Two blocks of masses m1 = 2kg. and m2 = 4kg. are each released from rest at a height of h = 5m. on a frictionless track, and undergo an elastic head-on collision. a)Determine the velocity of each block just before the collision. b) Determine the velocity of each block immediately after the collision. c) Determine the maximum heights to which m1 and m2 rise after the collision.

Question

Two blocks of masses m1 = 2kg. and m2 =  4kg. are each released from rest at a height of h = 5m. on a frictionless track, and undergo an elastic head-on collision. a)Determine the velocity of each block just before the collision. b) Determine the velocity of each block immediately after the collision. c) Determine the maximum heights to which m1 and m2 rise after the collision.

Elena · Answer

m₁gh= m₁v₁₀²/2 => v₁₀=sqrt(2gh)
m₂gh= m₂v₂₀²/2 => v₂₀ =sqrt(2gh)

m₁v₁₀ - m₂v₂₀= - m₁v₁ + m₂v₂
v₁= {-2m₂v₂₀ +(m₁-m₂)v₁₀}/(m₁+m₂)
v₂={ 2m₁v₁₀ - (m₂-m₁)v₂₀}/(m₁+m₂)

m₁v₁²/2= m₁gh₁ => h₁=v₁²/2g
m₂v₂²/2= m₂gh₂ => h₁=v₁²/2g

Kutreya · Answer

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