This is a course on engineering mechanics in which we would be studying interaction

or let me be more precise mechanical interaction between different bodies

when they interact through the forces applied on each other This would consist of 2 parts

statics and dynamics In statics we would mainly be concerned with

equilibrium between different bodies I would specify later what we mean by equilibrium

And in dynamics we would be concerned with how different bodies move under the influence

of different forces they apply on each other or when the force is applied from outside

In the 1st part we are going to focus on statics which is the study of equilibrium between

different bodies

So…of equilibrium between bodies When we say equilibrium in

general it means that there is no acceleration on any part of the system In statics specifically

we are concerned with when all the subsystems all the systems or subsystems are not only

not exhilarating but are static That is they are not moving

The study of statics or dynamics is based on Newton’s 3 laws

of motion

So let us start by the discussion The 1st law

states that a body does not change its state of motion

So if a bodies moving in a straight line it will keep moving in this that state line until

a forces applied Similarly if a body is static and sitting somewhere unless a force is applied

it will not start moving spontaneously The 1st law is a part observe it is based on observation

and it is part definition You may ask definition of what

It gives you the definition of an inertial frame

and we do most of our calculation in an inertial frame And inertial frame by definition then

is the one in which the body does not change its state of motion unless a force is applied

For example in this room for all practical purposes this room is a good inertial frame

because if I see somebody or some body somewhere it is not going to change its state of motion

without a force being applied

On the other hand suppose I am on a train It suddenly starts moving As soon as it starts

moving you see objects outside which are accelerating in the opposite direction by the same acceleration

So without any apparent force So that accelerating train is not a good inertial frame It is not

an inertial frame at all

Then the 2nd law states that the force applied on a body is proportional to the acceleration

that it produces Then we write F equals MA which defines for us the mass as well as the

force So this is also based on observation And part definition it defines for us something

called as inertial mass Suppose I take a standard body apply a force

on it and produce an isolation A1 so that F equals M1A1

And I take another body apply the same force on it maybe by a spring maybe by hitting it

from something and find that acceleration is A2 Then the mass of the 2nd body is going

to be M1 times A1 over A2 This becomes the operational definition of inertial mass So

this is part definition

Then it also tells us given a mass I can also measure the force in Newtons as M times A

Mind you this is operational definition I cannot always use it though Because suppose

I am pushing a wall the wall does not accelerate So I cannot really determine its mass by measuring

the acceleration when I am pushing it

Then there is Newton’s 3rd law that states that for an action there is always a reaction

That means if there is a body A it is pushing another body B by a force F then there is

going to be a reaction on A by B in the opposite direction A very confusing situation arises

in this Most of the students ask if the forces are in opposite direction why do not they

cancel each other

They do not because you see force A is applying a force on B It produces something on B On

the other hand A is being pushed by a force by B in the opposite direction So it is acting

on a different body Therefore they both cancel However if I take the entire system as one

then they being internal forces they do cancel But be very careful when applying it

Having given this preliminary discussion of Newton’s laws of which we will mostly be

using the 3rd law in statics part and we will be using the 2nd and 3rd law in the dynamics

part let us now start with a review of vectors

Because we will be using vectors extensively to represent forces velocities and things

like those So it is a good way to start this course by reviewing what we know about vectors

I am sure most of you have learnt about it in the 12th grade but we now make it slightly

more sophisticated Why do we need vectors It is because there are certain quantities

which have magnitude as well as direction

For example if somebody tells you that I am pushing a box by a force of 10 Newton does

not convey the full meaning until I say that I am pushing it to the right to the left in

this direction or in this direction Until the direction is specified the complete description

is not there To specify a force I need both it is magnitude as well as its direction Similarly

suppose somebody comes and asks you where is your friend’s house And you say it is

500 m from here

Again it will be a meaningless statement unless you tell him that it is 500 m to the east

to the west to the north to the south south east So plus a direction is also needed So

there are certain quantities for which you need the magnitude as well as the direction

and these quantities we call vectors Having defined vectors how do we represent them Let

us ask that question

There are 2 ways one is graphical and one is algebraic We will 1st do graphical method

and see that it is gets little complicated when we go into many many vectors and do many

operations Then we will do a a algebraic way of writing vectors So graphical method

of representing a vector is that you make an arrow with the arrow showing the direction

and the length of the arrow showing the magnitude of the vector

In this manner if we now have 2 vectors how do we decide whether the 2 vectors are equal

or not

If there are 2 vectors given they will be equal if they produce the same effect So their

direction and magnitude must be the same Graphically that means that if there is a vector A another

vector which is parallel to it and has the same magnitude B is equal to A I can have

a vector parallely shifted compared to A but still it can be equal to A So in this case

A is equal to B because both of them have the same direction and the same magnitude

On the other hand if I make a vector here C it is magnitude may be the same as A but

it is not it does not have the same direction as A Therefore A is not equal to C

One has to be very careful in the effect of equal vectors Two vectors being equal does

not mean that their effect will always be the same For example if I take a wheel I apply

a force on its top say 10 Newtons If I apply the same force on the axle in the same direction

although the 2 vectors are equal their effect would not be the same In the 1st case the

wheel will start rolling In the 2nd case it will just move forward without rolling

So although the factors are equal their effect is not the same On the other hand think of

of the same wheel If a rope is pulling it which is tied to its end Whether I apply a

force here here or here along the line of action its effect would be the same I can

also hit the disc from this side by the same force and that would also produce the same

effect So equality of vector has to be further specified by something else

And that is if there is a vector and no matter where I apply it along the line of its application

if the effect is the same then it is known as transmissible vector So not only equal

but if I can apply it at any point along the line of its action and it produces the same

effect then it is plausible vector For example force is a transmissible vector So force has

this quality called the transmissibility