The kinetic energy of a rolling billiard ball is given by KE = 1/2 mv². Suppose a 0.17-kg billiard ball is rolling down a pool table with an initial speed of 4.5 m/s. As it travels, it loses some of its energy as heat. The ball slows down to 3.8 m/s and then collides head-on with a second billiard ball of equal mass. The first billiard ball completely stops and the second one rolls away with a velocity of 3.8 m/s. Assume the first billiard ball is the system. Calculate q.

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Identify the initial kinetic energy (KE_initial) of the first billiard ball using the formula KE = \frac{1}{2}mv^2, where m is the mass and v is the initial velocity.

Calculate the initial kinetic energy: KE_initial = \frac{1}{2} \times 0.17 \text{ kg} \times (4.5 \text{ m/s})^2.

Identify the final kinetic energy (KE_final) of the first billiard ball just before the collision using the same formula with the final velocity.

Calculate the final kinetic energy: KE_final = \frac{1}{2} \times 0.17 \text{ kg} \times (3.8 \text{ m/s})^2.

Determine the heat lost (q) by the system, which is the difference between the initial and final kinetic energies: q = KE_initial - KE_final.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Kinetic Energy

Kinetic energy (KE) is the energy an object possesses due to its motion, calculated using the formula KE = 1/2 mv², where m is the mass and v is the velocity of the object. In this scenario, the billiard ball's kinetic energy changes as it slows down and eventually transfers its energy during a collision.

Conservation of Momentum

The principle of conservation of momentum states that in a closed system, the total momentum before an event must equal the total momentum after the event. In this case, the momentum of the first billiard ball is transferred to the second ball during the collision, allowing us to analyze the system's behavior before and after the impact.

Heat Transfer (q)

Heat transfer, denoted as q, refers to the energy that is transferred from one system to another due to a temperature difference. In this problem, as the first billiard ball slows down, some of its kinetic energy is converted into heat, which can be quantified to understand the energy lost during its motion.

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