Question

Two balls of mass 4kg and 2kg are moving with speed 10m/s and 8m/s respectively with ball of heavier mass behind the lighter ball. The two balls collide each other elastically. Total impulse imparted by ball of mass 2kg to ball of mass 4 kg is ?

Answer 1

Answer:

ANSWER

Applying conservation of linear momentum in x direction

u

1

=2 and u

2

=3 (in −x direction)

initial momentum =m2−m3

final momentum =mv

2

−mv

1

equating both

−m=mv

2

−mv

1

⟹v

2

−v

1

=−1 ..............eq(1)

from definition of coeficient of restitution which states that

velocity of separation=e×(velocity of approach)

⟹v

2

−(−v

1

)=u

1

−(−u

2

)

v

2

+v

1

=2+3=5...............eq(2)

solving eq(1) and eq(2), we get

v

1

=3 and v

2

=2

considering ball B

J(impulse)=mv

2

−m(−u

2

)=m(v

2

+u

2

)=4(2+3)

J=20N−s

solution

Answer 2

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

J

R

=m

2

(ν

2

−ν)=4(1−0)=4Ns

also J

R

=eJ

D

=0.5×8=4Ns