Understanding Elastic and Inelastic Collisions in Classical Mechanics

1. Classical MechanicsUnit 11 examplesUnit 12 Concepts • Unit 12 Concepts: • Elastic Collisions • Conservation of Momentum • Conservation of Kinetic Energy Unit 11 Examples: Inelastic Collisions Conservation of Momentum (Kinetic Energy not Conserved!)

2. Main Points

3. Main Points

4. Checkpoint 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 C) same 1 2

5. CheckPoint 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. Think of a 2-step “bounce”

6. Clicker Question 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? B A A) A B) B C) They both have the same chance.

7. B A DPB DPA > DPB DPA The change in the momentum of the ball is bigger in A

8. Ballistic Pendulum http://hyperphysics.phy-astr.gsu.edu/hbase/balpen.html

9. 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+Mrise to a height of H. Given H, what is the initial speed v of the projectile?

10. Breaking it down into steps M before during after V m v H splat Which quantities are conserved before the collision? A) momentum B) mechanical energyC) both momentum and mechanical energy

11. Breaking it down into steps M before during after V m v H splat Which quantities are conserved during the collision? A) momentum B) mechanical energyC) both momentum and mechanical energy

12. Breaking it down into steps M before during after V m v H splat Which quantities are conserved after the collision A) momentum B) mechanical energyC) both momentum and mechanical energy

13. Ballistic Pendulum m v M H

15. Car-Truck Collision

18. Car-Truck Collision 2

19. Car-truck Collision 2

21. Two Train Cars 2

22. Two Train Cars 2

23. Classical MechanicsLecture 12 Today’s Concepts: a) Elastic Collisions b) Center-of-Mass Reference Frame

24. Lecture Thoughts

25. Time spent on pre-lecture 12 Average = 9 min 43 sec for 12 min and 39 sec 12 did not watch at all. 12 apparently “scrolled” through…

26. Center of Mass & Collisions so far: The CM behaves just like a point particle If then momentum is conserved If you are in a reference frame moving along with the CM then thetotal momentum you measure is 0.

28. Main Points

29. Main Points

30. Elastic Collisions: Analogy using spring • Mechanical Energy of system is if the form of kinetic energy moving block. • Moving block experiences a negative acceleration due to spring force. • Kinetic Energy of block is transferred to potential energy of spring. • Stationary block experiences an acceleration due to Spring force acting on formerly stationary block. • Potential Energy of Spring is transferred back to the Kinetic Energy of blocks after the collision. Mechanical Energy is conserved

31. Elastic Collisions

32. Elastic Collisions…final state? Quadratic Equation… Solvable !...but “tedious”…

33. A better way!! Eliminates Quadratic Equation…