1. a) Momentum before = (2 kg)(3 m/s) + (4 kg)(0 m/s) = 6 kg·m/s
Momentum after = (2 kg + 4 kg)(v) = 6v kg·m/s
Conservation: 6 = 6v → v = 1 m/s
b) Momentum before = (2 kg)(3 m/s) + (4 kg)(-1 m/s) = 6 - 4 = 2 kg·m/s
Momentum after = (2 kg + 4 kg)(v) = 6v kg·m/s
Conservation: 2 = 6v → v = 1/3 m/s ≈ 0.33 m/s
c) Momentum before = (2 kg)(3 m/s) + (4 kg)(-3 m/s) = 6 - 12 = -6 kg·m/s
Momentum after = (2 kg + 4 kg)(v) = 6v kg·m/s
Conservation: -6 = 6v → v = -1 m/s
2. a) Momentum before = (1 kg)(5 m/s) + (4 kg)(0 m/s) = 5 kg·m/s
Momentum after = (1 kg + 4 kg)(v) = 5v kg·m/s
Conservation: 5 = 5v → v = 1 m/s
b) Kinetic energy before = (1/2)(1 kg)(5 m/s)² + (1/2)(4 kg)(0 m/s)² = 12.5 J
Kinetic energy after = (1/2)(5 kg)(1 m/s)² = 2.5 J
Energy lost = 12.5 J - 2.5 J = 10 J
3. Momentum before = (0.02 kg)(300 m/s) + (2 kg)(0 m/s) = 6 kg·m/s
Momentum after = (0.02 kg + 2 kg)(v) = 2.02v kg·m/s
Conservation: 6 = 2.02v → v = 6 / 2.02 ≈ 2.97 m/s
Parent Tip: Review the logic above to help your child master the concept of conservation of momentum worksheet answers chapter 8.
