Lesson_1_-_Momentum___Impulse

Momentum & Impulse

Introduction to Concepts

• Momentum: Defined as the product of an object’s mass and its velocity, denoted as [ p = mv ]

  • Unit of measurement: kg ● m/s

• Impulse: Defined as the product of the net force acting on an object and the time duration over which the force acts.

  • Expressed as: [ J = F_{net} imes t ]

  • Same units as momentum: kg ● m/s or N ● s

Do Now Activity

• Scenario: A football player's attempt to score at the goal line while a defender tries to stop him.

  • Key Determining Factors:

    • The momentum of the player and defender.

    • The net forces acting on both players.

Collisions

Considerations

• Instances of Collisions: Examples may include vehicle crashes, sports, and object impacts. Description varies.

• Factors Affecting Collisions:

  • Mass and speed of the colliding objects.

  • Angle and point of impact.

  • Type of collision (elastic vs. inelastic).

Key Terms

• Momentum: vector quantity (mass times velocity).

• Inelastic Collision: two objects stick together post-collision.

• Elastic Collision: two objects bounce off each other.

• Conservation of Momentum: total momentum before collision equals total momentum after.

Formulas

• Total Momentum: [ p = mv ]

• Impulse: [ J = F_{net} t ]

• Acceleration: [ a = \frac{\Delta v}{t} ]

• Motion equations:

  • [ v_f = v_i + at ]

  • [ d = v_i t + \frac{1}{2}a t^2 ]

  • [ v^2_f = v^2_i + 2ad ]

Defining Momentum

• [ p = mv ]

  • Where:

    • ( p ): momentum

    • ( m ): mass (kg)

    • ( v ): velocity (m/s)

• Key Properties:

  • Vector quantity with magnitude and direction.

  • Conserved in isolated systems.

  • Influenced by net forces acting on an object.

Understanding Momentum

• Characteristics:

  • Proportional to both mass and speed.

  • A big, slow object can have equivalent momentum as a small, fast object.

Equivalent Momenta Examples

• School Bus:

  • Mass: 9000 kg

  • Velocity: 16 m/s

  • Momentum: ( p = 1.44 \times 10^5 \text{ kg ● m/s} )

• Sports Car:

  • Mass: 1800 kg

  • Velocity: 80 m/s

  • Momentum: ( p = 1.44 \times 10^5 \text{ kg ● m/s} )

• Hogwarts Express:

  • Mass: 36000 kg

  • Velocity: 4 m/s

  • Momentum: ( p = 1.44 \times 10^5 \text{ kg ● m/s} )

Impulse

• Defined as:

  • [ J = (F_{net}) t ]

  • Units: N ● s = kg ● m/s

• Implication: Impulse and momentum share the same units.

Impulse-Momentum Theorem

• States that impulse is equal to the change in momentum:

  • [ F_{net} t = \Delta p ]

  • Implication: Any net force can bring an object to rest if applied over a sufficient time.

Concept Questions

Stopping Force Comparison

• Situation: Compare magnitudes to stop a car in 12 seconds vs. 6 seconds.

Skater Impulses

• Scenario: Two ice skaters pushing off from each other. Impulse and resulting speeds.

  1. Which skater experiences greater impulse?

  2. Which skater has greater speed after push-off?

Examples

Example 1

• Object: 5.0 kg with initial velocity 8.0 m/s (East).

• Force duration: 3.0 seconds, velocity decreases to 2.0 m/s (East).

• Calculate: Magnitude and direction of unbalanced force.

Example 2

• Object: 2.0 x 10^3 kg car accelerates from rest to 15 m/s in 5.0 seconds.

• Find: Magnitude of net force acting on the car.

Example 3

• Bullet: Traveling at 5.0 x 10^2 m/s, brought to rest by a 50 N ● s impulse.

• Calculate: Mass of the bullet.

Example 4

• Baseball: 145 g ball hits the bat at 15 m/s, leaves at 20 m/s (opposite direction).

  • Find: Magnitude of impulse delivered by the bat. Average force if contact time is 1.5 ms.