Velocity after Collision: Analyzing the Impact of Mass and Velocity
How does the mass and velocity of objects affect their final velocity after collision?
Given the scenario of a red wagon with a mass of 7 kg moving towards a blue wagon at rest, where the red wagon's mass is 7 times that of the blue wagon and the final velocity of the red wagon is 3 m/s, how can we calculate the final velocity of the blue wagon after the collision?
Calculating the Final Velocity of the Blue Wagon
Using the principle of conservation of momentum, we can determine the final velocity of the blue wagon after the collision.
When analyzing collisions between objects with different masses and velocities, the final velocities are influenced by both the mass and initial velocities of the objects involved. In this scenario, the red wagon with a mass of 7 kg and an initial velocity of 4 m/s collides with the blue wagon at rest, whose mass is 1 kg (mass ratio of 1:7).
After the collision, the final velocity of the red wagon is given as 3 m/s. To calculate the final velocity of the blue wagon, we can apply the equation:
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
where m₁ and u₁ represent the mass and initial velocity of the red wagon respectively, m₂ and u₂ represent the mass and initial velocity of the blue wagon, and v₁ and v₂ represent the final velocities of the red and blue wagons respectively.
Plugging in the values:
(7 x 4) + (1 x 0) = (7 x 3) + (1 x v₂)
28 + 0 = 21 + v₂
28 - 21 = v₂
v₂ = 7 m/s
Therefore, the final velocity of the blue wagon after the collision is 7 m/s. This result highlights the impact of mass and velocity on the outcome of collisions, demonstrating the importance of conservation laws in analyzing such scenarios.