Question

1. First, an object 1 with mass m and an object 2 with mass 2 m are moving on a straight line at velocities v1i = 1.00 m / s and v2i = -2.00 m / s. Two objects collided inelastically, and the velocities of object 1 and object 2 changed to v1f and vf2, respectively. The velocity is positive in the right direction, and no external force is acting on these two objects. Find v1f and vf2 for cases (1) and (2) below, respectively.
(1) When two objects have a completely inelastic collision.
(2) When two objects have a rebound coefficient e = 0.8.

Answer 1

Solution:

Given,

mass of object 1 = m

mass of object 2 = 2m

initial velocity of object 1

initial velocity of object 2

Final velocities of object 1 and object 2 are and .

(1) Under perfectly inelastic collision.

The two objects stick together after collision. They move with a common velocity.

Thus,

  

By conservation of momentum,

They have a common velocity of after collision.

(2) Given,

The rebound coefficient is given by,

   .......... (1)

By conservation of momentum we have,

......... (2)

On solving (1) & (2), we get,