Conservation of energy

Definition

Conservation of energy is a fundamental principle in physics stating that the total energy in a closed system remains constant over time, meaning energy cannot be created or destroyed, only transformed from one form to another. This principle connects various forms of energy, including kinetic and potential energy, and applies to many physical scenarios, illustrating how systems behave under different forces and conditions.

5 Must Know Facts For Your Next Test

1. In a closed system, the total mechanical energy is the sum of kinetic and potential energy, which remains constant if no external forces do work.
2. Energy transformations occur in many processes, such as converting potential energy to kinetic energy when an object falls.
3. The principle applies universally, whether it involves simple machines like pulleys or complex systems like roller coasters.
4. In thermodynamics, conservation of energy also includes internal energy changes, heat transfer, and work done by the system.
5. The law emphasizes that while energy can change forms—like from chemical energy in food to kinetic energy in motion—it never disappears.

Review Questions

• How does the principle of conservation of energy explain the relationship between kinetic and potential energy in an isolated system?
  • In an isolated system, the principle of conservation of energy states that total mechanical energy remains constant. This means that as an object moves, it can convert potential energy into kinetic energy and vice versa. For instance, when an object falls from a height, its gravitational potential energy decreases while its kinetic energy increases, keeping the total mechanical energy unchanged.
• Discuss how conservation of energy applies to inclined planes and the calculations involved when objects slide down.
  • When an object slides down an inclined plane, it converts its gravitational potential energy into kinetic energy. As it descends, potential energy decreases proportionally to the height lost while kinetic energy increases as speed increases. The total mechanical energy at the top equals the total mechanical energy at any point along the plane if we neglect friction. This relationship allows us to calculate speeds or heights at various points using equations derived from both forms of energy.
• Evaluate the implications of conservation of energy on Bernoulli's equation and how it describes fluid flow behavior.
  • Bernoulli's equation exemplifies conservation of mechanical energy in fluid dynamics by relating pressure, kinetic energy per unit volume, and potential energy per unit volume within a flowing fluid. The equation states that as fluid moves through varying diameters in a pipe, the increase in velocity results in a decrease in pressure or elevation. This illustrates how total mechanical energy remains constant throughout the flow, showing practical applications in designing systems like airplane wings and water pipelines.

Related terms

Kinetic Energy:

The energy possessed by an object due to its motion, calculated using the formula $$KE = \frac{1}{2}mv^2$$, where 'm' is mass and 'v' is velocity.

Potential Energy:

The stored energy of an object due to its position or configuration, commonly represented by gravitational potential energy, calculated as $$PE = mgh$$, where 'm' is mass, 'g' is acceleration due to gravity, and 'h' is height.

Work:

A measure of energy transfer that occurs when a force is applied over a distance, defined mathematically as $$W = Fd \cos(\theta)$$, where 'F' is the force applied, 'd' is the distance moved, and '\theta' is the angle between the force and the direction of movement.