Question

A body of mass 8kg moving with a velocity of 20m/s collides head on with another body of mass 5kg moving with velocity of 10m/s. If the collision is perfectly inelastic, calculate the velocity of the first body after collision and the loss of K.E. during collision.

Answer 1

Answer:

ANSWER

Given :            m1=2kg         m2=1kg           u1=3  m/s        u2=4   m/s

Let the common velocity of the combined body be V

Mass of combined body      M=2+1=3kg

Applying conservation of momentum :          

2×3−1×4=3×V              ⟹V=32   m/s

Momentum of the system     P=2×3−1×4=2 kg m/s

Loss in kinetic energy of the system due to collision         ΔK.E=K.Ei−K.Ef

  ΔK.E=21(2)×32+21(1)×42−21(3)×(32)2

⟹ΔK.E=349  J

Answer 2

Answer:

Given : m

1

=2kg m

2

=1kg u

1

=3 m/s u

2

=4 m/s

Let the common velocity of the combined body be V

Mass of combined body M=2+1=3kg

Applying conservation of momentum :

2×3−1×4=3×V ⟹V=

3

2

m/s

Momentum of the system P=2×3−1×4=2 kg m/s

Loss in kinetic energy of the system due to collision ΔK.E=K.E

i

−K.E

f

ΔK.E=

2

1

(2)×3

2

+

2

1

(1)×4

2

−

2

1

(3)×(

3

2

)

2

⟹ΔK.E=

3

49

J