In the arrangement of Fig. 9-21, billiard ball 1 moving at a...

In the arrangement of Fig. 9-21, billiard ball 1 moving at a speed of $2.2 \mathrm{~m} / \mathrm{s}$ undergoes a glancing collision with identical billiard ball 2 that is at rest. After the collision, ball 2 moves at speed $1.1 \mathrm{~m} / \mathrm{s}$, at an angle of $\theta_{2}=60^{\circ}$. What are (a) the magnitude and (b) the direction of the velocity of ball 1 after the collision? (c) Do the given data suggest the collision is elastic or inelastic?

Key Concepts

Elastic Collision

An elastic collision is one in which both momentum and kinetic energy are conserved. Analyzing a collision for elasticity involves comparing the total kinetic energy before and after the event, and understanding that in perfectly elastic collisions, the bodies rebound without any loss of energy to other forms such as heat or deformation.

Vector Decomposition in Two-Dimensional Collisions

In oblique or glancing collisions, the velocities of objects are best analyzed by breaking them down into components (typically horizontal and vertical). This step is essential for applying conservation laws in each direction independently and solving for unknown magnitudes and angles, ultimately determining the post-collision trajectories.

Conservation of Momentum

In collision problems, the law of conservation of momentum states that the total momentum of a system remains constant if no external forces act on it. This principle must be applied separately to the horizontal and vertical components when dealing with oblique collisions, ensuring that the vector sum of momenta before the collision equals the vector sum afterwards.

Conservation of Kinetic Energy

For elastic collisions, not only is momentum conserved, but the total kinetic energy of the system is also conserved. This concept is crucial when determining whether a collision is elastic or inelastic and when calculating the final speeds of colliding bodies in cases where energy is not lost to sound, heat, or deformation.

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