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?

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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

                            v₂ = 2v - 2v₁

                            v₂ = 2(v - v₁)

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