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# Momentum and its Conservation

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### Momentum and its Conservation

1. 1. MOMENTUM & ITS CONSERVATION Chapter 9
2. 2. The inertia of motion
3. 3. Momentum Every moving object has momentum. - Measure of HOW HARD IT WILL BE ABLE TO STOP A MOVING OBJECT. Momentum = Mass x Velocity •Equation: p = m x v • Unit: kg*m/s
4. 4. What is the relationship of momentum to mass and velocity of objects?
5. 5. • Mass and velocity are both directly proportional to the momentum.
6. 6. If the boulder and the boy have the same momentum, will the boulder crush the boy? Hint: think about the momentum formula! p = mv
7. 7. IMPULSE CHANGES MOMENTUM • TO STOP/SLOW DOWN A MOVING OBJECT - apply force to an object • IMPULSE – average net force exerted on the object multiplied by the time interval over which the force acts (application of force over a period of time) • Equation: Impulse = FΔt • Unit: N.s
8. 8. Impulse-momentum Theorem The force in the baseball increases then it decreases with collision FΔt = pf − pi
9. 9. PROBLEM SOLVING, page 237 • Under the curve is about 15N.s • Suppose the batter hits the ball. Assume that the positive direction is toward the pitcher. • Before collision of the ball and the bat, the ball with a mass of 0.145kg, has velocity of -47m/s. Therefore, the baseball’s momentum is -6.8kg.m/s. What is the momentum of the ball after the collision?
10. 10. pf = (-6.8kg.m/s) + (15kg.m/s) = +8.2 kg.m/s Impulse and Momentum Impulse-Momentum Theorem (Cont.) • Solve the impulse-momentum theorem for the final momentum. pf = pi + FΔt What is the baseball’s final velocity? Because pf = mvf, solving for vf yields the following: • 𝒗𝒇 = 𝒑 𝒇 𝒎 = +𝟖.𝟐 𝒌𝒈.𝒎/𝒔 +𝟎.𝟏𝟒𝟓 𝒌𝒈 = +57m/s
11. 11. Why it’s better for a falling tightrope- walker to hit a surface that will stretch and give (like a net), rather than a rigid surface (like the concrete floor)?
12. 12. Mass of tightrope walker = 50 kg Speed before impact = 20 m/s Momentum before contact = 1, 000 kg·m/s Momentum after impact = 0 kg · m/s Time of impact: A. concrete floor = 0.0001 s B. net = 1 s
13. 13. Force = Δ momentum / time a. Concrete Floor Force = 1,000 kg · m/s ÷ 0.0001 s = 10,000,000 kg · m/s2 b. Net Force = 1,000 kg · m/s ÷ 1 s = 1,000 kg · m/s2
14. 14. Philippe Petit • a French high-wire artist who gained fame for his high-wire walk between the Twin Towers of the World Trade Center in New York City, New York, on 7 August 1974. • He used a 450-pound (200-kilogram) cable and a custom-made 26-foot (8-metre) long, 55-pound (25-kilogram) balancing pole.
15. 15. Example of producing large impulse in a short amount of time: • a martial art expert breaking a stack of bricks using only his bare hands • Snap motions
16. 16. Before the space shuttle lands, why does it take giant S curves? To increase landing time and decrease the force of the landing
17. 17. Impulse-momentum can save lives The airbag increases time interval during which the force acts on passenger. Therefore, the required force is less. It also spreads the force over a larger area of the person’s body, therefore, reducing injuries.
18. 18. Page 238
19. 19. Date: January 12, 2016 Topic: Angular Momentum and Moment of Inertia (Chapter 9) Objective (s): To observe how conservation of momentum and changes in moment of inertia affect angular velocity. NGSS Standard:PS2.A – Forces and Motion
20. 20. Changing moment of inertia Demo Materials: rotating stools, two heavy objects Procedure: 1. sit on the stool holding the heavy object close to your body. 2. Gently spin the student seated on the stool 3. To the student seated on the stool, extend your arms and bring them back in.
21. 21. Changing moment of inertia Demo Materials: rotating stools, two heavy objects Procedure: 4. Do it again, this time, have your arms extended first before spinning, then while spinning, hold the heavy object close to your body.
22. 22. Observation: What did you observe as you spin and the heavy object is close to your body? What happened when you extended your arms?
23. 23. Getting familiar with terminologies… • Rotation action of rotating about an axis or center • Torque a force that can cause the object to rotate • Angular momentum
24. 24. Getting to our topic…page 240-241 • Observe the ball’s movement? Is it rotating or going on a linear movement? • Can angular momentum be observed in this situation?
25. 25. Getting to our topic…page 240-241 What is Angular momentum? - the product of a rotating object’s moment of inertia and angular velocity. Angular Momentum L = Iω • Angular momentum is measured in kg·m2/s.
26. 26. Angular impulse – angular momentum theorem Can angular momentum be changed? In what way? • It can be changed when angular impulse acts on it. Angular Impulse-Angular Momentum Theorem τΔt = Lf − Li
27. 27. Relating to the rotating stool demo: How does the extending and tucking the arm affects conservation of angular momentum and changes in moment of inertia? How does the extending and tucking the arm affects affect angular velocity Decrease of moment of inertia = increase in angular velocity Decrease of moment of inertia = increase in angular velocity
28. 28. Relating to the rotating stool demo: Note: • If the net force of the object is zero, its linear momentum is constant (coz mass of object cannot change). • If the net torque acting on the object is zero, its angular momentum is also constant. But this can change if the shape of the object changes thus increasing its velocity.
29. 29. Relating to the rotating stool demo: Why? Moment of inertia depends on the object’s mass and the way it is distributed about the axis of rotation or revolution, so angular velocity can change even if no torque acts on it.
30. 30. Angular Momentum: Practical Applications Decrease of moment of inertia = increase in angular velocity
31. 31. Practical Applications: - In what way the knowledge on Angular impulse – angular momentum theorem be useful to your everyday life?
32. 32. Problem solving, page 242
33. 33. Problem solving, page 242
34. 34. Conservation of Momentum
35. 35. CONSERVATION OF MOMENTUM • a total momentum of a closed system can never increase or decrease (conserved property). • The increase of momentum in one part of the system means a decrease in momentum in another part. • So, if you want to change the momentum of an object, it must be with an outside force (similar to Newton’s 2nd law).
36. 36. Two particle Collision closed system - a system, which does not gain or lose mass isolated system - When the net external force on a closed system is zero Law of conservation of momentum – momentum of any closed, isolated system does not change.
37. 37. Dale Earnhardt Sr. • While driving in the 2001 Daytona 500, Earnhardt died of basilar skull fracture in a last-lap crash at Daytona International Speedway on February 18, 2001
38. 38. • The apparatus below consists of 5 suspended balls of equal masses. If one of the ball was lifted and made to swing towards the 4 other stationary balls, what will happen? Explain how this is an example of the conservation of momentum.
39. 39. ANALYSIS 2. There is something wrong with this scenario. What is it? Explain your answer. BEFORE COLLISION 2 m/s 0 m/s A B C A B C AFTER COLLISION 0 m/s 1 m/s 1m/s A B C
40. 40. Problem solving, page 246 A 1875-kg car going 23 m/s rear-ends a 1025-kg compact car going 17 m/s on ice in the same direction. The two cars stick together. How fast do the two cars move together immediately after the collision? Known: mC = 1875 kg vCi = +23 m/s mD = 1025 kg vDi = +17 m/s Unknown: vf = ?
41. 41. Problem solving, page 246 pi = pf pCi + pDi = pCf + pDf mCvCi + mDvDi = mCvCf + mDvDf vCf = vDf = vf mCvCi + mDvDi = (mC + mD) vf
42. 42. Recoil The skaters’ momentums after the push are equal in magnitude but opposite in direction. The backward motion of skater C is an example of recoil.
43. 43. Recoil: Practical Applications The rocket and the chemicals form: closed system Forces that expel the gases are internal forces: Isolated system Thus, objects in space can accelerate using the law of conservation of momentum and Newton’s third law of motion.
44. 44. Two-Dimensional Collisions The momentum is conserved in a closed, isolated system, regardless of the velocities of the objects before a collision.
45. 45. Problem solving, page 250
46. 46. Conservation of Angular Momentum law of conservation of angular momentum - if no net external torque acts on an object, then its angular momentum does not change. Lf = Li Li = Lf thus, Iiωi = Ifωf
47. 47. Conservation of Angular Momentum law of conservation of angular momentum - if no net external torque acts on an object, then its angular momentum does not change. Lf = Li Li = Lf thus, Iiωi = Ifωf