Ball 1, with a mass of 100 g and traveling at 10 m / s, collides head-on with ball 2, which has

step 1 Hi, here in this given problem, mass of the ball 1, that is given as M1 is equal to 100 gram and

Ball 1, with a mass of 100 g and traveling at 10 m / s,...

Ball $1,$ with a mass of 100 g and traveling at $10 \mathrm{m} / \mathrm{s},$ collides head-on with ball $2,$ which has a mass of $300 \mathrm{g}$ and is initially at rest. What are the final velocities of each ball if the collision is (a) perfectly elastic? (b) perfectly inelastic?

Key Concepts

Coefficient of Restitution

This quantity measures the elasticity of a collision by comparing the relative speeds of separation and approach of the colliding bodies. A coefficient of 1 indicates a perfectly elastic collision (no kinetic energy loss), while a coefficient of 0 indicates a perfectly inelastic collision (maximum kinetic energy loss, with objects coalescing).

Inelastic Collisions

In inelastic collisions, momentum is conserved, but kinetic energy is not; some is converted to other forms like heat or sound. In the special case of a perfectly inelastic collision, the colliding bodies stick together post-collision, and their common velocity is found solely by applying the conservation of momentum.

Conservation of Kinetic Energy

In a perfectly elastic collision, the total kinetic energy of the system is conserved along with momentum. This ensures that the energy before impact equals the energy after impact, which is critical for solving the final velocities when no kinetic energy is lost due to factors like heat or deformation.

Conservation of Momentum

This principle states that in the absence of external forces, the total momentum of a system remains constant before and after a collision. It is fundamental in collision problems, where the momentum (mass times velocity) of all objects is summed and set equal to the total momentum after the interaction, allowing for the determination of unknown velocities.

Elastic Collisions

Elastic collisions are interactions in which both momentum and kinetic energy are conserved. Their analysis involves using the conservation laws to derive equations that describe the final velocities of the objects involved, assuming that no energy dissipates during the collision.

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