Momentum

Momentum and Impulse

Definitions of Momentum

• General Definition: Momentum can be anything, yet it poses complexity in its definition.

• Scientific Definition: Inertia in motion.

Stopping Force Comparison

• Question A: Which will be harder to stop?

• Context: Examination of objects with different masses and velocities affecting stopping force.

Linear Momentum

• Definition: Linear momentum (𝑝) = mass (𝑚) × velocity (𝑣)

• Equation: 𝑝 = 𝑚𝑣

Momentum Calculation Examples

• Example A: Calculate the momentum of a 110-kg football player running at 8.00 m/s.

• Example B: Compare the football player’s momentum to that of a 0.410-kg football thrown at 25.0 m/s.

Relationship of Momentum and Force

• Equations:1. 𝐹 = 𝑚𝑎 = 𝑚(∆𝑣/∆𝑡)2.** 𝐹 = ∆𝑝/∆𝑡

• Key Concept: Force applied over time changes momentum.

• Importance of Momentum-Focused Measurements: Energy is force over distance; Momentum is force over time.

Impulse

• Definition: Effect of force depends on duration and magnitude.

• Equation: 𝐹Δ𝑡 = Δ𝑝

• Key Aspects: Larger force or longer application time leads to larger impulse and momentum change.

Importance of Impulse in Real-Life Scenarios

• Consideration: Certain objects withstand a limited impulse; changing force or time impacts impulse.

Example Problem: Force Exerted by Seat Belt

• Scenario: A car stopped quickly after crashing into a tree.

• Details:

  • Speed: 10 m/s

  • Stopping Time: 0.26 s

  • Passenger's Mass: 70 kg

• Calculation Requirement: Find the seat belt force to halt the passenger.

Conservation of Momentum

• Fundamental Principle: Like energy, momentum is conserved. Initial momentum equals final momentum if no net force acts.

• Formulation: P_initial = P_final

Analyzing Collisions

• Context: Momentum is often analyzed in collisions.

• Types of Collisions:

  • Elastic: Both momentum and kinetic energy conserved.

  • Inelastic: Momentum conserved, kinetic energy not conserved.

Elastic Collisions

• Characterization: Objects collide and separate, conserving both momentum and kinetic energy.

• Collision Formula:

  • For two objects: PiA + PiB = PfA + PfB

Inelastic Collisions

• Characterization: Objects collide and move as one mass; only momentum is conserved.

• Collision Formula:

  • For two objects: PiA + PiB = PfA + PfB; Vf is the same post-collision.

Calculation Examples for Collisions

• Example 1:

  • 0.500 kg and 3.50 kg collide; find velocity of 3.50 kg object post-elastic collision.

  • Initial conditions and post-collision velocities provided.

• Example 2:

  • Find velocity of a 70.0-kg goalie catching a 0.150-kg hockey puck.

  • Puck moves at 35.0 m/s initially, rebounds at 30 m/s.

Recoil Velocity Example

• Scenario: Find the recoil velocity of a goalie who catches a puck after a collision that initiates from rest.

• Details: 70.0 kg goalie, 0.150 kg puck, starting referenced speed provided.