Question

A blue marble of mass 15 g moving to the right with velocity 8 ms^ - 1 collides with a red marble of the same mass but moving at the opposite direction with velocity 4.0 ms^ - 1 If the collision is perfectly elastic collision, determine the final velocity of each marble after the collision​

Answer 1

Step-by-step explanation:

Let's assume:

m = mass of each marble = 15 g = 0.015 kg (converting from grams to kilograms)

v1_initial = initial velocity of the blue marble = 8 m/s (moving to the right)

v2_initial = initial velocity of the red marble = -4.0 m/s (moving at the opposite direction)

Using the conservation of momentum:

m * v1_initial + m * v2_initial = m * v1_final + m * v2_final

Using the conservation of kinetic energy:

(1/2) * m * v1_initial^2 + (1/2) * m * v2_initial^2 = (1/2) * m * v1_final^2 + (1/2) * m * v2_final^2

Solving these equations simultaneously, we get:

v1_final = (v1_initial * (m - m) + 2 * m * v2_initial) / (m + m)

v2_final = (v2_initial * (m - m) + 2 * m * v1_initial) / (m + m)

Substituting the given values:

v1_final = (8 * (0.015 - 0.015) + 2 * 0.015 * (-4.0)) / (0.015 + 0.015) ≈ -4.0 m/s

v2_final = (-4.0 * (0.015 - 0.015) + 2 * 0.015 * 8) / (0.015 + 0.015) ≈ 8.0 m/s

After the perfectly elastic collision, the blue marble will have a final velocity of approximately -4.0 m/s (moving to the left), and the red marble will have a final velocity of approximately 8.0 m/s (moving to the right).