1.6 MOMENTUM

Definitions

• Momentum: The product of an object's mass and velocity. It is a vector quantity.

• Impulse: The change in momentum of an object when a force acts on it for a certain time.

• Principle of Conservation of Momentum: The total momentum of a system remains constant, provided no external force acts on it.

• Elastic Collision: A collision where total kinetic energy and momentum are both conserved.

• Inelastic Collision: A collision where momentum is conserved but some kinetic energy is lost (as heat, sound, or deformation).

Formulas

• Momentum (p) = mass (m) × velocity (v)

• Impulse (F × t) = Change in momentum (Δp) = m × v – m × u

• Principle of Conservation of Momentum: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Worked Examples

1. Momentum Calculation A 5 kg object moves at 4 m/s. p = m × v = 5 × 4 = 20 kg·m/s

2. Impulse A force of 10 N acts on a body for 5 s. Impulse = F × t = 10 × 5 = 50 Ns = Δp

3. Inelastic Collision (Objects Stick Together) Trolley A: 2 kg, 3 m/s Trolley B: 1 kg, 0 m/s (at rest)

Initial momentum = (2 × 3) + (1 × 0) = 6 Final mass = 2 + 1 = 3 kg Final velocity = 6 ÷ 3 = 2 m/s

4. Elastic Collision (Momentum Conserved) Ball A: 1 kg, 4 m/s Ball B: 1 kg, -2 m/s (opposite direction) After collision: Ball A = 2 m/s, Ball B = 0 m/s

Initial momentum = (1 × 4) + (1 × -2) = 2 Final momentum = (1 × 2) + (1 × 0) = 2 → Conserved

5. Explosion (Inelastic) A stationary firework of mass 2 kg explodes into two pieces: Piece 1: 0.5 kg, 8 m/s right Piece 2: 1.5 kg, v m/s left

Initial momentum = 0 Final momentum = (0.5 × 8) + (1.5 × v) 0 = 4 + 1.5v v = -2.67 m/s (left)

Diagram References (for illustration):

1. Object moving with momentum (p = m × v)

2. Two bodies colliding and sticking together

3. Explosion showing conservation of momentum

 Made by Hiba Shakeel

Curated by Yassein