Question

State the law of conservation of energy. Describe how it explains the motion of a child on a swing.

Short answer

The law of conservation of energy states that energy can neither be created nor destroyed, only transformed from one form to another. A child on a swing converts potential energy into kinetic energy and vice versa, demonstrating this law as the total mechanical energy remains constant during the swing's motion, minus any small losses due to non-ideal conditions like friction.

Step-by-step solution

Stating the Law of Conservation of Energy

Define the law of conservation of energy. The law states that energy cannot be created or destroyed in an isolated system. The total energy within the system remains constant over time.

Describing the Motion of a Child on a Swing

Explain the application of the conservation of energy to the swing's motion. As the child swings, potential energy at the highest points converts to kinetic energy at the lowest points. When the child is at the highest point, the swing has maximum potential energy and minimum kinetic energy. As the child descends, the potential energy decreases and kinetic energy increases. At the lowest point, the motion is at maximum speed and kinetic energy, with the potential energy at its minimum. The process then reverses as the child moves back up.

Relating the Energy Forms During the Swing

Discuss the transfer of energy forms without loss of total energy. The swing's motion demonstrates the law of conservation of energy, as the potential and kinetic energies transform into one another with no energy lost from the system; mechanical energy is conserved. Air resistance and friction convert some mechanical energy into thermal energy, which is typically disregarded in an ideal scenario.

Key concepts

Potential and Kinetic Energy

Potential and kinetic energy are like the two sides of a coin in physics, both integral to understanding the motion of objects. Potential energy is stored energy, based on an object's position or state. Imagine standing on a hill; the effort it took to climb stores energy due to your high position, and this is gravitational potential energy. Kinetic energy, on the other hand, is the energy of motion. It's the rush you feel when sliding down the hill, as your potential energy is converted into kinetic energy, propelling you forward.

When a child is on a swing, at the highest points, the child has a staff of energy waiting to be used – this is potential energy, specifically due to gravity and height. As the swing descends, this energy transforms into kinetic energy, like water spilling from a glass, fueling the motion. The higher the swing goes, the more potential energy it stores, ready to cascade into kinetic energy as the child swoops down.

Energy Conversion

Energy conversion is a fundamental concept explaining how one form of energy changes into another. This continual transformation happens all around us. In the case of a swing, as a child moves through the air, energy efficiently shifts back and forth between potential and kinetic forms. This energy swap isn't just limited to playgrounds – it's how your muscles work when you walk, how power plants generate electricity, and even how the Earth orbits the sun.

In a swing's journey, energy's dance is quite evident: the child's rise converts kinetic energy to potential energy. On the way back down, gravity takes the reins, and potential energy gracefully transforms back into kinetic energy, pushing the swing forward. Even if we can't see energy, its effects are always on display, showcasing an intricate energy balancing act.

Mechanical Energy Conservation

Mechanical energy conservation is a principle that the total mechanical energy in a system remains constant, as long as only conservative forces, such as gravity, are at work. In a frictionless world, a swing would keep moving eternally, a never-ending trade-off between kinetic and potential energy. But the real world isn't perfect; friction with the air, and resistance at the swing's chains nibble away at mechanical energy, turning some of it into thermal energy – the warmth you might feel on the swing's seat after a long session.

The concept of mechanical energy conservation helps explain the swing's arc: energy isn't lost but transformed. However, in practice, other forms of energy, mainly heat due to non-conservative forces like friction, slightly reduce the swing's mechanical energy over time, eventually bringing the swing to a halt.