Conservation of Energy

Conservation of Energy

Fundamentals

  • The law of conservation of energy states that the total energy of a closed system is constant.
  • It can be inferred that energy can neither be created nor destroyed, but it can be converted from one form to another.
  • The sum of kinetic and potential energy in the system is always the same, representing the mechanical energy of an object.

Kinetic Energy and Work

  • The kinetic energy of an object is the energy it possesses due to its motion.
  • Described mathematically, kinetic energy (K.E) = 1/2 mv^2 where m is the mass of the object and v is its speed.
  • The work done by forces, excluding the force of gravity, is equal to the change in kinetic energy of an object. This is the basis of work-energy theorem.
  • Physically, work done on an object transfers energy to the object.

Potential Energy

  • The potential energy of an object is the energy it possesses due to its position relative to other objects.
  • Potential energy usually refers to energy that an object has because of its position in a force field, such as gravitational potential energy, or due to its configuration, like elastic potential energy.
  • Gravitational potential energy is given by P.E = mgh where m is the mass of the object, g is acceleration due to gravity, and h is height above the ground.

Energy Transformations

  • Due to the law of conservation of energy, energy may be converted between different forms.
  • For example, an object in free fall will convert potential energy into kinetic energy as it falls towards the Earth.
  • In an ideal, frictionless system, the sum of the kinetic and potential energies will remain constant, signifying conservation of mechanical energy.

Power

  • Power is the rate at which energy is transferred, or the amount of energy per unit time.
  • The unit of power is Joule per second (J/s), which is also known as a Watt (W).
  • The power resulting from force F moving an object at velocity v is given by P=Fv.

Remember, understanding the principles of energy conservation and how to apply them in problem-solving scenarios is crucial for mastering this topic.