Physics 218 Lecture 16 Dr David Toback Physics
Physics 218 Lecture 16 Dr. David Toback Physics 218, Lecture XVI 1
Checklist for Today • Things that were due Monday: – Chapter 8 Quizzes on Web. CT • Things due today: – Read Chapters 10 & 11 • Things that are due tomorrow in Recitation – Chapter 9 problems Physics 218, Lecture XVI 2
The Schedule This Week: (3/17) • Chapter 8 quizzes due in Web. CT • Reading for Chapters 10 & 11 • Lecture on Chapter 10 (11 in recitation) • Chapter 9 and Exam 2 Review in recitation Next Week: (3/24) • Chapter 9 due in Web. CT (mini-practice exam 2 available) • Exam 2 on Tuesday • Recitation on Chapters 10 & 11 • Reading for Chapters 12 & 13 for Thursday • Lecture 12 & 13 on Thursday Following week • Chapter 10 & 11 material in Web. CT • Reading: Chapters 14 -16 • Lectures on 14 -16 (Lectures 1 and 2 of Four) • Recitation on Chapters 12 & 13 Physics 218, Lecture XVI 3
Chapter 10: Momentum Want to deal with more complicated systems • Collisions • Explosions Newton’s laws still work, but we need some new ideas Physics 218, Lecture XVI 4
Physics 218, Lecture XVI 5
Today’s Lecture • Different style than in the textbook • Begin with a definition of Linear Momentum • Then show that conservation of momentum helps us solve certain types of problems – Things colliding – Things exploding Physics 218, Lecture XVI 6
Definition of Linear Momentum Vector equation! Physics 218, Lecture XVI 7
Restating Newton’s Second Law “The rate of change of momentum of an object is equal to the net force applied to it” If we exert a net force on a body, the momentum of the body changes Physics 218, Lecture XVI 8
What if SF=0? If SF=0, then dp/dt = 0, p = constant Momentum doesn’t change momentum before = momentum after Physics 218, Lecture XVI 9
Conservation of Momentum For a system, by Newton’s laws, SF=0 èConservation of Momentum Sum of all momentum before = momentum after True in X and Y directions separately! Physics 218, Lecture XVI 10
Problem Solving For Conservation of Momentum problems: 1. BEFORE and AFTER 2. Do X and Y Separately Physics 218, Lecture XVI 11
Before Y X Physics 218, Lecture XVI 12
After X Y Physics 218, Lecture XVI 13
So what? Momentum is useful when we don’t know anything about the forces Examples from everyday life: –When ice skating, if you push someone, why do you go backwards? –Why does a gun recoil when you shoot it? Physics 218, Lecture XVI 14
Everyday Experience? Question: Why do you go backwards when you push someone on the ice? Newton’s Law’s answer: When you exert a force on another person, then, by Newton’s law, the person exerts an equal and opposite force on you Physics 218, Lecture XVI 15
Everyday Experience? Cont… Question: Why do you go backwards when you push someone on the ice? Momentum Conservation Answer: • Before: – The system starts with zero momentum (nobody is moving) • After: – The system ends with zero momentum. You and your friend move in opposite directions Physics 218, Lecture XVI 16
Simple Gun Example A gun of mass MG is sitting at rest with a bullet of mass MB inside it. You shoot the gun and the bullet comes out with a speed V at angle Q. What is the recoil velocity of the gun? Physics 218, Lecture XVI 17
Weird example Ball of mass m is dropped from a height h: • What is the momentum before release? • What is the momentum before it hits the ground? • Is momentum conserved? Physics 218, Lecture XVI 18
What if we add the Earth? • What is the force on the ball? • What is the force on the earth? • Is there any net force in this system? • Is momentum conserved? SF=0, then dp/dt = 0, → p = constant Physics 218, Lecture XVI 19
Momentum for a system is Conserved • Momentum is ALWAYS conserved for a SYSTEM, you just have to look at a big enough system to see it correctly. – Not conserved for a single ball • A ball falling is not a big enough system. You need to consider what is making it fall. – Newton’s Law: For every action there is an equal and opposite reaction • Add up all the momentums in the problem – The forcer and the forcee Physics 218, Lecture XVI 20
Energy and Momentum in Collisions Definitions: • Elastic collision = kinetic energy is conserved • Inelastic collision = kinetic energy is not conserved. • Momentum conserved? • Total Energy conserved? Physics 218, Lecture XVI 21
Inelastic Collisions • By definition: Inelastic = mechanical energy not conserved = kinetic energy not conserved • Inelastic Example: Two trains which collide and stick together Physics 218, Lecture XVI 22
Colliding Trains: 1 Dimension The train car on the left, mass m 1, is moving with speed Vo when it collides with a stationary car of mass m 2. The two stick together. 1. What is their speed after the collision? 2. Show that this is inelastic Physics 218, Lecture XVI 23
Ballistic Pendulum A bullet of mass m and velocity Vo plows into a block of wood with mass M which is part of a pendulum. How high, h, does the block of wood go? Is the collision elastic or inelastic? Physics 218, Lecture XVI 24
Bottom line: When to use Momentum • When you don’t know the forces in the system • When you are studying all of the pieces of the system which are doing the forcing Before and After Problems Physics 218, Lecture XVI 25
Coming up… • Yesterday: Chapter 8 quizzes in Web. CT if you haven’t finished them already • Tomorrow: Recitation on Chapter 9 and exam review • Next Lecture: Finish Chapter 10 • Next week: – Homework 9 due – Mini-practice exam 2 and bonus points – Exam 2, Tuesday March 25 th – Start Chapters 12 -16 Physics 218, Lecture XVI 26
Physics 218, Lecture XVI 27
Notes • • Exam coming up next time…. : – Here. Usual class time: Covering: • Exam 1 material, Chapter 3(9) • Chapter 4(1 -8), Chapter 5(1 -3) • Chapter 6(1 -8), Chapter 7(1 -4), Calculus 2 Today’s material NOT ON EXAM 5 Bonus points on the mini-practice exam II. Requires a 100 on all 10 math quizzes, all HW and HW quizzes up through and including Chapter 7 Physics 218, Lecture XVI 28
Next time: • Exam coming up next time…. : – Here. Usual class time: Covering: • • Exam 1 material, Chapter 3(9) • Chapter 4(1 -8), Chapter 5(1 -3) • Chapter 6(1 -8), Chapter 7(1 -4), Calculus 2 5 bonus points for getting a 100 on mini-practice exam II – Must complete everything to Chap 7. • Reading for next lecture: – Rest of Chapter 9 on Momentum – Reading was due today, but I’ll grant an extension. Questions: 1 & 14 Physics 218, Lecture XVI 29
Head On Collision A ball of mass m 1 collides head on (elastically) with a second ball at rest and rebounds (goes in the opposite direction) with speed equal to ¼ of its original speed. What is the mass of the second ball m 2? Physics 218, Lecture XVI 30
Next time: • Exam Thursday – Extra credit if you have 100’s on all HW’s, HW quizzes and math quizzes before the exam • Reading for Tuesday: – Rest of Chapter 9 on Momentum Physics 218, Lecture XVI 31
Two Balls Collide Two billiard balls of equal and known mass m are traveling with known velocities V 1 and V 2. They collide elastically What are the velocities after the collision? Physics 218, Lecture XVI 32
A Ball collides with a Stationary Ball We have two billiard balls of • different and known masses m 1 and m 2. Ball one is traveling with known velocity V 1. They collide elastically What are the velocities after the collision? Physics 218, Lecture XVI 33
Collisions and Impulse Physics 218, Lecture XVI 34
Playing Pool: 2 Dimensions Before the collision, ball 1 moves with speed V 1 in the x direction, while ball 2 is at rest. Both have equal mass. After the collision, the balls go off at angles Q and –Q. What are v’ 1 and v’ 2 after the collision? Q -Q Physics 218, Lecture XVI 35
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