PHYS 1441 – Section 002 Lecture #14AnnouncementsSlide 3Reminder: Special ProjectWork-Kinetic Energy TheoremEx. Deep Space 1Ex. Satellite Motion and Work By the GravityWork and Energy Involving Kinetic FrictionEx. Downhill SkiingEx. Now with the X componentExample of Work Under FrictionPotential EnergyGravitational Potential EnergyEx. A Gymnast on a TrampolineEx. ContinuedExample for Potential EnergyMonday, Oct. 25, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu1PHYS 1441 – Section 002Lecture #14Monday, Oct. 25, 2010Dr. Jaehoon Yu•Work – Kinetic Energy Theorem Revisited•Work and Energy Involving Kinetic Friction•Potential Energy•Gravitational Potential Energy•Elastic Potential Energy•Mechanical Energy ConservationToday’s homework is homework #8, due 10pm, Tuesday, Nov. 2!!Announcements•Quiz #3–Class average: 6.6/10•Equivalent to 66/100•Previous quizzes: 53/100 and 56/100–Top score: 10•2nd non-comprehensive term exam–Date: Wednesday, Nov. 3–Time: 1 – 2:20pm in class–Covers: CH3.5 – CH6.7–There will be a review in class Monday, Nov. 1•Bring your own problems to solve•Mid-term grade discussion this Wednesday–Dr. Yu’s office, CPB342•A – F: 12:45 – 1:15•F – N: 1:15 – 1:50•N – Y: 1:50 – 2:20•Colloquium this week–On the subject of renewable energyMonday, Oct. 25, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu2Monday, Oct. 25, 2010 3PHYS 1441-002, Fall 2010 Dr. Jaehoon YuMonday, Oct. 25, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon YuReminder: Special Project•Using the fact that g=9.80m/s2 on the Earth’s surface, find the average density of the Earth.–Use the following information only•The gravitational constant •The radius of the Earth•20 point extra credit•Due: This Wednesday, Oct. 27•You must show your OWN, detailed work to obtain any credit!! G =6.67×10−11N ⋅m2kg2 RE=6.37×103km4Monday, Oct. 25, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu5When a net external force by the jet engine does work on and object, the kinetic energy of the object changes according toW =Work-Kinetic Energy Theorem KEf−KEo= 12mvf2−12mvo2Monday, Oct. 25, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu6The mass of the space probe is 474-kg and its initial velocity is 275 m/s. If a 56.0-mN force acts on the probe parallel through a displacement of 2.42×109m, what is its final speed?Ex. Deep Space 1 = 275 m s( )2+ 2 5.60 × 10-2N( )cos 0o2.42 × 109m( )474 F∑( )cosθ⎡⎣⎤⎦s=vf=805m s 12mvf2−12mvo2Solve for vf vf= vo2+2 F∑cosθ( )s mMonday, Oct. 25, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu7A satellite is moving about the earth in a circular orbit and an elliptical orbit. For these two orbits, determine whether the kinetic energy of the satellite changes during the motion.Ex. Satellite Motion and Work By the GravityFor a circular orbitFor an elliptical orbit No change! Why not?Gravitational force is the only external force but it is perpendicular to the displacement. So no work.Changes! Why?Gravitational force is the only external force but its angle with respect to the displacement varies. So it performs work.Monday, Oct. 25, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu8Work and Energy Involving Kinetic Friction•What do you think the work looks like if there is friction?–Static friction does not matter! Why?–Then which friction matters?MMdvivfFriction force Ffr works on the object to slow down The work on the object by the friction Ffr is Wfr=The final kinetic energy of an object, taking into account its initial kinetic energy, friction force and other source of work, isFfrKED =fKE =t=0, KEiFriction,Engine workt=T, KEfIt isn’t there when the object is moving. Ffrd cos 180( )= −Ffrd −FfrdiKEW+� −FfrdKinetic FrictionThe negative sign means that the work is done on the friction!!Monday, Oct. 25, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu9What are the forces in this motion? yF =�Ex. Downhill SkiingA 58kg skier is coasting down a 25o slope. A kinetic frictional force of magnitude fk=70N opposes her motion. At the top of the slope, the skier’s speed is v0=3.6m/s. Ignoring air resistance, determine the speed vf at the point that is displaced 57m downhill. Gravitational force: Fg Normal force: FN Kinetic frictional force: fk xyWhat are the X and Y component of the net force in this motion? Y componentNF =From this we obtainWhat is the coefficient of kinetic friction?gyFNF+ =cos 25mg- +oNF =0cos 25mg =o58 9.8 cos 25 515N� � =okf =km =kNfF=700.14515=k NFmMonday, Oct. 25, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu10xF =�Ex. Now with the X componentX componentW =W =fKE =2fv =fv =Total work by this force From work-kinetic energy theorem Solving for vfgxFkf- =sin 25kmg f- =o( )58 9.8 sin 25 70 170N� � - =oma=( )xF s�=� mg sin 25o−fk( )⋅s=( )58 9.8 sin 25 70 57 9700J� � - � =of iKE KE-212fmv =iW KE+ =2012W mv+202W mvm+202W mvm+=( )22 9700 58 3.61958m s� + �=What is her acceleration?xF ma=�a =xFm=�21702.9358m s=Monday, Oct. 25, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu11Example of Work Under FrictionA 6.0kg block initially at rest is pulled to East along a horizontal surface with coefficient of kinetic friction k=0.15 by a constant horizontal force of 12N. Find the speed of the block after it has moved 3.0m.Work done by the force F isThus the total work is WF=MFMd=3.0mvi=0vffv =Work done by friction Fk isFk Wk=rFk⋅rd ==0.15 × 6.0 × 9.8 × 3.0 cos180 = −26 J( )WUsing work-kinetic energy theorem and the fact that initial speed is 0, we obtainW =Solving the equation for vf, we obtain μkmg durcosθkFWW)(102636 JF kW W+ =212fmv2Wm=2 101.8 /6.0m s�= rFrd cosθ =( )12 3.0cos 0 36 J� =coskF d q =rrMonday, Oct. 25, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu12Potential EnergyEnergy associated with a system of objects Stored energy which has the potential or the possibility to work or to convert to kinetic energyWhat does this mean?In order to describe potential energy, U, a system must be defined.What are other forms of energies in the universe?The concept of potential energy can only be used under the special class of forces called the conservative force which results in the principle of conservation of mechanical energy.Mechanical EnergyBiological EnergyElectromagnetic EnergyNuclear EnergyChemical EnergyME �These different types of energies are stored in the universe in many different forms!!!If one takes
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