WORK, ENERGY AND POWER - INTRODUCTION

In our daily life, the word work has different meanings. Mental work, hardwork, etc.But physics word 'work' is used whenever there is a displacement for a particle or for a body under action of a force.

Scalar product ( dot product)

Scalar product of two vectors Ā and B can be defined as Ā.B. It is read as  Ā dot B and hence also called dot product of Ā and B. It is scalar quantity, hence called scalar product. The dot product is commuting.

i.e, A. B=B. A

If A and B are magnitudes of vectors and θ the angle between A and B  then

  A. B= ABcosθ

case I when θ=0⁰

A.B=ABcos0= AB

i.e when the two vectors are in the same direction the dot product will be maximum

case II θ=90⁰

A.B= ABCOS0 when two vectors are at right angles  the dot product will be zero

case III θ=180⁰

A.B= ABCOS180=-AB

When the two vectors are in opposite directions the dot product will be negative and minimum

SCALAR PRODUCT OF ORTHOGONAL UNIT VECTORS

Let i, j and k be the unit vectors along X, Y and Z directions respectively. The dot product among unit vectors are as given  below

i.i=1       j.j=1        k.k=1

i.k=0      j. k=0        k.j=0

i.j=0      j.i= 0           k.i=0

Energy

Energy is defined as capacity for doing work. It can be measured by the work that the body can do

Unit - Joule

example : heat energy, mechanical energy, light energy, electrical energy, sound energy

Mechanical energy

The energy possessed by a body due to its position or due to its motion is called mechanical energy. There are two types of mechanical energy

i) kinetic energy ii)Potential energy