1. Define the system and choose a direction as positive.
- System: The two cars.
- Let the rightward direction be positive.
2. Write the conservation of momentum equation.
- Total momentum before collision = Total momentum after collision
- (m₁ * v₁i) + (m₂ * v₂i) = (m₁ * v₁f) + (m₂ * v₂f)
3. Substitute the known values into the equation.
- m₁ = 1 kg, v₁i = +2 m/s, v₁f = -1 m/s
- m₂ = 2 kg, v₂i = -2 m/s, v₂f = ?
- (1 kg * +2 m/s) + (2 kg * -2 m/s) = (1 kg * -1 m/s) + (2 kg * v₂f)
4. Calculate the total momentum before the collision.
- (1)(+2) + (2)(-2) = +2 - 4 = -2 kg·m/s
5. Calculate the total momentum after the collision (leaving v₂f as unknown).
- (1)(-1) + (2)(v₂f) = -1 + 2*v₂f
6. Set the two expressions equal and solve for v₂f.
- -2 = -1 + 2*v₂f
- -2 + 1 = 2*v₂f
- -1 = 2*v₂f
- v₂f = -1 / 2
- v₂f = -0.5 m/s
7. State the final answer with direction.
- The final velocity of the car on the right-hand side is 0.5 m/s to the left.
Parent Tip: Review the logic above to help your child master the concept of worksheet conservation of momentum.
