Answer:
Explanation:
Let mass m₁ is colliding in-elastically with stationary mass m₂ with velocity v₁ . Let v₂ be their conjugate velocity after collision .
Initial KE =1/2 m₁ v₁²
Final KE = 1/2 ( m₁ + m₂ ) v₂²
from conservation of momentum
v₂ = m₁v₁ / ( m₁ + m₂)
Final KE = 1/2 ( m₁ + m₂ ) m₁²v₁² / ( m₁ + m₂ )²
= 1/2 m₁²v₁² / ( m₁ + m₂ )
Loss of KE = ΔK
= 1/2 m₁ v₁² - 1/2 m₁²v₁² / ( m₁ + m₂ )
= 1/2 m₁ v₁² ( 1 - m₁ / m₁ + m₂ )
= 1/2 m₁ v₁² m₂ / (m₁ + m₂ )
ΔK / K= m₂ / (m₁ + m₂ )
= β / (1 + β)
where β = m₂ / m₁
b )
If ΔK / K = .25
.25 = β / (1 + β)
β = 1/3
c )
If
ΔK / K = .75
.75 = β / (1 + β)
β = 3
