Announcements 6 Oct 2009 Where are we now 1 Exam 2 still going on a ends tomorrow late fee after 1 pm Topics 2 Next HW due Sat night HW 9 3 Don t forget Oct 24 Deadline to get extra point on extra credits a You automatically get 1 if you turn in extra credit before Oct 24 Kinematics velocity acceleration Vectors 2D Motion Forces Newton s Laws Mechanics Work Energy Momentum Rotations Torque and Angular Momentum Pressure Fluids Solids Thermodynamics Temperature Heat and Heat Flow Laws of Thermodynamics Vibrations Waves Part Mechanics Part Sound Part Optics Colton Lecture 11 pg 1 Conserved quantities Colton Lecture 11 pg 2 Momentum used for Collision Problems Mass If not converted to from energy total mass bef total mass aft Charge total charge bef total charge aft I e if some positive charge flows out of a neutral object it will leave the object with a negative charged Often conserved used to balance chemical reactions Number of each type of atom Number of electrons Etc A new conserved quantity momentum Define for each object then p mv pbefore pafter if no external forces Another blueprint equation Colton Lecture 11 pg 3 v2 initial v1 initial Energy When no non conservative work done Ebef Eaft m1 m2 Derivation of conservation law F1 m1a1 F2 m2a2 Newton s 3rd Law the forces in the collision are and If no other forces then F2 1 F1 2 m1a1 m2a2 0 m1 v1 t m2 v2 t Multiply by t which is the same for both m1 v1 m2 v2 0 m1 v1 final v1 initial m2 v2 final v2 final 0 m1v1 initial m2 v2 initial m1 v1 final m2 v2 final and there you have it From warmup The total momentum of an isolated system of objects is conserved a only if conservative forces act between the objects b regardless of the nature of the forces between the objects Colton Lecture 11 pg 4 From warmup A truck always has more mass than a roller skate Does a truck always have more momentum than a roller skate a yes b no Demo Problem A cart moving at 4 m s runs into a second cart of the same mass and sticks to it What velocity do the two stuck together carts now have Why use conservation of momentum Demo Problem A cart moving at 4 m s runs into a second cart of with twice the mass and sticks to it What velocity do the two stuck together carts now have Limitation Like conservation of energy conservation of momentum is a before and after law which doesn t tell you about If you want to know about you have to know Demo Problem Two carts with the same mass spring apart If one moves at 4 m s to the right afterwards what velocity does the second cart have Another useful equation F t p Impulse equation if only one force Derivation F ma m v t multiple both sides by t Colton Lecture 11 pg 5 Dr Colton s Guide How to Solve Conservation of Momentum Problems 1 Draw initial and final pictures Colton Lecture 11 pg 6 Problem In the new sport of ice football a 100 kg defensive end running north at 4 m s tackles a 75 kg quarterback running east at 7 m s There s no friction What is their combined velocity right after the tackle 2 Draw momentum or velocity vectors arrows in each picture 3 Use pbefore p after as blueprint equation 4 Divide into separate x and y equations if needed 5 Fill in both sides of blueprint equation s using initial and final pictures one term in equation for each arrow in picture 6 Reminder be careful with signs Momentum is a vector Compare to previous two blueprint equations F ma Ebefore Eafter if no non conservative forces Similarities Differences Answers vx 3 m s vy 2 28 m s v 3 77 at 37 3 north of east Colton Lecture 11 pg 7 Colton Lecture 11 pg 8 Problem An artillery shell of mass 20 kg is moving east at 100 m s It explodes into two pieces One piece mass 12 kg is seen moving north at 50 m s What is the velocity magnitude and direction of the other piece From warmup Suppose Ralph is floating in outer space with no forces acting on him He is at rest so his momentum is zero Now he throws a ball The ball goes one way and he goes the other way Before the collision there was no momentum and after the collision there is plenty of momentum Was momentum conserved Answer from the class From warmup do as clicker quiz A ping pong ball moving forward with a momentum p strikes and bounces off backwards from a heavier tennis ball that is initially at rest and free to move The tennis ball is set in motion with a momentum a greater than p b less than p c equal to p What about if ping pong ball thuds and falls flat Demo Elastic and Inelastic Pendulum which will cause the wood to be knocked over Question Is energy conserved in collisions All Some None Answers vx 250 m s vy 75 m s v 261 m s at 16 7 south of east Colton Lecture 11 pg 9 Special Case Elastic Collisions Colton Lecture 11 pg 10 Dr Colton s guide cont 7 If it s an elastic collision In some special collisions energy is also conserved KEbefore KEafter This is in addition to Elastic collisions no lost kinetic energy they are bouncy p before p after The two equations can be put together to give used in addition to cons of mom for elastic collisions v1 v2 bef v2 v1 aft but not all bouncy looking collisions are elastic don t assume Careful with signs Right positive left negative still applies Inelastic collisions Derivation Cons mom Cons energy 1 2 m1v1i m2 v2i m1v1 f m2 v2 f Perfectly inelastic collisions m1 v1i v1 f m2 v2 f v2i m1v1i 2 12 m2 v2i 2 12 m1v1 f 2 12 m2 v2 f 2 v m1 v1i 2 v1 f 2 m2 v2 f 2 v2i 2 m1 v1i v1 f 1i Divide the two equations m1 v1i v1 f v 1i m1 v1i v1 f v1 f m v 2 2f v2i v v1i v2i v2 f v1 f Colton Lecture 11 pg 11 2f m2 v2 f v2i v1i v1 f v2 f v2i Colton Lecture 11 pg 12 v1 f m2 v2 f v2i v2 f v2i v2i Demo Problem A cart moving at 4 m s bounces elastically off of a second cart of twice the mass which is moving at 2 m s in the same direction What velocity does each cart now have Demo problem Elastic collision between very large and very small mass Bowling ball and a marble Marble is at rest vm going towards bowling ball vb What are final speeds Hint vbowling ball final vbowling ball initial Demo Problem A cart moving …