Work, Power & Energy

Work Done By a Constant Force
Zero Work Done & Work Done
Work Done By A Varying Force
Kinetic & Potential Energy
Work-Energy Theorem

Work





Defination Work is said to be done if due to application of an external force on a body there is actual displacement of the body, except when the displacement is perpendicular to the direction of force.

Work = Force x displacement of the point of application (body on which force is applied) in the direction of force.
If W = work done, F = applied force, d = displacement of the point of application in the direction of force, then from the definition of work,

W = F x d


Units of work

In C.G.S. the unit of work is Erg . In M.K.S. it is Joule .
1 Joule = 107 Erg.

Work Done By A Constant Force







Consider an object undergoes a displacement S along a straight line while acted on a force F that makes an angle θ with S as shown.

The work done W by the agent is the product of the component of force in the direction of displacement and the magnitude of displacement.

W = FScosθ

From this defination, we conclude the following points :

(1) force does no work if point of application of force does not move (S = 0).
(2) work done by a force is zero if displacement is perpendicular to the force (θ = 90o).
(3) if angle between force and displacement is acute (θ < 90o), we say that work done by the force is positive.
(4) if angle between force and displacement is obtuse (θ > 90o), we say that work done by the force is negative.

Zero Work Done & Work Done


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Work Done By A Varying Force

If a body is moving away from the centre of the earth, the magnitude of the gravitational force continuously decreases, i.e. the gravitational force continuously varies. The body can move both with, varying magnitude of force and varying direction of force.
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Power

Rate of work done by an agent is known as its power . If w work is done by a body or a system in time t , then the power P of the body or the system is given by ,

P = W / t

In other words, the rate of doing work is known as power.

Units of Power

C.G.S. unit is Erg / second . In S.I. it is Watt .(Joule / second).


Energy


A body is said to possess energy if it has the capacity to do work. When a body possesing energy does some work, part of its energy is used up. Conversely if some work is done upon an object, the object will be given some energy.

There are various forms of energy, Heat, electricity, light, sound etc., are all familiar forms. In studying mechanics, we are however concerned mainly with mechanical energy.

The energy that a body or a system acquires by virtue of its motion, position or configuration is known as mechanical energy .
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Kinetic Energy


Kinetic Energy (K.E.), is the capacity of a body to do work by virtue of its motion.
If a body of mass m has the velocity v its kinetic energy is equivalent to the work, which an external force would have to do to bring from rest up to its velocity v.

The numerical value of the kinetic energy can be calculated from the formula :

K.E. = ½ mv2


Potential Energy

Potential energy is the same as stored energy . It is the energy possessed by a body by virtue of its state, position or configuration .
There are two common forms of potential energy, gravitational and elastic.

Work-Energy Theorem

The energy associated with the work done by the net force does not disappear after the net force is removed (or becomes zero), it is transformed into the Kinetic Energy of the body. We call this the Work-Energy Theorem.

Wnet = ½ mvf2 - ½ mvo2

Wnet = Kf - Ko = ΔK









Law of Conservation of Energy


Conversion of one type of matter into another are always accompanied by the conversion of one form of energy into another. Usually heat is leveled or absorbed , but sometimes the conversion involves light or electrical energy instead of, or in addition to heat. Many transformations of energy, do not involve chemical changes . Electrical energy can be changed into either mechanical, light, heat or potential energy without chemical changes. Mechanical energy is converted into electrical energy in a generator. Potential and kinetic energy can be converted into one another. Many other conversions are possible, but all of the energy involved in any change always appears in some form after the change is completed .

The Law of Conservation of Energy states that energy cannot be created or destroyed , but can change its form .

The total quantity of matter and energy available in the universe is a fixed amount and never any more or less .
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