Answer:
v₁ = 3.9 m/s
v₂ = 5.4 m/s
The loss in the kinetic energy = 1.05 J
Explanation:
Given:
mass, m₁ = 2 kg
m₂ = 3 kg
initial speed of mass m₁, u₁ = 6 m/s
Initial speed of the mass m₂, u₂ = 4 m/s
coefficient of restitution, e = (3/4)
let, the final speed of mass m₁ and m₂ be v₁ and v₂ respectively
Now,
on substituting the values, we get
or
1.5 = v₂ - v₁
or
v₂ = 1.5 + v₁
also,
from the conservation of momentum, we have
( 2 × 6 ) + ( 3 × 4 ) = ( 2 × v₁ ) + ( 3 × v₂ )
or
24 = 2 × v₁ + ( 3 × ( 1.5 + v₁ ) )
or
24 = 2 × v₁ + 4.5 + 3 × v₁
19.5 = 5 × v₁
or
v₁ = 3.9 m/s
and
v₂ = 1.5 + v₁
or
v₂ = 1.5 + 3.9
or
v₂ = 5.4 m/s
now,
the loss in the kinetic energy = initial kinetic energy - Final kinetic energy
or
=
or
=
or
the loss in the kinetic energy = 1.05 J
