WEEK 1_MOMENTUM AND IMPULSE. Grade 9 momentum.pptx

Momentum: A Comprehensive Exploration

Introduction

Momentum is a fundamental concept in physics that describes the quantity of motion an object possesses. It plays a crucial role in understanding the behavior of moving objects and is widely applied in various fields, including engineering, sports, transportation, and even finance. This article delves into the principles of momentum, its mathematical formulation, applications, conservation laws, and real-world significance.

Defining Momentum

Momentum, denoted by p, is a vector quantity defined as the product of an object's mass (m) and velocity (v):



Since velocity is a vector quantity, momentum also has both magnitude and direction. The unit of momentum in the International System (SI) is kilogram meter per second (kg·m/s).

Types of Momentum

Momentum can be categorized into different types based on the context of motion:

Linear Momentum: The standard definition of momentum, which applies to objects moving in a straight line.

Angular Momentum: The rotational equivalent of linear momentum, which applies to rotating bodies and depends on moment of inertia and angular velocity.

The Concept of Impulse

Impulse is the change in momentum caused by an external force acting over a period of time. Mathematically, impulse (J) is given by:



where F is the force applied, and Δt is the time duration for which the force is exerted. By Newton’s Second Law, impulse is equal to the change in momentum:



This principle explains why airbags in vehicles reduce injuries; they increase the time over which a force acts, thereby reducing the impact.

Conservation of Momentum

One of the most crucial principles in physics is the Law of Conservation of Momentum, which states:

“In a closed system with no external forces, the total momentum remains constant before and after an event.”

Mathematically:



This law is particularly useful in analyzing collisions and explosions.

Types of Collisions

Momentum conservation is widely used in understanding different types of collisions:

Elastic Collisions: Both momentum and kinetic energy are conserved. Example: Collisions between gas molecules.

Inelastic Collisions: Momentum is conserved, but kinetic energy is not. Example: A car crash where the vehicles stick together.

Perfectly Inelastic Collisions: The colliding objects stick together and move as one unit after collision.

Applications of Momentum

Momentum is extensively applied across various domains:

Sports: Understanding momentum helps athletes improve performance in sports like football, baseball, and tennis.

Transportation: Car safety designs rely on momentum principles, such as crumple zones and seatbelts.

Space Science: Rockets use momentum conservation principles for propulsion.

Finance and Economics: In stock markets, momentum investing strategies predict trends based on past performance.

Advanced Concepts

Relativistic Momentum

In Einstein’s theory of relativity, momentum is modified for objec

1. LEARNING TARGETS Define momentum and impulse and relate them to each other. Solve situational problems using Impulse – Momentum Theorem Associate the concept of momentum and impulse to the collision of objects.

2. Momentum & Impulse

3. Momentum & Impulse VS. Which ball would likely hurt you and why? A ball being tossed or a ball being thrown?

4. Which would likely receive more damage when it hits a wall? The car or the truck? VS. Momentum & Impulse

5. Momentum object - mass object - motion

6. Momentum property of a moving object depends on two factors: mass and velocity product of mass and velocity p = mass x velocity or p = mv p = kg m/s

7. Which of the pair of objects in the list has a greater magnitude of momentum? Use the symbol > or < . A 50-kg man running   A 50-kg lady walking > A car at rest   A car in motion < A bowling ball rolling with a velocity of 2 m/s   A basketball rolling with a velocity of 2 m/s > An egg dropped from a height of 1 m   A feather dropped from a height of 1 m > An airplane parked in a hangar   A car going down a hill <

8. Key concepts about the momentum of the object The heavier the object, the greater the momentum. The faster the object, the greater the momentum. When comparing two objects with same mass… the faster object has greater momentum. When comparing two objects with the same velocity… the heavier object has greater momentum.

9. How can you increase your momentum as you run? a. by stopping suddenly b. by slowing down c. by sitting down d. by running faster Learning Check…

10. What happens to the momentum of an object when its mass is doubled and its velocity is constant? a. reduced to one - half b. doubled c. increased four times d. remains the same Learning Check… p = mv      

11. Can the momentum be transferred from one object to another? Yes, the momentum can  be  transferred  from one  object  to another. In an interaction, the  momentum lost by one object is equal the  momentum gained by the other. 

12. Can the momentum of the object change? A force acting for a given amount of time can  change  an  object's momentum . A force will  change  the velocity of an object. If the velocity of the object is changed, then the momentum of the object is changed.

13. Sample Problem no. 1 What is the momentum of a 1.5 x 10 4 kg truck traveling 25 m/s to the East? Given: m = 1.5 x 10 4 kg v = 25 m/s, East Solution: p = mv p = (1.5 x 10 4 kg)(25 m/s, East) p = 375,000 kg m/s, East

14. Impulse force needed to change the momentum force act in an interval of time product of the force and time I = Force x time or I = Ft I = Ns or kg m/s

15.   Impulse

16. VS. Who apply a greater impulse to the ball? The girl who toss the ball or the girl who throw the ball? Learning Check… Answer: The girl who throw the ball.

17. Key concepts about the impulse of the object If the force is applied in a shorter time, the lesser the impulse of the object. If the force is applied in a longer time, the greater the impulse of the object. In order to have a greater change in the momentum of the object, the force should be applied in a longer span of time.

18. Key concepts about the force of impact on the object The shorter the span of time of contact between two objects, the greater the force of impact. The longer the span of time of contact between two objects, the lesser the force of impact. The lighter the object, the greater the force of impact. The heavier the object, the lesser the force of impact.

19. Which would likely receive more damage when it hits a wall? The car or the truck? VS. Momentum & Impulse Answer: The car

20. Which of the following activities does not lessen the force of impact? Learning Check… A. Falling to the ground of a taekwondo player. B. Following through in racket sports. C. Hitting a hay stack. D. Using of vehicular seatbelts.

21. Impulse – Momentum Theorem The impulse on an object is equal to the change in its momentum.             X

22. If a 15 - N force acts on a body, what is the change in momentum of that body? A. 5 kg m/s B. 10 kg m/s C. 15 kg m/s D. 20 kg m/s Learning Check…

23. Sample Problem no. 1 What is the momentum of a 1.5 x 10 4 kg truck traveling 25 m/s to the East? Given: m = 1.5 x 10 4 kg v = 25 m/s, East Solution: p = mv p = (1.5 x 10 4 kg)(25 m/s, East) p = 375,000 kg m/s, East

24. Sample Problem no. 2 What is the impulse of a 1000-kg mass if a force of 3500N is applied in a span of 3 seconds in a southward direction? Given: m = 1000 kg F = 3500 N t = 3 seconds Solution: I = Force x Time I = (3500 N)(3 s) I = 10,500 Ns Southward

25. Sample Problem no. 3 How much impulse will give a 10 – kg mass a momentum change of 1000 kg m/s? Ans: I = 1000 kg m/s Impulse = change in momentum ⧍ p = 1000 kg m/s I = 1000 kg m/s

26. Sample Problem no. 4 A 45 - kg child is riding on a 15 - kg sled that is moving down a hill at a speed of 20 m/s. What is the total momentum of the child and the sled? Given: m 1 = 45 kg m 2 = 15 kg v = 20 m/s Unknown: p total = ? Solution: p total = (m 1 + m 2 ) v p total = (45 kg + 15 kg)(20 m/s) p total = 1,200 kg m/s, downhill

27. Let’s Answer This! Jenny, who has a mass of 60-kg , was riding in her car at a speed of 15 m/s . But suddenly she slammed on the brakes to avoid hitting a child who was crossing along the road. She hit the air bag that brought her body to a stop in 0.50 seconds . What average force did the air bag exert on her?

28.   Jenny, who has a mass of 60-kg , was riding in her car at a speed of 15 m/s . But suddenly she slammed on the brakes to avoid hitting a child who was crossing along the road. She hit the air bag that brought her body to a stop in 0.50 seconds . What average force did the air bag exert on her?

29.   Jenny, who has a mass of 60-kg , was riding in her car at a speed of 15 m/s . But suddenly she slammed on the brakes to avoid hitting a child who was crossing along the road. She hit the air bag that brought her body to a stop in 0.50 seconds . What average force did the air bag exert on her?

30. Let’s Answer This!  

31. ESSENTIAL QUESTION Why is it important to consider safety when driving or riding an automobile?

32. FORMATIVE ASSESSMENT NO. 1 Analyze each problem. Show your process/ computation and box your final answer.

33. FORMATIVE ASSESSMENT NO. 1 What is the impulse of a 1000-kg mass if a force of 3500 Newtons is applied in a span of 3 seconds in a southward direction?

34. FORMATIVE ASSESSMENT NO. 1 2. A 0.05 kg tennis ball is initially moving with a velocity of 22.2 m/s to the right toward a racket. After being hit by the racket, the ball rebounds and begins to move to the left at 27.8 m/s . If the ball and the strings are in contact for 0.005 s , calculate the: change in the momentum of the ball average force exerted by the racket on the ball