Question

A sandbag motionless in outer space is hit by a three-times-as massive sandbag moving at 12 m/s. They stick together. This is an example of ____________ collision and it loses ________ % of initial kinetic energy.

Answer 1

Answer:

This is an example of inelastic collision and it loses zero(0) % of initial kinetic energy

Explanation:

Let the mass of the motionless sandbag = m₁

Let the mass of the moving sandbag = m₂ = 3m₁

initial velocity of the motionless sandbag, u₁ = 0

initial velocity of the moving sandbag, u₂ = 12 m/s

Let their final velocity, = v

Collision between two particles can either be elastic or inelastic.

Since they stick together after the impact, then the collision is inelastic

Apply the principle of conservation of linear momentum;

Initial kinetic energy = final kinetic energy

¹/₂m₁u₁² + ¹/₂m₂u₂² = ¹/₂v²(m₁ + m₂)

¹/₂m₁(0)² + ¹/₂(3m₁)(12)² = ¹/₂v²(m₁+3m₁)

216m₁ = 2m₁ v²

v² = 108

v = √108

v = 10.392 m/s

Change in kinetic energy = Final kinetic energy - initial kinetic energy

Initial Kinetic energy, KE₁ = ¹/₂m₁u₁² + ¹/₂m₂u₂²

                                   KE₁ = ¹/₂m₁(0)² + ¹/₂(3m₁)(12)²

                                   KE₁ = 216m₁ J

Final kinetic energy, KE₂ = ¹/₂v²(m₁ + m₂)

                                  KE₂ = ¹/₂(108)(m₁ + 3m₁)

                                  KE₂ = 216m₁ J

ΔKE = KE₂ - KE₁ =  216m₁ J -  216m₁ J = 0%

Therefore, this is an example of inelastic collision and it loses zero(0) % of initial kinetic energy