Science 9 Momentum

Momentum

• Definition: The tendency of an object to remain in motion.

  • Factors:

    • Mass

    • Velocity

Calculation of Momentum

• Formula: p = m * v

  • Where p is momentum, m is mass, and v is velocity.

  • Unit of momentum: kg·m/s.

Practice Problem 1

• Given: Mass = 4.5 kg, Velocity = 20 m/s [east].

• Task: Calculate momentum.

Momentum and Impulse

• Concept: Momentum is a frequently used term in sports; an object with momentum is challenging to stop.

  • To stop it, a force must be applied over time, changing the object’s velocity and momentum.

Real-World Observations

• Examples:

  • In football, momentum influences gameplay.

  • Driving Example: The brakes apply force to stop the car’s momentum when approaching a stop sign.

Newton’s Second Law and Momentum

• Newton's 2nd Law: F_net = m * a can be rewritten relating to momentum:

  • F_net = m * (Δv/t)

  • Rewritten as F_net * t = m * Δv.

Impulse

• Definition: Impulse (J) = F * t = Δp

  • Dimension: kg·m/s = Newton·second

  • Impulse delivered changes momentum: Impulse = Change in Momentum.

Practice Problem 2

• Given: 5 kg object, Initial Velocity = 3 m/s, Final Velocity = 7 m/s [east].

• Tasks: a) Calculate initial momentum. b) Calculate final momentum. c) Determine change in momentum. d) Compute impulse delivered. e) Calculate force magnitude and direction, given time of 0.20 seconds.

Conservation of Momentum

• Closed System: In collisions without external forces, momentum is conserved.

  • Forces between two objects are equal in magnitude and opposite in direction (Newton's 3rd Law).

Collision Dynamics

• Force-Time Relationship: F1 * t1 = -F2 * t2.

• Momentum Change: m1 * Δv1 = -m2 * Δv2.

Momentum Equation Manipulation

• Manipulation: m1 * v1,f - m1 * v1,i = - (m2 * v2,f - m2 * v2,i)

  • Final expression: m1 * v1,i + m2 * v2,i = m1 * v1,f + m2 * v2,f

  • Conclusion: p_before = p_after (Law of Conservation of Momentum).

Overview of Conservation of Momentum

• Law: The momentum lost by one object equals the momentum gained by another in a collision.

Example Problem: Collision

• Objects: Car (mass = 1000 kg, velocity = 20 m/s) vs Truck (mass = 3000 kg, velocity = -20 m/s).

  • Calculate momentum for both.

Additional Practice

• Task: Gun fires bullet - calculate the recoil velocity of the gun when bullet exits at 800 m/s [east].

Review Materials

• Practice: Review specific problems from the practice book related to momentum.

Real-World Applications

• Collision Force Applications: The effect of time on collision force experienced by objects during impact.

Effect of Collision Time

• Example Calculations: For 100 kg·m/s momentum:

  • More time reduces force:

    • 200 N * 0.5 sec = 100 kg·m/s

    • 100 N * 1 sec = 100 kg·m/s

    • 50 N * 2 sec = 100 kg·m/s

    • 25 N * 4 sec = 100 kg·m/s

Minimizing Collision Impact

• Strategy: Increase collision time reduces force; decrease time increases force.

• Examples:

  • Boxers extend the time of a punch to minimize force.

  • Rock climbers use nylon ropes that stretch to reduce the force in falls.

Behavioral Insights on Collision Physics

• Quote from Einstein: "Teaching should be such that what is offered is perceived as a valuable gift and not as a hard duty."

The Effect of Rebounding

• Rebounding Definition: Objects bounce off each other, changing direction post-collision.

Rebounding Dynamics

• Automobiles: Cars are designed to minimize rebounding through crumple zones that extend collision time.