conservation

Examples of conservation in the following topics:

• Conservation of Mechanical Energy

  • In any real situation, frictional forces and other non-conservative forces are always present, but in many cases their effects on the system are so small that the principle of conservation of mechanical energy can be used as a fair approximation.
  • Let us consider what form the work-energy theorem takes when only conservative forces are involved (leading us to the conservation of energy principle).
  • If only conservative forces act, then Wnet=Wc, where Wc is the total work done by all conservative forces.
  • This equation is a form of the work-energy theorem for conservative forces; it is known as the conservation of mechanical energy principle.
  • An example of a mechanical system: A satellite is orbiting the Earth only influenced by the conservative gravitational force and the mechanical energy is therefore conserved.

• Conservative and Nonconservative Forces

  • A conservative force is dependent only on the position of the object.
  • Gravity and spring forces are examples of conservative forces.
  • We can extend this observation to other conservative force systems as well.
  • The total work by the conservative force for the round trip is zero:
  • For a conservative force, work done via different path is the same.

• Conservation of Angular Momentum

  • These examples have the hallmarks of a conservation law.
  • The conserved quantity we are investigating is called angular momentum.
  • Just as linear momentum is conserved when there is no net external forces, angular momentum is constant or conserved when the net torque is zero.
  • This is an expression for the law of conservation of angular momentum.
  • Conservation of angular momentum is one of the key conservation laws in physics, along with the conservation laws for energy and (linear) momentum.

• Problem Solving With the Conservation of Energy

  • To solve a conservation of energy problem determine the system of interest, apply law of conservation of energy, and solve for the unknown.
  • If you know the potential energies ($PE$) for the forces that enter into the problem, then forces are all conservative, and you can apply conservation of mechanical energy simply in terms of potential and kinetic energy.
  • The equation expressing conservation of energy is: $KE_i+PE_i=KE_f+PE_f$.
  • where $OE$ stand for all other energies, and $W_{nc}$ stands for work done by non-conservative forces.
  • The problems are taken from "The Joy of Physics. " This one deals with energy conservation.

• Linear Momentum

  • Momentum is conserved in both inelastic and elastic collisions.
  • Momentum, like energy, is important because it is conserved.
  • "Newton's cradle" shown in is an example of conservation of momentum.
  • Only a few physical quantities are conserved in nature.
  • Total momentum of the system (or Cradle) is conserved.

• Energy Conservation

  • Energy is conserved in the movement of a charged particle through an electric field, as it is in every other physical situation.
  • Energy is conserved in the movement of a charged particle through an electric field, as it is in every other physical situation.
  • The terms involved in the formula for conservation of energy can be rewritten in many ways, but all expressions are based on the simple premise of equating the initial and final sums of kinetic and potential energy.
  • Formulate energy conservation principle for a charged particle in an electric field

• Rotational Collisions

  • In a closed system, angular momentum is conserved in a similar fashion as linear momentum.
  • During a collision of objects in a closed system, momentum is always conserved.
  • Is momentum still conserved ?
  • So rotating objects that collide in a closed system conserve not only linear momentum p in all directions, but also angular momentum L in all directions.
  • When a bowling ball collides with a pin, linear and angular momentum is conserved

• Static Electricity, Charge, and the Conservation of Charge

  • Electric charge is a physical property that is perpetually conserved in amount; it can build up in matter, which creates static electricity.
  • In physics, charge conservation is the principle that electric charge can neither be created nor destroyed.
  • The net quantity of electric charge, the amount of positive charge minus the amount of negative charge in the universe, is always conserved.
  • For any finite volume, the law of conservation of charge (Q) can be written as a continuity equation:

• Inelastic Collisions in Multiple Dimensions

  • While inelastic collisions may not conserve total kinetic energy, they do conserve total momentum.
  • While inelastic collisions may not conserve total kinetic energy, they do conserve total momentum .
  • Since there are no net forces at work (frictionless surface and negligible air resistance), there must be conservation of total momentum for the two masses.
  • By applying conservation of momentum in the y-direction we find:

• Conservation of Energy in Rotational Motion

  • Energy is conserved in rotational motion just as in translational motion.
  • Just as in translational motion (where kinetic energy equals 1/2mv2 where m is mass and v is velocity), energy is conserved in rotational motion.