A 3.0 kg object moving 8.0 m/s in the positive x direction has a one-dimensional elastic collision with an object (mass = M) initially at rest. After the collision the object of unknown mass has a velocity of 6.0 m/s in the positive x direction. What is M?

1 - 4.2 kg2 - 5.0 kg3 - 6.0 kg4 - 7.5 kg

Option 2 is the correct answer.

Explanation:

Elastic collision means kinetic energy and momentum are conserved.

Let the mass of object be m and M.

Initial velocity object 1 be u₁, object 2 be u₂

Final velocity object 1 be v₁, object 2 be v₂

Initial momentum = m x u₁ + M x u₂ = 3 x 8 + M x 0 = 24 kgm/s

Final momentum = m x v₁ + M x v₂ = 3 x v₁ + M x 6 = 3v₁ + 6M

Initial kinetic energy = 0.5 m x u₁² + 0.5 M x u₂² = 0.5 x 3 x 8² + 0.5 x M x 0² = 96 J

Final kinetic energy = 0.5 m x v₁² + 0.5 M x v₂² = 0.5 x 3 x v₁² + 0.5 x M x 6² = 1.5 v₁² + 18 M

We have

Initial momentum = Final momentum

24 = 3v₁ + 6M

v₁ + 2M = 8

v₁ = 8 - 2M

Initial kinetic energy = Final kinetic energy

96 = 1.5 v₁² + 18 M

v₁² + 12 M = 64

Substituting v₁ = 8 - 2M

(8 - 2M) ² + 12 M = 64

64 - 32M + 4M² + 12 M = 64

4M² = 20 M

M = 5 kg

Option 2 is the correct answer.