A Classical Approach of Newtonian Mechanics

6 CONSERVATION OF MOMENTUM 6.7 Collisions in 2 - dimensions

i

2 i1^

f

2 f1^2 f2^

The^ above^ pair^ of^ equations^ can^ be^ combined^ to^ give^

and

vf1

v

vi1

2 cos θ

=

m 1

v

4.5

2 × cos 30 ◦

=

5 × 2.5981

= 2.5981 m/s,

= 5.1962 m/s.

f2 (^) m
2
f1
2.5
The initial kinetic energy of the system is
1
K = m v 2 = 0.5 × 5 × 4.5^2 = 50.63 J.
The final kinetic energy of the system is
1
K = m
1
v 2 + m v 2 = 0.5 × 5 × 2.5981^2 + 0.5 × 2.5 × 5.1962^2 = 50.63 J.
Since Ki = Kf, the collision is elastic.
= =
1
1 2