Chapter 11––>Work and Energy

Introduction

 In day-to-day life, we consider any useful physical or mental labor as work, which is being defined differently in science.

• Two conditions are need to be satisfied for work to be done in science :-
• A force should act on object.
• The object must be displaced.

If either of these conditions does not satisfy, we say work done is zero.

Work done by a constant Force

We define work done as :

• Work done by 1N force in displacing the object 1m will be 1N-m.
• Unit of work is (N-m) or Joule (J).
• Work is scalar quantity. It has only magnitude, no direction.
• If displacement is in the direction of force, then work is taken as positive.
• If displacement is in the opposite direction of force, then work is taken as negative.

Energy

• An object having a capability to do work is said to possess energy.
• The object which does work looses energy and in accordance with the law of conservation of energy the object on which work is done gains energy.
• The energy possessed by an object is thus measured in terms of its capacity of doing work.
• The unit of energy is, therefore, the same as that of work, that is, joule (J).

Forms of energy

Mechanical energy can be further divided into

• Kinetic energy
• Potential energy

Kinetic energy (K.E.)

• It is the energy possessed by an object due to its motion.

Derivation of KE :-

We know that  F = ma

And   v² – u² = 2as , if body starts from rest then u=0    =>  s = v²/2a

  By definition :

• The KE of a body moving with a certain velocity is equal to the work done on it to make it acquire that velocity.

KE = WD = F s

KE = (ma) x( v² / 2a)

KE = (mv²)/ 2

Potential energy (P.E.)

• The energy possessed by an object by virtue of its position or configuration is called as potential energy.
• Potential energy is a relative term, you can choose reference position where it is zero

• An object’s energy increases when it is raised through a height, this is because work is done on it against gravity while it is being raised.
• The energy present in such an object is the gravitational potential energy.
• The gravitational potential energy of an object at a point above the ground is defined as the work done in raising it from the ground to that point against gravity

• Work done by gravity depends only on vertical height difference of initial and final positions.
• In both the cases shown, WD is same, thus the potential energy is mgh.

Law of conservation of energy

• Energy can neither be created nor be destroyed
• It can be converted to one form to another, but total energy remains constant.

Power

• Power is defined as the rate of doing work or the rate of transfer of energy.
• If a body does a work W in time t, then power is given by: Power = work/time 

• The unit of power is Watt. 1 W = 1 J/s
• Average power = Total WD / Total 

Commercial unit of power

1 kWh = 1000 W x 1 h

1 kWh = 1000 W x 3600 s

1 kWh = 3.6 x 10⁶ J

• 1 Joule is a very small quantity.
• The energy used in households, industries and commercial establishments are usually expressed in kilowatt hour 1 kWh.
• 1 unit = 1 kWh.