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

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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.

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Tài Đức 6 months 2021-07-21T12:57:55+00:00 1 Answers 28 views 0

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  1. mit
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    2021-07-21T12:58:56+00:00
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    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

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