PHY 101 1nd Edition Lecture 14 Outline of Last Lecture I Energy II 5 1 Work III Work Done by Force of Kinetic Friction IV 5 2 Kinetic Energy Work Energy Theorem Outline of Current Lecture I 5 2 continued II Conservative vs Nonconservative Forces III 5 3 Gravitational Potential Energy IV Gravitational Potential Energy Work V Conservation of Mechanical Energy VI 5 5 Energy Conservation Work Energy Theorem Revisted Current Lecture 5 2 Continued Ex A car of mass 1000kg is traveling at 35m s To avoid collision with another car which is at rest the driver slams on the break The friction force on the car is 8x10 3 N 1 What minimum distance should the brake be applied to avoid the collision Analysis o Initial KE 1 2 mv2 o Final KE 0 o The change in KE work done by the friction force o M 1000kg o Vi 35m s vf 0 o Fk 8x103 N Solution o Kef Kei 0 1 2 mv2 These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute o Work done by friction force is Wg Fk x Using work energy theorem Wf Kef Kei o Fk x 1 2 mv2 o x 1 2 mv2 fk 0 5 x 1000 x 352 8x103 76 6m o minimum separation to avoid collision 2 If the initial distance between the 2 cars is 30m what is the speed of the 1 st car at impact o Wf KEf Kei o Fk x 1 2 mvi2 1 2 mvf2 o Fk x 1 2 mvf2 1 2 mvi2 o 8x103 30 1 2 1000 352 1 2 1000 vf2 Solve for vf2 o vf2 745 745 1 2 27 3 m s o deadly impact Conservative vs Nonconservative Forces There are generally two kinds of forces o One is called conservative eg Gravitational force o The other is called nonconservative eg Friction force Work done against a conservative force is transferred into another form of mechanical energy potential energy which can be transformed back into kinetic energy A force is conservative if the work it does on an object moving between two points is independent of the path the objects take between the points Work done by nonconservative force does depend on the path However the work energy theorem always holds o Wnet Wc Wnc KEf Kei o Wc work done by the conservative force o Wnc work done by the nonconservative force o Ex Conservative force gravitational force electric force o Ex Nonconservative force friction Gravitational Potential Energy When taking the slide did you ever wonder where energy came from o You start from rest zero kinetic energy o You gains speed while sliding down gain kinetic energy Gravitational potential energy While you re climbing up you do work against the gravitational force The energy is stored in the potential energy When you slide down the potential energy is then converted into kinetic energy you gain speed neglect the friction of the slide Two kinds of mechanical friction o Kinetic energy we discussed 1 2mv2 o Potential energy Lifting an object up you do positive work potential energy increases the gravitation force does negative work While the object falls down gravitational force does the positive work the potential energy is converted into kinetic energy Gravitational potential energy relative to the reference point where y 0 o PE mg y The higher the position of the object the greater the potential energy Work done by the gravitational force while moving from an initial position yi to a final position vf o Wg PE PE PEf Pei mg y o If PEi PEf the object falls gravitational force does positive work o If Pei PEf the object rises gravitational force does negative work Gravitational Potential Energy Work Wg PEf PEi PE The work done by the gravitational force is equal to the negative of the change in gravitational potential energy If the gravitational force is the only force acting on the object from the work energy theorem o Wg KE o We have PE KE or KE PE 0 Conservation of Mechanical Energy When Gravitational Force is the Only Force That Does The Work KE PE 0 This is the conservation of mechanical energy KE PE KEf KEi PEf PEi 0 Rewrite the equation by moving initial values to the right and final values to the left KEf PEf KEi PEi The sum of the kinetic energy and the gravitational potential energy remains constant at all times In other words the mechanical energy is a conserved quantity This is why the gravitational force is called a conservative force Example Platform Diver A diver of mass m drops from rest from a platform 10m above the water Calculate the speed of the diver when he is 5m above the water We could use several methods to solve this problem o Kinematic equations o Newton s second law o Conservation of mechanical energy KEf PEf KEi PEi o Solution from the conservation of mechanical energy 1 2 mv2 mgyf 1 2 mv2 mgyi Vi 0 1 2 v2 mgyf gyi 1 2 vf2 gyi gyf g yi yf vf2 2g yi yf vf 2g yi yf 1 2 2x9 8x 10 5 1 2 9 9m s 5 5 Energy Conservation Work Energy Theorem Revisited in addition to the gravitational force if there are nonconservative forces involved the work energy theorem becomes as discussed before o Wnet Wg Wnc KEf KEi o Wnc work done by the nonconservative force Since Wg PEi Pef we have o Wnc KEf KEi Wg KEf KEi PEi PEf o Wnc KEf KEi PEf PEi o Wnc KE PE Emech o Emech KE PE