A popcorn kernel at rest in a hot pan bursts into two pieces, with masses \(91 \mathrm{mg}\) and \(64 \mathrm{mg} .\) The more massive piece moves horizontally at \(47 \mathrm{cm} / \mathrm{s}\). Describe the motion of the second piece.

Momentum is a fundamental concept in physics, defined as the product of an object's mass and its velocity. It is a vector quantity, meaning it has both magnitude and direction. The momentum of an object can tell us a lot about its state of motion. For example, a freight train moving slowly may have the same momentum as a small car speeding down the highway because the train’s large mass compensates for its slower speed.

In the exercise about the popcorn kernel, the momentum principle is central to solving the problem. Before the popcorn bursts, its momentum is zero because it is at rest. After bursting, the kernel splits into two pieces, each moving with its own velocity. The law of conservation of momentum states that, in the absence of external forces, the total momentum of a system remains constant. Therefore, the sum of the momenta of the two pieces must be zero, just as it was before bursting. The conservation of momentum allows us to set up the equation needed to find the velocity of the second piece.

Kinematics is the branch of mechanics that deals with the motion of objects without considering the forces that cause this motion. It uses a set of equations to describe an object's position, velocity, acceleration, and time, which are the core kinematics variables. While kinematics equations are not explicitly used in this problem, understanding them helps to appreciate the nature of the motion being analyzed.

Despite the popcorn kernel exercise not requiring a detailed kinematic analysis since there's no acceleration involved, the concept of velocity is a kinematics concept and is pertinent in determining how the two pieces of the kernel move after bursting. Knowing how to manipulate the kinematics equations can also be useful in more complex problems where acceleration is a factor and initial or final velocities must be found over time.

Problem-solving in physics is much like solving a puzzle; it involves understanding concepts, applying laws or principles, and conducting calculations to find a solution. In the popcorn kernel problem, we approach solving by first identifying the known and unknown quantities, then applying the law of conservation of momentum to relate these quantities.

To effectively solve physics problems, it’s important to:

• Understand the relevant concepts, like momentum and its conservation.
• Visualize the scenario, possibly with the aid of diagrams.
• Use mathematical equations to set up relationships between variables.
• Carry out algebraic manipulations to solve for the unknowns.

Following these steps not only provides a structured method for tackling problems across physics but also reinforces your understanding of the fundamental concepts and their applications.