A 500 g air-track glider attached to a spring with spring...

A $500 \mathrm{g}$ air-track glider attached to a spring with spring constant $10 \mathrm{N} / \mathrm{m}$ is sitting at rest on a frictionless air track. $\mathrm{A} 250 \mathrm{g}$ glider is pushed toward it from the far end of the track at a speed of $120 \mathrm{cm} / \mathrm{s}$. It collides with and sticks to the $500 \mathrm{g}$ glider. What are the amplitude and period of the subsequent oscillations?

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Key Concepts

Inelastic Collisions

Inelastic collisions are events where colliding objects stick together after impact, resulting in the conservation of momentum but not kinetic energy. The loss of kinetic energy is often converted into other forms of energy, such as heat, sound, or stored as potential energy in a spring, which is essential for analyzing subsequent motion in such systems.

Conservation of Momentum

This principle states that within a closed system, the total momentum remains constant during any interaction, such as a collision. It is especially useful for determining the velocity of objects after collisions, even when other quantities like kinetic energy are not conserved, as in inelastic collisions.

Simple Harmonic Motion

Simple harmonic motion (SHM) describes the oscillatory movement of a system where the restoring force is directly proportional to the displacement from equilibrium, as characterized by Hooke’s law. The period of oscillation in a mass-spring system is determined by both the mass and the spring constant, typically given by the formula T = 2??(m/k).

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