PHYS 1441 – Section 501 Lecture #9AnnouncementsConservative and Non-conservative ForcesMore Conservative and Non-conservative ForcesConservative Forces and Potential EnergyConservation of Mechanical EnergyExample for Mechanical Energy ConservationExample 6.8Work Done by Non-conservative ForcesExample for Non-Conservative ForceWednesday, June 30, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu1PHYS 1441 – Section 501Lecture #9Wednesday, June 30, 2004Dr. Jaehoon Yu•Conservative and Non-conservative Forces•Mechanical Energy ConservationToday’s Homework is #4, due at 6pm, next Wednesday, July 7!!Wednesday, June 30, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu2Announcements•Term1 exam results–Average: 58.3–Top score: 88–Could do better…•2nd quiz next Monday, July 5–Beginning of the class–Sections 6.1 – whatever we cover today•2nd term exam Monday, July 19–Covers: Ch 6 – wherever we cover by Jul 14Wednesday, June 30, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu3Conservative and Non-conservative ForcesWhen directly falls, the work done on the object isThe work done on an object by the gravitational force does not depend on the object’s path.gW =How about if we lengthen the incline by a factor of 2, keeping the height the same??gW =Still the same amount of workThe forces like gravitational or elastic forces are called conservative forcesSo the work done by the gravitational force on an object is independent on the path of the object’s movements. It only depends on the difference of the object’s initial and final position in the direction of the force.mghWg1. If the work performed by the force does not depend on the path2. If the work performed on a closed path is 0.hlmmgWhen sliding down the hill of length l, the work isgW =lmg sinNmghTotal mechanical energy is conserved!!ffiiMPEKEPEKEE g inclineF l-�( )sinmg l qmghWednesday, June 30, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu4More Conservative and Non-conservative ForcesA work done on a object by a conservative force is the same as the potential energy change between initial and final statesA potential energy can be associated with a conservative forceUUUWficSo what is a conservative force?The force that conserves mechanical energy.OK. Then what is a non-conservative force?FrictionThe force that does not conserve mechanical energy.The work by these forces depends on the path.Can you give me an example?Why is it a non-conservative force?Because the longer the path of an object’s movement, the more work the friction forces perform on it.What happens to the mechanical energy?Kinetic energy converts to thermal energy and is not reversible.Total mechanical energy is not conserved but the total energy is still conserved. It just exists in a different form.OtherMTEEE i iKE PE+ =f f FrictionKE PE W+ +Wednesday, June 30, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu5Conservative Forces and Potential EnergyThe work done on an object by a conservative force is equal to the decrease in the potential energy of the systemcW U=- DWhat else does this statement tell you?The work done by a conservative force is equal to the negative of the change of the potential energy associated with that force.cW =We can rewrite the above equation in terms of potential energy U( )f c iU x W U=- +So the potential energy associated with a conservative force at any given position becomesOnly the changes in potential energy of a system is physically meaningful!!Potential energy functionWhat can you tell from the potential energy function above?Since Ui is a constant, it only shifts the resulting Uf(x) by a constant amount. One can always change the initial potential so that Ui can be 0.U- D =f iU U- +Wednesday, June 30, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu6Conservation of Mechanical EnergyTotal mechanical energy is the sum of kinetic and potential energiesmghUgLet’s consider a brick of mass m at a height h from the groundf iU U UD = -The brick gains speedv =The lost potential energy is converted to kinetic energy of the brick!What does this mean?The total mechanical energy of a system remains constant in any isolated system of objects that interacts only through conservative forces: Principle of Principle of mechanical energy mechanical energy conservationconservationmmghWhat is its potential energy?What happens to the energy as the brick falls to the ground?mh1By how much?So what?The brick’s kinetic energy increasedK =And?UKE i fE E=i iK U+ =�212mv =2 212mg tmgh=gt212mg gt� �=� �� �f fK U+�Wednesday, June 30, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu7Example for Mechanical Energy ConservationA ball of mass m is dropped from a height h above the ground. Neglecting air resistance determine the speed of the ball when it is at a height y above the ground.ffiiUKUK b) Determine the speed of the ball at y if it had initial speed vi at the time of release at the original height h.mghmymUsing the principle of mechanical energy conservationffiiUKUK Again using the principle of mechanical energy conservation but with non-zero initial kinetic energy!!!This result look very similar to a kinematic expression, doesn’t it? Which one is it?mgh0 yhmgmv 221 yhgv 2PE KEmghmgy00mv2/2mgymv 221mghmvi221( )2 212f im v v- = yhgvvif 22mvi2/2mvf2/2mgymvf221( )mg h y-Reorganize termsWednesday, June 30, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu8Example 6.8If the original height of the stone in the figure is y1=h=3.0m, what is the stone’s speed when it has fallen 1.0 m above the ground? Ignore air resistance. 21 112mv mgy+ =22 212mv mgy+ =2211.02mv mg+ =2212.02mv mg=2212.02v g=2v =mgh =3.0mgAt y=3.0mAt y=1.0m2211.02mv mg+Since Mechanical Energy is conserved3.0mgCancel mSolve for v4.0g =4.0 9.8 6.3 /m s� =Wednesday, June 30, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu9Work Done by Non-conservative ForcesMechanical energy of a system is not conserved when any one of the forces in the system is a non-conservative force.Two kinds of non-conservative forces:Applied forces: Forces that are external to the system. These forces can take away or add energy to the system. So the mechanical energy of the system is no longer conserved.If you were to carry around a ball, the force you apply to the ball is external to the system of ball and the Earth. Therefore,
View Full Document
Unlocking...