the transfer of energy into out of a system W Esystem U K EInternal Ethermal For an isolated system the total energy within a system remains a constant value Esystem U K EInternal Ethermal constant or for any 2 moments Esystem U1 K1 EInternal 1 Ethermal 1 U2 K2 EInternal 2 Ethermal 2 Deeper Thoughts on Cons of Energy Physicists have identified by experiment 3 fundamental conservation laws associated with isolated systems 1 Conservation of Energy 2 Conservation of Mass 3 Conservation of Electric Charge Treated as accepted facts these laws have allowed for experimental predictions that would not have been foreseen otherwise 1 Conservation of Energy led to the discovery of the neutrino during neutron decay within the atomic nucleus 2 Conservation of Mass is fundamental in the prediction of new substance formed during chemical processes 3 Conservation of Electric Charge predicts the formation of neutrons do to the collision of protons with electrons a process called Electron Capture Considered as accepted facts these laws have allowed for experimental predictions that would not have been foreseen otherwise 5 Feynman on Energy There is a fact or if you wish a law governing natural phenomena that are known to date There is no known exception to this law it is exact so far we know The law is called conservation of energy it states that there is a certain quantity which we call energy that does not change in …