Classical Mechanics Lecture 11 Todays Examples Center of

Classical Mechanics Lecture 11 Today’s Examples Center of Mass Today’s Concept: Conservation of Momentum Inelastic Collisions Mechanics Lecture 11, Slide 1

Unit 10 Homework Problems Mechanics Lecture 10, Slide 2

Homework Problem Mechanics Lecture 10, Slide 3

m 5 CM moves toward m 5 cm Mechanics Lecture 10, Slide 4

Man on Boat Let d be the distance the boat moves to the left. The man’s new position is L-d. The boat’s new position in L/2 -d. Mechanics Lecture 10, Slide 5

Let’s try two men on a Boat… Mechanics Lecture 10, Slide 6

Mechanics Lecture 10, Slide 7

Mechanics Lecture 10, Slide 8

Mechanics Lecture 10, Slide 9

Classical Mechanics Lecture 11 Today’s Concept: Conservation of Momentum Inelastic Collisions Mechanics Lecture 11, Slide 10

Unit 11 Lecture Thoughts Mechanics Lecture 11, Slide 11

Main Points Mechanics Lecture 11, Slide 12

Main Points Mechanics Lecture 11, Slide 13

Conservation of Total Momentum Mechanics Lecture 11, Slide 14

Conservation of Total Momentum Mechanics Lecture 11, Slide 15

Total Momentum & Center of Mass Velocity Mechanics Lecture 11, Slide 16

Conservation of Total Momentum Mechanics Lecture 11, Slide 17

Conservation of Momentum http: //hyperphysics. phy-astr. gsu. edu/hbase/hframe. html Mechanics Lecture 11, Slide 18

Example Mechanics Lecture 11, Slide 19

Example Mechanics Lecture 11, Slide 20

Example Mechanics Lecture 11, Slide 21

Momentum in 2 -d More about this later… Mechanics Lecture 11, Slide 22

Collisions: Conservation of. Total Momentum Mechanics Lecture 11, Slide 23

Collision and Momentum Conservation Mechanics Lecture 11, Slide 24

Collision and Momentum Conservation What about internal forces? Mechanics Lecture 11, Slide 25

Checkpoint A. B. C. Mechanics Lecture 11, Slide 26

Checkpoint Mechanics Lecture 11, Slide 27

Inelastic Collisions q Internal forces do not affect conservation of momentum ! q Kinetic Energy of Center of Mass motion also unchanged q However sum of Kinetic Energy of individual element may be reduced Mechanics Lecture 11, Slide 28

Collisions: Kinetic Energy Mechanics Lecture 11, Slide 29

Collisions: Kinetic Energy Total Kinetic Energy is not conserved Total Kinetic Energy is reduced in inelastic Collisions… Mechanics Lecture 11, Slide 30

Inelastic Collision Mechanics Lecture 11, Slide 31

Which Kinetic Energy ? Mechanics Lecture 11, Slide 32

Energy loss in collision Totally Inelastic “Stick Together” Mechanics Lecture 11, Slide 33

Mechanics Lecture 11, Slide 34

Center of Mass Frame Mechanics Lecture 11, Slide 35

Center of Mass Frame Mechanics Lecture 11, Slide 36

Center of Mass Frame Mechanics Lecture 11, Slide 37

Center of Mass Frame Mechanics Lecture 11, Slide 38

Checkpoint A. B. C. Mechanics Lecture 11, Slide 39

Mechanics Lecture 11, Slide 40

What is the different between conservation of Momentum and conservation of energy? How do I know if the Momentum is conserved or energy is conserve? Momentum (Prelecture 11) Energy (Prelecture 8) Mechanics Lecture 11, Slide 41

Clicker Question A. B. C. D. E. A wood block rests at rest on a table. A bullet shot into the block stops inside, and the bullet plus block start sliding on the frictionless surface. The momentum of the bullet plus block remains constant Before A) Before the collision. B) During the collision C) After the collision D) All of the above E) Only A and C above After As long as there are no external forces acting on the system Mechanics Lecture 11, Slide 42

Recap Mechanics Lecture 11, Slide 43

Check. Point Suppose you are on a cart initially at rest that rides on a frictionless track. If you throw a ball off the cart towards the left, will the cart be put into motion? Left Right A) Yes, and it moves to the right. B) Yes, and itofmoves to the left. the cart must Conservation momentum means move right since the ball moves to the left. C) No, toitthe remains in place. Mechanics Lecture 11, Slide 44

Check. Point Suppose you are on a cart which is initially at rest that rides on a frictionless track. You throw a ball at a vertical surface that is firmly attached to the cart. If the ball bounces straight back as shown in the picture, will the cart be put into motion after the ball bounces back from the surface? Left Right A) Yes, and it moves to the right. B) Yes, and it moves to the left. C) No, it remains in place. Mechanics Lecture 11, Slide 45

Clicker Question A. B. C. Suppose you are on a cart that is moving at a constant speed v toward the left on a frictionless track. If you throw a massive ball straight up (relative to the cart), how will the speed of the cart change? Left Right v A) Increase B) Decrease C) Will not change As long as there are no external forces acting on the system, Ptotal is conserved Mechanics Lecture 11, Slide 46

Check. Point Two balls of equal mass are thrown horizontally with the same initial velocity. They hit identical stationary boxes resting on a frictionless horizontal surface. The ball hitting box 1 bounces back, while the ball hitting box 2 gets stuck. Which box ends up moving faster? A) Box 1 B) Box 2 1 C) same 2 Mechanics Lecture 11, Slide 47

Check. Point Which box ends up moving faster? A) Box 1 B) Box 2 C) same 1 2 A) As the ball bounces to the left, cart 1 moves faster to the right to conserve momentum. B) Some of the energy is not transferred to box 1, since the ball bounces back C) The starting velocity and mass is all the same so the momentum will be the same in both cases. Think of a 2 -step “bounce” Mechanics Lecture 11, Slide 48

A. Clicker Question B. C. Two equal-mass balls swing down and hit identical bricks while traveling at identical speeds. Ball A bounces back, but ball B just stops when it hits the brick. Which ball is more likely to knock the brick over? A B A) A B) B C) They both have the same chance. Mechanics Lecture 11, Slide 49

demo B A DPB DPA > DPB The change in the momentum of the ball is bigger in A Mechanics Lecture 11, Slide 50

Ballistic Pendulum http: //hyperphysics. phy-astr. gsu. edu/hbase/balpen. html Mechanics Lecture 11, Slide 51

Ballistic Pendulum m v M H A projectile of mass m moving horizontally with speed v strikes a stationary mass M suspended by strings of length L. Subsequently, m + M rise to a height of H. Given H, what is the initial speed v of the projectile? Mechanics Lecture 11, Slide 52

Breaking it down into steps before m during after V v M H splat Which quantities are conserved before the collision? A) momentum B) mechanical energy C) both momentum and mechanical energy Mechanics Lecture 11, Slide 53

Breaking it down into steps before m during after V v M H splat Which quantities are conserved during the collision? A) momentum B) mechanical energy C) both momentum and mechanical energy Mechanics Lecture 11, Slide 54

Breaking it down into steps before m during after V v M H splat Which quantities are conserved after the collision A) momentum B) mechanical energy C) both momentum and mechanical energy Mechanics Lecture 11, Slide 55

Ballistic Pendulum m v M H Mechanics Lecture 11, Slide 56

Ballistic Pendulum http: //hyperphysics. phy-astr. gsu. edu/hbase/balpen. html Mechanics Lecture 11, Slide 57