If I were to drop a bowling ball and a marble from the same height which one will hit the floor first?

When a moving marble it’s a stationary marble, the velocity of the moving marble will decrease as the velocity of the stationary marble increases. Since momentum is product of mass and velocity, the momentum of the moving marble will decrease as the momentum of stationary marble increases. To prove that this is true, let mass of the moving marble be 0.05 kg and mass of the stationary marble be 0.025 kg.

Let the velocity of the moving marble be 4 m/s. Initial momentum = 0.05 * 4 = 0.2 Final momentum = 0.05 * v1 + 0.025 v2 0.05 * v1 + 0.025 v2 = 0.2 2 * v1 + v2 = 8 v2 = 8 – 2 * v1 Let’s assume the collision is elastic. Initial KE = ½ * 0.05 * 4^2 = 0.4 Final KE = ½ * 0.05 * v1^2 + ½ * 0.025 * v2^2 = 0.025 * v1^2 + 0.125 * v2^2 0.025 * v1^2 + 0.0125 * v2^2 = 0.4 2 * v1^2 + v2^2 = 32 v2 = 64 – 32 * vi + 4 * v1^2 2 * v1^2 + 64 – 32 * vi + 4 * v1^2 = 32 6 * v1^2 – 32 * v1+ 32 = 0 The solutions to this equation are 4 m/s and 1?

M/s. Since velocity of moving marble decreased, its velocity after the collision is 1? M/s.

Final momentum = 0.05 * 1? This is approximately 0.0667 kg * m/s This proves that the momentum of the moving marble decreased. Let’s use the following equation to determine the velocity of the stationary marble after the collision.

Moving marble loses its energy. A part is given to stationary marble. It gains the kinetic energy.

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