Question

derive an expression for loss of kinetic energy in completely inelastic collision in two body

​

Answer 1

Answer:

From conservation of momentum

m

1

v

1

=(m

1

+m

2

)v

2

→v

2

=

m

1

+m

2

m

1

v

1

The ratio of kinetic energies before & after collision is

KE

i

KE

f

=

2

1

m

1

v

1

2

2

1

(m

1

+m

2

)[

m

1

+m

2

m

1

v

1

]

2

=

m

1

+m

2

m

1

The fraction of kinetic energy lost is

KE

i

KE

i

−KE

f

=

KE

i

[1−

m

1

+m

2

m

1

]

KE

i

=

m

1

+m

2

m

2

Hence energy always loss in inelastic collision.