2. Unit 06 Momentum and Collisions

3. Class Plans and Demos Equations List – Literal Equations “What if’s?” (later slide) Egg throw into sheet Draw momentum and impulse vector Finding Vf of egg “What if?” example Air track collisions Bouncing balls of diff sizes toy - astroblaster Basketball and tennis ball launch – same thing Read “Attractive Force of Glass” article from intuitor.com Math examples: Holt # 2 p. 213 –and –and # 1 p. 214 HW: Momentum FR Quiz #1 and HW and Review Handout

4. Class Plans Day 4: Monday 01/11/10 BW: Astroblaster Question 1 st 1 st pd : Red pen grade take home quiz: FR with spring, 6 th 6 th grade the projectile one Check HW and Review Handout for grade Give answers and explanations sheet for study 1 st 1 st pd : discuss change in lab report calc’s Report due tomorrow Give out Midterm practicum (Pendulum lab) Momentum clicker quiz tomorrow Get names of students who plan on taking the AP exam this spring Simple Harmonic motion (SHM) starts tomorrow Momentum exam Thursday, w/ a bit of SHM Ranking Tasks for impulse if time

5. Videos Julius Sumner Miller – 2 part episode on energy and momentum Podcasts: Collision (funny, anticipatory event) – Best of YouTube #298 Mic Mishap Bouncing (use with Conceptual Physics section on bouncing and impulse) – Best of Youtube #392 – “Beach ball ownage”

6. Unit Plans Day 1: Egg throw, mic mishap vid, Notes, ‘quiz 1’ for HW Day 2: Lab – discuss HW, “bumper cars” lab, Quiz 2 for HW Day 3: bouncing vid, Astroblaster problem, finish/discuss lab, discuss quiz 2 (HW), partner quiz: ‘quiz 3’, Jocko the clown (BW)

7. Introductory BW: Energy Review A ballistic pendulum apparatus has a 40-g ball that is caught by a 500-g suspended mass. After impact, the two masses rise a vertical distance of 45 mm. Find the velocity of the combined masses just after impact. m 1 = 0.04 kg m 2 = 0.500 kg h = 0.045 m KE 0 = PE f

8. PE f = (m 1 +m 2 ) gh f = (0.04+0.500)(9.8)(0.045) = 0.24 J KE 0 = PE f = 0.24 J = 0.94 m/s

9. Bellwork: Day 3

10. Bellwork

11. BW’s Day 3- Astroblaster The Astroblaster is a toy version of what’s called a “multiple collision accelerator” It quickly transfers momentum from larger objects to smaller and smaller ones, giving them faster and faster speeds. We will calculate the velocity of the last and smallest ball as it is launched from the astroblaster First we must know how much momentum is put into the system of balls If you drop the astroblaster from ½ m above the ground, how fast will the smallest (red) ball be going when it is launched from the astroblaster?

12. BW’s Day 3- Astroblaster Data Measurements: Drop height: 0.5 m g = 10 m/s 2 Ball masses: Red ball: m r = 4 g = 0.004 kg Yellow ball: m y = 9 g = 0.009 kg Green ball: m G = 30 g = 0.030 kg Blue ball: m B = 47 g = 0.047 kg Assumptions: linear momentum is conserved in all collisions (p i = p f ) Mass of earth is so large compared to mass of astroblaster that earth’s mass (m E )may be approximated as infinite and therefore the velocity of earth before and after colliding with the astroblaster is negligible (0 m/s)

13. IMPULSE AND MOMENTUM The impulse (F  t) is a vector quantity equal in magnitude to the product of the force and the time interval in which it acts. Its direction is the same as that of the force. It is abbreviated with a capital “J”… J = F  t Units: newton.second (N.s) The momentum (p) of a particle is a vector quantity equal in magnitude to the product of its mass m and its velocity v. Abbreviated with a lower case “p”. p = m vUnits: (kg.m/s)

14. Impulse Example: A 3 N baseball moving toward the batter with a velocity of 15 m/s is struck with a bat which causes it to move in a reversed direction with a velocity of 30 m/s. Find the impulse and the average force exerted on the ball if the bat is in contact with the ball for 0.01 s. F g = 3 N v 0 = - 15 m/s v f = 30 m/s t = 0.01 s This is why follow through is important in batting, golf swings, lacrosse and hockey shots: more time in contact with the ball gives greater change in momentum!

15. m = 0.31 kg v 0 = - 15 m/s v f = 30 m/s t = 0.01 s FΔt = mΔv =m(v f - v 0 ) =0.31(30-(-15)) = 13.95 Ns = 1395 N

16. Area = Impulse

18. CONSERVATION OF LINEAR MOMENTUM According to the law of conservation of linear momentum, when the vector sum of the external forces that act on a system of bodies equals zero (a.k.a.: the system is isolated), the total linear momentum of the system remains constant no matter what momentum changes occur within the system. Although interactions within the system may change the distribution of the total momentum among the various bodies in the system, the total momentum does not change. Such interactions can give rise to two general classes of events:

19. a. explosions, in which an original single body flies apart into separate bodies

20. b. collisions, in which two or more bodies collide and either stick together or move apart, in each case with a redistribution of the original linear momentum.

21. For two objects interacting with one another, the conservation of momentum can be expressed as: v 1 and v 2 are initial velocities, and are final velocities

22. ELASTIC AND INELASTIC COLLISIONS If the Kinetic energy remains constant in a collision, the collision is said to be completely elastic. If the colliding bodies stick together and move off as a unit afterward, the collision is said to be completely inelastic. In inelastic collisions only the momentum is conserved.

23. In elastic collisions no permanent deformation occurs; objects elastically rebound from each other. In head-on elastic collisions between equal masses,velocities are exchanged. Kinetic energy is conserved as well as momentum

24. Inelastic collisions are characterized by objects sticking together and permanent deformation. Kinetic energy is lost but momentum still conserved.

25. Inelastic Collision Example: A 12-g bullet is fired into a 2-kg block of wood suspended from a cord. The impact of the bullet causes the block to swing 10-cm above its original level. Find the velocity of the bullet as it strikes the block. m 1 = 0.012 kg m 2 = 2 kg h = 0.1 m KE 0 = PE f m 1 v 1 = ( m 1 +m 2 )v'

26. m 1 = 0.012 g m 2 = 2 kg h = 0.1 m KE 0 = PE f m 1 v 1 = ( m 1 +m 2 )v' = 1.4 m/s = 234.7 m/s

27. Egg “What if” Question What if someone smacked the egg in mid-flight with a force straight up of 50 N for 0.025 s? 1. Draw impulse vector 2. Get final momentum (add impulse to initial momentum) 3. Find Vf and angle of egg

28. “What if’s” 1. What happens to momentum if mass is doubled? 2. What about kinetic energy? 3. What happens to momentum if velocity is halved? 4. What about kinetic energy?

29. Collisions Lab “Bumper Cars” Using carts and tracks, create 3 different situations described where momentum is conserved Measure each cart’s initial and final velocity using any equipment necessary Describe each event as either elastic or inelastic and show whether K and p is conserved using measurements and calculations. Using conservation of momentum, find the ratio of one cart’s mass to the other (mp = X mc, where ‘X’ is the ratio) Ideally, this ratio should be exactly 1.00, however friction will cause this to be slightly higher or less, giving your experiment an unavoidable source of error. Find out how much error friction introduced in each case One report per group. Should describe your materials, and how they were used (procedure), you may want to use labeled diagrams to avoid writing alot Organize your measurements into a data table(s) Show all calculations clearly and neatly in a separate section (points awarded for neatness) Extra credit: Discover an accurate method for finding the time and/or force involved in each collision/event!!!

30. Collisions Lab “Bumper Cars” Photogate setup tips Don’t let friction become a large factor: setup your gates so they measure velocities just before and after the event LabQuest tips: Plug in both gates and make sure they read blocked or unblocked on the meter screen Check the timing mode: it should be “Photogate timing” and “Gate” enter the diameter of the metal column on the carts as the object length Don’t use the graph screen, use the data table screen Scroll the screen over and down to find the velocities recorded by each gate.