MOMENTUM

1. MOMENTUM Linear Momentum Impulse Conservation of Momentum Types of Collision 2-D Momentum

2. MOMENTUM How do you chop through cement blocks with a bare hand? Why does falling on a wooden floor hurt less than onto a cement floor? Why do people in larger vehicles end up with fewer injuries in accidents?

3. Linear Momentum • Measure of how hard it is to stop a moving object or change the motion’s direction • How a mass moves in a straight path • Momentum = mass times velocity • p = m v • Units: kg m/s (SI) • Vector; same direction as velocity

4. IMPULSE • Directly proportional to force and time • Force exerted over time • Derived from Newton’s 2nd Law of motion • F = ma = mv/t = p/t • I = F t • Units: Ns (SI)

5. IMPULSE • Area under the curve of the F vs t

6. IMPULSE-MOMENTUM THEOREM • Impulse is the change in momentum • I = Δp = pf - p° • Ft = mvf – mv° = m (vf - v°) • Units : Ns = kg m/s • Momentum is in the same direction as Force

7. IMPULSE MOMENTUM THEOREM • Bouncing causes a greater change in momentum and impulse.

8. EFFECT OF COLLISION TIME UPON FORCE • Air bags • Seat Belts • Boxing • Padding • Baseball • Throwing an egg on the bed sheet • Car collisions…crumple zones

9. IMPULSE-MOMENTUM THEOREM

10. IMPULSE-MOMENTUM THEOREM

11. CONSERVATION OF MOMENTUM • For a collision in an isolated system, the total momentum before the collision = the total momentum after collision. • If one object gains momentum then the second object has lost the same amount. • Momentum is ALWAYS conserved so constant • pbefore = pafter • Number of momentum equations = number of drawings

12. CONSERVATION OF MOMENTUM • p° = pf • ptruck + pcar = ptruck’ + pcar’ • mtruckvtruck + mcarvcar = mtruckvtruck’ + mcarvcar’

13. CONSERVATION OF MOMENTUM • p° = pf • pbigfish + plittlefish = ptotal • mbigfishvbigfish + mlittlefishvlittlefish= mbigfish+littlefishvt

14. TYPES OF COLLISION • Types of collision • Elastic collision • Momentum is conserved • KE is conserved • Bounce off of each other • Inelastic collision • Momentum is conserved • KE is NOT conserved • Damaged or stick together

15. TYPES OF COLLISION • Two types of inelastic collision • Perfectly inelastic collision • Objects collide and stick together • Inelastic collision • Objects collide and damage is present

16. LINEAR MOMENTUM • Jocko, who has a mass of 60 kg and stands at rest on ice, catches a 20 kg ball that is thrown to him at 10 km/h. How fast does Jocko and the ball move across the ice? • The momentum before the catch is all in the ball, 20 kg x 10 km/h = 200 kg km/h •  This is also the momentum after the catch, where the moving mass is 80 kg 60 kg for Jocko and 20 kg for the caught ball.

17. LINEAR MOMENTUM • The roads in Dr. J's neighborhood are slightly more crowded in the mornings these days since he has taken up jogging. The crowding comes from the crew that helps Dr. J get through this physical fit that is overrunning the country. J. Jr. marks off a new course each day while Timex mans the stopwatch. Tripod is there at the end supporting a tray of cereal, fruit, and bacon on his nose (his idea of a balanced breakfast). Dr. J does have one quirk - he doesn't use shoelaces. As a result, his shoes always look like they are ready to come apart when he finishes. (Don't most joggers finish with their tongues hanging out?) But alas, this is the day that Dr. J finally gets tired of it all. His course takes him through the local park, but a thick fog has decreased visibility. As a result, he runs into a swing made from an old tire suspended by a long rope. Dr. J experiences a new high as he and the tire rise 0.3 m above their initial level.  If Dr. J weighs 750 N and the mass of the tire is 10 kg, how fast was Dr. J running?

18. Chapter 9: R pg 178 • 1) A compact car, mass 725 kg, is moving at +100 km/h. a) Find its momentum. b) At what velocity is the momentum of a larger car, mass 2175 kg , equal to that of the smaller car? • 2.02 x 10 4 kgm/s; 33.4 km/h

19. Chapter 9: R pg 178 • 2) A snowmobile has a mass of 2.50 x 102 kg. A constant force is exerted on it for 60.0 s. The snowmobile’s initial velocity is 6.00 m/s and its final velocity 28.0 m/s. a) What is its change in momentum? b) What is the magnitude of the force exerted on it? • 5.5 x 10 3 kgm/s; 91.7 N

20. Chapter 9: R pg 178 • 3) The brakes exert a 6.40 x 102 N force on a car weighing 15680 N and moving at 20.0 m/s. The car finally stops. a) What is the car’s mass? b) What is the initial momentum? c) What is the change in the car’s momentum? d) How long does the braking force act on the car to bring it to a halt? • 1.60 x 10 3 kg; 3.20 x 10 4 kgm/s; - 3.20 x 10 4 kgm/s; 50.0 s

21. Chapter 9: R pg 178 • 4) Figure 9-1 shows, as a function of time, the force exerted by a ball that collided with a box at rest. The impulse, Ft, is the area under the curve. a) Find the impulse given to the box by the ball. b) If the box has a mass of 2.4 kg, what velocity did it have after the collision. • 5.25 Ns; 2.2 m/s

22. Answers: R pg 193 • 351 kgm/s • 4.8 kgm/s • 42 m/s • 60 Ns; 20.0 m/s • 2.04 x 104 Ns; 300 N • 2.35 x 104 kgm/s; 2.6 x 104 N • 260 N • -250 N • 1100 kg • 1300 s

23. Momentum in 1-D Objects bounce apart A 0.15 kg blue billiard ball moving at 8.0 m/s to the right hits a similar red billiard ball at rest. If the blue ball continues to move to the right at 2.5 m/s, what is the velocity of the red ball. ptotal = ptotal’ pb + pr = pb’ + pr’ mbvb + mrvr = mbvb’ + mrvr’ 0.15 kg(8.0 m/s) + 0.15 kg(0m/s) = 0.15 kg(2.5 m/s) + 0.15kg(vr’) vr’ = 5.5 m/s right

24. Momentum in 1-D Objects stick together Two balls of clay, a blue one being 2.3 kg and the second red one being 5.6 kg, hit each other and stick together. If the blue one was moving to the right at 12 m/s, and the red was moving at 8.1 m/s to the left, what is their final velocity? ptotal = ptotal’ pb + pr = ptotal mbvb + mrvr = v’ (mb + mr) 2.3 kg(12.0 m/s) + 5.6 kg(-8.1m/s) = v’(2.3 kg + 5.6 kg) v’ = -2.2 m/s left

25. Chapter 9: R pg 185 • 5) A 0.105 kg hockey puck moving at 48 m/s is caught by a 75 kg goalie at rest. With what speed does the goalie slide on the ice? • 0.067 m/s • 6) A 35.0 g bullet strikes a 5.0 kg stationary wooden block and embeds itself in the block. The block and bullet fly off together at 8.6 m/s. What was the original velocity of the bullet? • 1200 m/s

26. Chapter 9: R pg 185 • 7) A 35.0 g bullet moving at 475 m/s strikes a 2.5 kg wooden block. The bullet passes through the block, leaving at 275 m/s. The block was at rest when it was hit. How fast is it moving when the bullet leaves? • 2.8 m/s • 8) A 0.50 kg ball traveling at 6.0 m/s collides head-on with a 1.00 kg ball moving in the opposite direction at a velocity of –12.0 m/s. The 0.50 kg ball moves away at –14 m/s after the collision. Find the velocity of the second ball. • - 2.0 m/s

27. Chapter 9: R pg 188 • 9) A 4.00 kg model rocket is launched, shooting 50.0 g of burned fuel from its exhaust at an average velocity of 625 m/s. What is the velocity of the rocket after the fuel has burned? • 7.91 m/s • 10) A thread holds two carts together on a frictionless surface as in the figure. A compressed spring acts upon the carts. After the thread is burned, the 1.5 kg cart moves with a velocity of 27 cm/s to the left. What is the velocity of the 4.5 kg cart? • 9.0 cm/s to the right

28. Chapter 9: R pg 188 • 11) Two campers dock a canoe. One camper steps onto the dock. This camper has a mass of 80.0 kg and moves forward at 4.0 m/s. With what speed and direction do the canoe and the other camper move if their combined mass is 110 kg? • 2.9 m/s in the opposite direction

29. Chapter 9: R pg 188 • 12) A colonial gunner sets up his 225 kg cannon at the edge of the flat top of a high tower. It shoots a 4.5 kg cannon ball horizontally. The ball hits the ground 215 m from the base of the tower. The cannon also moves, on frictionless wheels, and falls off the back of the tower, landing on the ground. a) What is the horizontal distance of the cannon’s landing, measured from the base of the back of the tower? b) Why do you not need to know the width of the tower? • 4.3 m/s; speed remains constant

30. Answer: R pg 193 11)30.0 s 12) 0.05 s; -4000 N; 410 kg: no; holding a child is dangerous to the child 13) 888 kgm/s; 43.6° SE 14) 63 kgm/s; 63 Ns; 20000 N; 4000 N 15) 150 kgm/s; 150 Ns; 3000 N; 5W 16) 780 kgm/s; -780 kgm/s; 780 kgm/s; 6.1 m/s 17) 1.0 x 10-3 kgm/s; -6.0 x 10-4 kgm/s; 6.0 x 10-4 kgm/s; 1.6 x 10-3 kgm/s; 16 cm/s 18) –100 kgm/s; - 500 kgm/s 19) 11m/s 20) 340 m/s 21) 10.6 m/s

31. Momentum in 2-D • A 1.20 kg red ball moving to the right at 17.1 m/s strikes a stationary 2.31 kg blue ball. If the final velocity of the red ball is 13.5 m/s at 23.0° above the horizontal, determine the final velocity of the blue ball.

32. Momentum in 2-D • Momentum is conserved • Write a x and y equation. • For x: prx + pbx = prx’ + pbx’ • For y: pry + pby = pry’ + pby’ • Resolve v in vx and vy or determine the resultant • Find angle • Blue ball is traveling at 3.66 m/s at an angle of 48.4° below the horizontal

33. Momentum in 2-D • A 1.20 kg red ball moving at 10.0 m/s strikes a 2.31 kg blue ball moving at 15.0 m/s. If the final velocity of the red ball is 13.5 m/s, determine the final velocity of the blue ball. Make use of the angles drawn in the following diagram.

34. Momentum in 2-D • Blue ball is moving at 10.5 m/s at an angle of 23 degree above the horizon

35. Chapter 9: R pg 191 • 13) A 1325 kg car moving north at 27.0 m/s collides with a 2165 kg car moving east at 17.0 m/s. They stick together. Draw vector diagram of the collision. In what direction and with what speed do they move after the collision? • 44.2 ° NE, 14.7 m/s

36. Chapter 9: R pg 191 • 14) A 6.0 kg object, A, moving at velocity 3.0 m/s, collides with 6.0 kg object, B, at rest. After the collision, A moves off in a direction 40.0° to the left of its original direction. B moves off in a direction 50.0° to the right of A’s original direction? a) Draw a vector diagram and determine the momenta of object A and object B after the collision. b) What is the velocity of each object after the collision? • pa’ = 14 kg m/s; pb’ = 12 kgm/s; va’ = 2.3 m/s 40° to left; vb’ = 2.0 m/s 60° to left

37. Chapter 9: R pg 191 • 15) A stationary billiard ball, mass 0.17 kg, is struck by an identical ball moving at 4.0 m/s. After the collision, the second ball moves off at 60° to the left of its original direction. The stationary ball moves off at 30° to the right of the second ball’s original direction. What is the velocity of each ball after the collision? • va’ = 3.5 m/s 30° to right; vb’ = 2.0 m/s 60° to left

38. Answers: R pg 194 22) 5.0 m/s west 23) 1: -1.5 24) 10 m/s 25) 0.041 m/s, yes 26) –0.500 kgm/s; -0.995 kgm/s 27) 0.22 m/s 28) 3.1 m/s; 1.24 m/s; 1.6 s; 0.99 m 29) 3.6 kgm/s 34° NW; 1.8 m/s 34° NW 30) 5.4 Ns 22° from original direction 31) 170 kg 34) 1800 N; 3600 N

39. LAB WRITE UP • Introduction (background, objective, theories etc.) • Materials • Procedure (You must include step by step directions including diagrams. Directions should be written so that anyone can follow the steps to rebuild your bridge.) • Data/Calculations Mass of the bridge, Mass of the load, Mass ratio of bridge/load • Conclusion (errors, theories summarize what happened, what can you do better, etc)

40. GRADING • Construction: (50 pts) A) 30 pts: building the bridge without any violation of the rules and materials above. B) 3 pts: lightest bridge C) 3 pts: holds the heaviest load D) 5 pts: lowest bridge to mass ratio in each respective class, the remaining 9 points will be distributed among the other teams in the class based on their ratios. • Lab Report: (50 pts)

41. DUE DATES • DUE DATE for the BRIDGE: Friday, January 12, 2007 • DUE DATE for the LAB REPORTS: The day after you test your bridge! • ALL LONG TERM PROJECTS ARE DUE ON THEIR DUE DATES!! A 10 % DEDUCTION FOR EACH DAY WILL BE ASSESSED ON LATE PROJECTS! THIS INCLUDES THE WEEKENDS! IF YOU PLAN TO BE ABSENT ON THAT DATE, YOU NEED TO TURN IT IN EARLIER OR HAVE SOMEONE BRING IT IN