Question

A body of mass 1 kg and a body of mass 2 kg collide on a smooth horizontal surface.
Before the collision, the 1 kg body has velocity 3 m/s directed due north and the 2 kg body has velocity 5 m/s directed northeast (i.e. 45° east of due north). The two bodies stick together, forming a body of
mass 3 kg.
a/ Find the magnitude and direction of the velocity of the 3 kg body.
b/ Is this collision elastic? Explain.

Answer 1

Explanation:

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