1. Introduction Part 1

Work and Energy

Introduction

Work done

Work done on an object is defined as the product of the magnitude of the force acting on the body and the displacement in the direction of the force. W = F.s
If a force acting on a body causes no displacement, the work done is 0. For example, pushing a wall.

Two conditions need to be satisfied for work to be done:

(i) A force should act on object
(ii) The object must be displaced

 

 

 

•    W = Fs
If F = 1 N and s = 1 m
W= 1 N x 1 Nm
W = 1 Nm
1j =1 Nm

  •     1 J is the amount of work done on an object when a force of 1 N displaces it by 1 m along the line of action of the force.

•    Work done has only magnitude and no direction i.e., work is a scalar quantity.
•    SI unit of work is joule (J).
•    1 joule (one joule)
 

 

2. Types of Work

Types of work

(i) Zero work: If the angle between force and displacement is 90°, then work done is said to be zero work.
Example: When a man carries a load on his hand and moves on a level road, work done by the man on the load is zero.


 

 

 

(ii) Positive work: Work done is said to be positive if force applied on an object and displacement are in the same direction.

 

 

 

Example: Work done by the force of gravity on a falling body is positive.

(iii) Negative work: Work done is said to be negative if the applied force on an object and displacement are in opposite direction.
W = -Fs
Here displacement is taken to be negative (-s).


 

 

Example: Work done by friction force is usually negative on a moving body.

3. Introduction Part 2

                                                Energy

Energy of a body is defined as the capacity or ability of a body to do work.
The SI unit of energy is joule (J)
Forms of energy

There are various forms of energy in the nature, few of them are mechanical energy (potential energy + kinetic energy) heat energy, chemical energy and light energy.

1. Mechanical energy
Mechanical energy includes kinetic energy and potential energy.

a)  Kinetic energy
The energy possessed by a body by the virtue of its motion is called kinetic energy.
Kinetic energy possessed by a body can be calculated by
EK=1/2 mv2
m = mass of body
V = velocity of body

Derivation of kinetic energy

Let us consider an object lying on a frictionless surface having mass ‘m’



 

A force of constant magnitude F is acting on the body. Here initial velocity of the body is u and final velocity is v. As there is no dissipative forces, work done on the body will be stored in the form of change in kinetic energy.
W=Fs

 

 

 

 

If the object is starting from a stationary position u = 0, then

 

 

 

Factors affecting Kinetic energy

•    Mass
•    Velocity
•    Momentum

b) Potential energy

The energy possessed by a body due to its position or configuration is called potential energy.

(i) Gravitational potential energy

Potential energy at any height (h) from a reference can be calculated by formula
Ep = mgh
where, m = mass of object
v = height from reference
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.

 

 

 

Derivation of potential energy
When work is done on the body, the work is stored in the form of energy. Consider an object of mass, m. Let it be raised through a height, h from the ground. A force is required to do this. The minimum force required to raise the object is equal to the weight of the object, mg. The object gains energy equal to the work done on it. Let the work done on the object against gravity be W.


 

 

 

 

W = force x displacement
= mgh.
Since work done on the object is equal to mgh, an energy equal to mgh units is gained by the object. This is the potential energy (Ep) of the object.
Ep = mgh
 

 

4. Law of Conversation of Energy

                           Law of Conservation of Energy

Energy can neither be created nor destroyed, it can only be transformed from one form to another. The total energy before and after transformation remains the same.

Total energy = KE + PE

For example: consider a ball falling freely from a height. At height h, it has only PE = mgh.
By the time it is about to hit the ground, it has a velocity and therefore has KE=  
 mv2. Therefore, energy gets transferred from PE to KE, while the total energy remains the same.

Power (P)
Power is defined as the rate of doing work or rate of transfer of energy.
Power = work/time
P=W/T

•    Unit of power is watt (W).
Watt



 

 

 

Commercial unit of energy

•    Kilowatt hour (kWh) or 1 unit
•    The energy used in households, industries and commercial establishments are usually expressed in kilowatt hour.
•    1 kWh is the energy used in one hour (1 h) at the rate of 1000 J/s or (1 kW).
∴1 kWh =l kW x U = 1000 W x 3600 s = 3600000 J
1 kWh = 3.6 x 106 J = 1 unit

 

 Power can also be represented as,
P = Fv
F = force applied
v = velocity of object
P=W/t=Fs/t=Fv
 

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