A ball of mass 0.5 kg moving at 4 m/s collides with a stationary ball of mass 1 kg. After the collision, the first ball moves at 1 m/s in the same direction. Find the velocity of the second ball after the collision. Verify that momentum is conserved.

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APPLYING CONSERVATION OF MOMENTUM: Given: m₁ = 0.5 kg, u₁ = 4 m/s, m₂ = 1 kg, u₂ = 0 (stationary). After collision: v₁ = 1 m/s. Find v₂. LAW: Total momentum before = Total momentum after (no external force). BEFORE COLLISION: p_before = m₁u₁ + m₂u₂ = (0.5 × 4) + (1 × 0) = 2 + 0 = 2 kg·m/s. AFTER COLLISION: p_after = m₁v₁ + m₂v₂ = (0.5 × 1) + (1 × v₂) = 0.5 + v₂. APPLYING CONSERVATION: p_before = p_after → 2 = 0.5 + v₂ → v₂ = 1.5 m/s. ANSWER: The second ball moves at 1.5 m/s in the SAME DIRECTION as the first ball's original motion. VERIFICATION: p_after = (0.5 × 1) + (1 × 1.5) = 0.5 + 1.5 = 2 kg·m/s = p_before ✓. Momentum is conserved.

Practice — Laws of Motion

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