Lecture on Momentum

Introduction to Momentum

• Momentum is symbolized by lowercase p.
• Defined as the product of mass and velocity (p = m × v).
• Described as "mass in motion".
• Mass:
  • Scalar quantity (no direction).
  • Example: 50 kg block (no directional component)
• Velocity:
  • Vector quantity (has magnitude and direction).
  • Example: Car moving 30 m/s east.
• Momentum:
  • Like velocity, it is a vector and has direction.

Calculating Momentum

• Formula: p = m × v
• Example Calculation:
  • 15 kg block moving at 8 m/s:
  • Momentum = 15 × 8 = 120 kg·m/s
  • Direction is same as velocity (e.g., east if velocity is east).

Example Problem: Bullet

• Given: Mass = 1.5 grams; Momentum = 1.2 kg·m/s
• Convert mass to kg: 1.5 grams = 0.0015 kg
• Calculate velocity:
  • v = p / m = 1.2 / 0.0015 = 800 m/s

Relationship Between Momentum and Force

• Momentum formula divided by time (t):
  • velocity/time = acceleration (a)
  • Change in momentum over time = mass × acceleration
• Newton's Second Law: Force = mass × acceleration
  • Rate of change in momentum equals net force.

Example Problem: Force and Block

• Given:
  • 5 kg block, initial velocity = 0, final velocity = 20 m/s, time = 4s.
• Calculate change in momentum:
  • Δp = m × Δv = 5 × (20 - 0) = 100 kg·m/s
• Calculate average force:
  • F = Δp / Δt = 100 / 4 = 25 N
• Alternative calculation using acceleration:
  • a = Δv / Δt = 20 / 4 = 5 m/s²
  • F = m × a = 5 kg × 5 m/s² = 25 N

Force Exerted by a Hose

• Given:
  • Mass flow rate = 15 kg/s, speed = 30 m/s
• Calculate force:
  • F = (Δm/Δt) × v = 15 × 30 = 450 N

Example Problem: Collision

• Given:
  • 10 kg ball at 6 m/s, 5 kg ball at rest, contact time = 0.5 s.
• Calculate force on 10 kg ball:
  • Δp = m × Δv = 10 × (0 - 6) = -60 kg·m/s
  • F = Δp / Δt = -60 / 0.5 = -120 N
• Calculate force on 5 kg ball:
  • By Newton's Third Law, force is +120 N.
• Conservation of Momentum:
  • Total momentum before and after collision is the same.
  • Purpose of force: Transfer momentum between objects.