A 0.300 -kg puck, initially at rest on a horizontal,...

A 0.300 -kg puck, initially at rest on a horizontal, frictionless surface, is struck by a 0.200 -kg puck moving initially along the $x$ axis with a speed of $2.00 \mathrm{m} / \mathrm{s}$. After the collision, the 0.200 -kg puck has a speed of $1.00 \mathrm{m} / \mathrm{s}$ at an angle of $\theta=53.0^{\circ}$ to the positive $x$ axis (see Active Fig. 8.11 ). (a) Determine the velocity of the 0.300 -kg puck after the collision. (b) Find the fraction of kinetic energy lost in the collision.

A 0.300 -kg puck, initially at rest on a horizontal, frictionless surface, is struck by a 0.200 -kg puck moving initially along the $x$ axis with a speed of $2.00 \mathrm{m} / \mathrm{s}$. After the collision, the 0.200 -kg puck has a speed of $1.00 \mathrm{m} / \mathrm{s}$ at an angle of $\theta=53.0^{\circ}$ to the positive $x$ axis (see Active Fig. 8.11 ).
(a) Determine the velocity of the 0.300 -kg puck after the collision. (b) Find the fraction of kinetic energy lost in the collision.

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Key Concepts

Conservation of Momentum

This principle states that in a closed system, the total momentum remains constant before and after a collision. When analyzing collisions, momentum must be conserved in both the horizontal and vertical directions independently, which allows for setting up simultaneous equations to solve for unknown variables such as speed and direction of the objects involved.

Vector Decomposition

When dealing with collisions that occur at angles, it is essential to break down velocity vectors into their respective horizontal and vertical components. This process facilitates the application of conservation laws along each coordinate axis, making it easier to compute the unknown components of velocity after the collision.

Kinetic Energy and Energy Loss

In collisions, particularly inelastic ones, kinetic energy is not generally conserved even though momentum is. By comparing the total kinetic energy before and after a collision, one can determine the amount or fraction of kinetic energy lost, which is often converted into other forms of energy such as heat or sound.

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