Work, Energy and Power

Work is said to be done by a force action on a body, provided the body is displaced actually in any direction except in a direction perpendicular to the direction of the force.  absolute unit of work is Joule and ergs. 1 joule = 10^7 ergs.

Gravitational unit of  work is Kg-m and g-cm

although work done is a scalar quantity, its value may be positive, negative or even zero.

When circular motion is not uniform, a tangential force is acting on the body in addition to radial force. Work done by radial force is zero, but work done by tangential force is not zero.

A weight lifter does work in lifting the weight off the ground, but does no work in holding the weight up.

Positive work on an arbitrary system means a transfer of energy to the system and negative work means a transfer of energy from the system.

A force is said to be conservative  if work done by  or against the force in moving a body depends only on the initial and final positions of the body and not on the nature of path followed between the initial and the final positions. example, gravitational force, electrostatic force,magnetic force, force in an elastic spring.

Non-conservative force examples; friction, induction force in a cyclotron.

Power: a rate at which a body can do the work: P =W/T= F.s/t= F.v

Energy of the body is defined as the capacity or ability of the body to do the work.

Energy is different from power. Whereas energy refers to the total amount of work a body can do, power determines the rate of doing work. Thus, in power, time taken to complete the work is significant. But in energy, time is irrelevant.

Kinetic energy of a body is the energy possessed by the body by virtue of its motion.

Work Energy Theorem

According to this principle, work done by a force in displacing a body measures the change in kinetic energy of the body.

W.D= Change in K.E of the body

When a light and heavy body are moving with same K.E, and same retarding force is applied on each, both the bodies will stop after travelling the same distance.

Potential energy of a body is defined as the energy possessed by the body by virtue of its position or configuration in some field.

Two important types of potential energy are:

  1. Gravitational PE
  2. 2. Elastic PE: it is due to potential energy of the compressed spring in a loaded pistol that the bullet is released with a large velocity on firing the pistol.

PE is defined only for conservative forces and not for non-conservative forces.

PE depends upon the frame of reference.

It may be positive or negative.

A body in motion may or may not have PE.

Potential energy of the spring is the energy associated with the state of compression or expansion of an elastic spring.

Mechanical Energy = K.E + P.E

Different forms of energy

  1. Heat Energy: it is the energy possessed by a body by virtue of random motion of the molecules of the body.
  2. Internal Energy: total energy possessed by the body by virtue of particular configuration of its molecules and also their random motion.  P.E is due to configuration of the molecules against intermolecular forces and K.E. is due to random motion of the molecules. Internal energy of a body is sometimes called the microscopic mechanical energy of the body.
  3. Electrical Energy arise on account of work required to be done in moving the free charge carriers in a particular direction through a conductor.
  4. Chemical Energy: it arise from the fact that the molecules participating in the chemical reaction have different binding energies.
  5. Nuclear energy

Conservation of energy: according to this principle, the sum total of energy of all kinds in an isolated system, remains constant at all times.

Two key rules of the collision game are:

  1. Law of conservation of linear momentum and
  2. Law of conservation of energy

Types of collision

  1. Elastic collision: a collision in which there is absolutely no loss of kinetic energy is called an elastic collision. For example, collision between atomic and sub atomic particles are elastic collision. Basic characteristic of an elastic collision are: (a) the linear momentum is conserved; (b) total energy of the system is conserved; and (c) K.E. is conserved. Mechanical energy not converted into any other form of energy like heat energy, sound energy etc.  Force involved during elastic collision must be conservative forces.
  2. Inelastic collision: a collision in which there occurs some loss of kinetic energy is called an inelastic collision.

If two bodies stick to each other, after colliding, the collision is said to be perfectly inelastic.

The basic characteristics of an inelastic collision are

  1. The linear momentum is conserved
  2. total energy is conserved
  3. K.E. is not conserved.
  4. Some or all the forces involved in an inelastic collision may be non-conservative in nature.

In a closed isolated system containing a collision, the linear momentum of each colliding body may change, but the total linear momentum P of the system remains constant, whether the collision is elastic or inelastic.

Conceptual points

  1. It is possible that a body by in accelerated motion under a force acting on the body, yet no work is being done by the force. For example, under centripital froce, a body moves uniformly in a circle with centripetal acceleration. But no work is done, as W= F.S. cos (90)= zero.
  2. Two protons are brought towards each other then the potential energy of the system will increase as in bringing two proton closer, work has to be done against the force of repulsion.
  3. Mountain roads rarely go straight up the slope, but wind up gradually because slope would have been large and the frictional force would be small.
  4. Whenever two body attracts each other then potential energy is decreasing and if they are repulsing each other then potential energy is increasing.
  5. Kinetic energy cannot be negative. K.E. does not depends on the direction of motion. Yes, value of K.E depends upon the frame of reference.
  6. K.E of a system be increased or decreased without applying any external force on the system by doing work through internal forces e.g. in explosion of a bomb.
  7.  Kilowatt hour is the largest practical unit of energy and eV is the smallest.
  8. linear momentum of a system is conserved only when the system is isolated.
  9. It is possible to have a collision in which the whole of K.E.  is lost. For example, in perfectly inelastic collision of two bodies moving towards each other with equal linear momentum.
  10. When a spring is compressed or stretched, potential energy of the spring increases in both the cases. This is because work is done by us in compression as well as stretching.
  11. In uniform circular motion, linear momentum change but K.E. does not.
  12. P.E. can be negative when forces involved are attractive.
  13. Work done does not involve time. Time is involve only in power.

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