Question

2. A ball of 0.4kg mass and a speed of 3 m/s has
- a head-on, completely elastic collision with
a 0.6-kg mass initially at rest. Find the
speeds of both balls after the collision:
(1) 0.6 m/s, 2.4 m/s
(2) 0.3 m/s, 1.2 m/s
(3) 0.2 m/s, 1.2 m/s
(4) 2.8 m/s, 3.4 m/s
​

Answer 1

Answer:

The  speeds of both balls after the collision will be

option (1) 0.6 m/s, 2.4 m/s

Explanation:

given data,

m₁ = 0.4 kg

v₁ = 3 m/s

m₂ = 0.6

v₂ = 0

v₁' = ?

v₂' = ?

According to the law of conservation of momentum, initial and final momentum should be conserved

=> m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'

=> 0.4 x 3 + 0.6 x 0 = 0.4v₁' + 0.6v₂'

=> 0.4v₁' + 0.6v₂' = 1.2

=> v₁' + 1.5v₂' = 3

=> v₁' = 3 - 1.5v₂'    ......................eqn1

Also it is given that the collision is elastic , which means the kinetic energy is also conserved,

=> m₁v₁²/2 + m₂v₂²/2 = m₁v₁'²/2 + m₂v₂'²/2

=> m₁v₁² + m₂v₂² = m₁v₁'² + m₂v₂'²

=> 0.4 x 3² + 0.6 x 0 = 0.4v₁'² + 0.6v₂'²

=> 0.4v₁'² + 0.6v₂'² = 3.6

=> v₁'² + 1.5v₂'² = 9

=> (3 - 1.5v₂')² + 1.5v₂'² = 9

=> 9 + 2.25v₂'² - 9v₂' + 1.5v₂'² = 9

=> 3.75v₂'² - 9v₂' = 0

=> v₂' =  9/3.75 = 2.4

=> v₁' = 3 - 1.5v₂' = 3 - 3.6 = -0.6 m/s

Hence the  speeds of both balls after the collision will be

option (1) 0.6 m/s, 2.4 m/s