Preview. Momentum and Collisions Section 1. Section 1 Momentum and Impulse. Section 2 Conservation of Momentum

Transcription

1 Momentum and Collisions Section 1 Preview Section 1 Momentum and Impulse Section 2 Conservation of Momentum Section 3 Elastic and Inelastic Collisions Houghton Mifflin Harcourt Publishing Company

2 Momentum and Collisions Section 1 TEKS The student is expected to: 6C calculate the mechanical energy of, power generated within, impulse applied to, and momentum of a physical system Houghton Mifflin Harcourt Publishing Company

3 Momentum and Collisions Section 1 What do you think? Imagine an automobile collision in which an older model car from the 1960s collides with a car at rest while traveling at 15 mph. Now imagine the same collision with a 2007 model car. In both cases, the car and passengers are stopped abruptly. List the features in the newer car that are designed to protect the passenger and the features designed to minimize damage to the car. How are these features similar? Houghton Mifflin Harcourt Publishing Company

4 Momentum and Collisions Section 1 What do you think? What are some common uses of the term momentum? Write a sentence or two using the term momentum. Do any of the examples provided reference the velocity of an object? Do any of the examples reference the mass of an object? Houghton Mifflin Harcourt Publishing Company

5 Momentum and Collisions Section 1 Momentum Momentum (p) is proportional to both mass and velocity. A vector quantity SI Units: kg m/s Houghton Mifflin Harcourt Publishing Company

6 Momentum and Collisions Section 1 Momentum and Newton s 2nd Law Prove that the two equations shown below are equivalent. F = ma and F = Δp/Δt Newton actually wrote his 2nd Law as F = Δp/Δt. Force depends on how rapidly the momentum changes. Houghton Mifflin Harcourt Publishing Company

7 Momentum and Collisions Section 1 Impulse and Momentum The quantity FΔt is called impulse. SI units: N m or kg m/s Impulse equals change in momentum. Another version of Newton s 2nd Law Changes in momentum depend on both the force and the amount of time over which the force is applied. Houghton Mifflin Harcourt Publishing Company

8 Momentum and Collisions Section 1 Impulse-Momentum Theorem Click below to watch the Visual Concept. Visual Concept Houghton Mifflin Harcourt Publishing Company

9 Momentum and Collisions Section 1 Changing momentum Greater changes in momentum(δp) require more force (F) or more time (Δt). A loaded truck requires more time to stop. Greater Δp for truck with more mass Same stopping force

10 Momentum and Collisions Section 1 Classroom Practice Problems A 1350 kg car has a velocity of 22.0 m/s to the north. When braking rapidly, it stops in 4.50 s. What was the momentum of the car before braking? What is the magnitude of the force required to stop the car? Answers: 2.97 x 10 4 kg m/s to the north 6.60 x 10 3 N Houghton Mifflin Harcourt Publishing Company

11 Momentum and Collisions Section 1 Stopping Time FΔt = Δp = Δmv When stopping, Δp is the same for rapid or gradual stops. Increasing the time (Δt) decreases the force (F). What examples demonstrate this relationship? Air bags, padded dashboards, trampolines, etc Decreasing the time (Δt) increases the force (F). What examples demonstrate this relationship? Hammers and baseball bats are made of hard material to reduce the time of impact. Houghton Mifflin Harcourt Publishing Company

12 Momentum and Collisions Section 1 Classroom Practice Problems A 65 kg passenger in a car travels at a speed of 8.0 m/s. If the passenger is stopped by an airbag in 0.75 s, how much force is required? Answer: 6.9 x 10 2 N If the car does not have an air bag and the passenger is instead stopped in s when he strikes the dashboard, by what factor does the force increase? Answer: F = 2.0 x 10 4 N so it is 29 times greater Houghton Mifflin Harcourt Publishing Company

13 Momentum and Collisions Section 1 Now what do you think? Imagine an automobile collision in which an older model car from the 1960s collides with a car at rest while traveling at 15 mph. Now imagine the same collision with a 2007 model car. In both cases, the car and passengers are stopped abruptly. List the features in the newer car that are designed to protect the passenger and the features designed to minimize damage to the car. How are these features similar? Houghton Mifflin Harcourt Publishing Company

14 Momentum and Collisions Section 1 Now what do you think? How is momentum defined? How is Newton s 2nd Law written using momentum? What is impulse? What is the relationship between impulse and momentum? Houghton Mifflin Harcourt Publishing Company

15 Momentum and Collisions Section 2 TEKS The student is expected to: 6D demonstrate and apply the laws of conservation of energy and conservation of momentum in one dimension

16 Momentum and Collisions Section 2 What do you think? Two skaters have equal mass and are at rest. They are pushing away from each other as shown. Compare the forces on the two girls. Compare their velocities after the push. How would your answers change if the girl on the right had a greater mass than her friend? How would your answers change if the girl on the right was moving toward her friend before they started pushing apart?

17 Momentum and Collisions Section 2 Momentum During Collisions When the bumper cars collide, F 1 = -F 2 so F 1 Δt = -F 2 Δt, and therefore Δp 1 = -Δp 2. The change in momentum for one object is equal and opposite to the change in momentum for the other object. Total momentum is neither gained not lost during collisions.

18 Momentum and Collisions Section 2 Conservation of Momentum Total momentum remains constant during collisions. The momentum lost by one object equals the momentum gained by the other object. Conservation of momentum simplifies problem solving.

19 Momentum and Collisions Section 2 Conservation of Momentum Click below to watch the Visual Concept. Visual Concept

20 Momentum and Collisions Section 2 Classroom Practice Problems A 62.0 kg astronaut on a spacewalk tosses a kg baseball at 26.0 m/s out into space. With what speed does the astronaut recoil? Step 1: Find the initial momentum of both astronaut and baseball. Answer: zero because v i = 0 for both Step 2: Since p i = 0, then p f, astronaut = -p f, baseball Step 3: Substitute and solve for v f,astronaut Answer: m/s or cm/s Does a pitcher recoil backward like the astronaut when throwing the ball? Explain.

21 Momentum and Collisions Section 2 Classroom Practice Problem Gerard is a quarterback and Tyler is a defensive lineman. Gerard s mass is 75.0 kg and he is at rest. Tyler has a mass of 112 kg, and he is moving at 8.25 m/s when he tackles Gerard by holding on while they fly through the air. With what speed will the two players move together after the collision? Answer: 4.94 m/s

22 Momentum and Collisions Section 2 Now what do you think? Two skaters have equal mass and are at rest. They are pushing away from each other as shown. Compare the forces on the two girls. Compare their velocities after the push. How would your answers change if the girl on the right had a greater mass than her friend? How would your answers change if the girl on the right was moving toward her friend before they started pushing apart?

23 Momentum and Collisions Section 3 TEKS The student is expected to: 6D demonstrate and apply the laws of conservation of energy and conservation of momentum in one dimension

24 Momentum and Collisions Section 3 What do you think? Collisions are sometimes described as elastic or inelastic. To the right is a list of colliding objects. Rank them from most elastic to most inelastic. What factors did you consider when ranking these collisions? 1. A baseball and a bat 2. A baseball and a glove 3. Two football players 4. Two billiard balls 5. Two balls of modeling clay 6. Two hard rubber toy balls 7. An automobile collision

25 Momentum and Collisions Section 3 Perfectly Inelastic Collisions Two objects collide and stick together. Two football players A meteorite striking the earth Momentum is conserved. Masses combine.

26 Momentum and Collisions Section 3 Classroom Practice Problems An 2.0 x 10 5 kg train car moving east at 21 m/s collides with a 4.0 x 10 5 kg fully-loaded train car initially at rest. The two cars stick together. Find the velocity of the two cars after the collision. Answer: 7.0 m/s to the east Now calculate the kinetic energy of the two cars before and after the collision. Was kinetic energy conserved? Answer: KE before = 4.4 x 10 7 J, KE after = 1.5 x 10 7 J KE is not conserved. It is less after the collision.

27 Momentum and Collisions Section 3 Inelastic Collisions Kinetic energy is less after the collision. It is converted into other forms of energy. Internal energy - the temperature is increased. Sound energy - the air is forced to vibrate. Some kinetic energy may remain after the collision, or it may all be lost.

28 Momentum and Collisions Section 3 Elastic Collisions Objects collide and return to their original shape. Kinetic energy remains the same after the collision. Perfectly elastic collisions satisfy both conservation laws shown below.

29 Momentum and Collisions Section 3 Elastic Collisions Two billiard balls collide head on, as shown. Which of the following possible final velocities satisfies the law of conservation of momentum? vf,a = 2.0 m/s, vf,b = 2.0 m/s vf,a = 0 m/s, vf,b = 4.0 m/s vf,a = 1.5 m/s, vf,b = 2.5 m/s Answer: all three m = 0.35 kg m = 0.35 kg v = 4.0 m/s v = 0 m/s

30 Momentum and Collisions Section 3 Elastic Collisions Two billiard balls collide head on, as shown. Which of the following possible final velocities satisfies the law of conservation of kinetic energy? vf,a = 2.0 m/s, vf,b = 2.0 m/s vf,a = 0 m/s, vf,b = 4.0 m/s vf,a = 1.5 m/s, vf,b = 2.5 m/s Answer: only vf,a = 0 m/s, vf,b = 4.0 m/s m = 0.35 kg m = 0.35 kg v = 4.0 m/s v = 0 m/s

31 Momentum and Collisions Section 3 Types of Collisions Click below to watch the Visual Concept. Visual Concept

32 Momentum and Collisions Section 3 Types of Collisions

33 Momentum and Collisions Section 3 Now what do you think? To the right is a list of colliding objects. Rank them from most elastic to most inelastic. What factors did you consider when ranking these collisions? 1. A baseball and a bat 2. A baseball and a glove 3. Two football players 4. Two billiard balls 5. Two balls of modeling clay 6. Two hard rubber toy balls 7. An automobile collision