Answer:
a) 0.20 m/s
b) 0.40 m/s
c) 0.12 m/s
Explanation:
Momentum before collision = momentum after collision
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
a) After the collision, they stick together and move at the same speed, so v₁ = v₂.
m₁u₁ + m₂u₂ = (m₁ + m₂) v
(0.20 kg) (0.60 m/s) + (0.40 kg) (0 m/s) = (0.20 kg + 0.40 kg) v
0.12 kg m/s = 0.60 kg v
v = 0.20 m/s
b) If v₂ = 0.10 m/s:
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
(0.20 kg) (0.60 m/s) + (0.40 kg) (0 m/s) = (0.20 kg) v + (0.40 kg) (0.10 m/s)
0.12 kg m/s = 0.20 kg v + 0.04 m/s
0.08 kg m/s = 0.20 kg v
v = 0.40 m/s
c) If v₁ = v₂ / 2:
(0.20 kg) (0.60 m/s) + (0.40 kg) (0 m/s) = (0.20 kg) v₁ + (0.40 kg) (2v₁)
0.12 kg m/s = 0.20 kg v₁ + 0.80 kg v₁
0.12 kg m/s = 1.00 kg v₁
v₁ = 0.12 m/s
