Question

Now assume that the mass of object 1 is 2m, while the mass of object 2 remains m. If the collision is elastic, what are the final velocities v1 and v2 of objects 1 and 2?

Answer 1

`v_(1) = v -(v_(2))/(2)` ,
`v_(2) = 2(v - v_(1))`

Step-by-step explanation:

COMPLETE QUESTION: Let two objects of equal mass m collide. Object 1 has initial velocity v, directed to the right, and object 2 is initially stationary. Now assume that the mass of object 1 is 2m, while the mass of object 2 remains m. If the collision is elastic, what are the final velocities v1 and v2 of objects 1 and 2?

A perfectly elastic collision is defined as one in which there is no loss of kinetic energy in the collision. The total momentum before collision equals total momentum after collision.

⇒ m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

From the question, two objects of equal mass m collide. Object 1 has initial velocity v, directed to the right, and object 2 is initially stationary. Therefore, the formula correctly expressing the conservation of linear momentum between the two objects is;

mv = mv₁ + mv₂

Now assume that the mass of object 1 is 2m, while the mass of object 2 remains m.

2mv = 2mv₁ + mv₂

2mv = m (2v₁ + v₂)

2v = 2v₁ + v₂

`v = (2v_(1) + v_(2))/(2)`

`v_(1) = v -(v_(2))/(2)`

v₂ = 2v - 2v₁

v₂ = 2(v - v₁)