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. If the colliston is perfectly elastic, what are the final velocities v1 and v2 of objects 1 and 2? Give the velocity v1 of object 1 followed by the velocity v2 of object

Answer 1

In an elastic collision where two objects of equal mass collide and one is initially at rest, their velocities are exchanged. The initially moving object will come to rest, while the initially stationary object will take over the initial velocity of the first object.

Step-by-step explanation:

When two objects with equal mass m collide elastically, and one of them is initially at rest, the principles of conservation of momentum and conservation of kinetic energy apply. According to the conservation of momentum, if object 1 with mass m and initial velocity v collides with object 2, which is initially stationary, the total momentum before and after the collision will be the same.

Furthermore, since the collision is perfectly elastic, kinetic energy is also conserved, meaning that the total kinetic energy before the collision is equal to the total kinetic energy after the collision.

With these principles in mind, we find that when two objects of equal mass m collide in this manner, the velocities are exchanged. Object 1, after the collision, comes to a complete stop (v1 = 0), and object 2, previously at rest, moves with the initial velocity of object 1 (v2 = v).