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
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.
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2021-07-21T12:57:55+00:00
2021-07-21T12:57:55+00:00 1 Answers
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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