1. Mechanics Part-1

2. Newton’s Laws
There are three main laws Newton expressed
about motion.
1. 1st Law or the Law of inertia
2. 2nd Law
3. 3rd Law
The next slides will explain what these laws mean
and how they are applied in nature

3. Newton’s First Law
(Law of Inertia)
An object at rest remains at rest, unless acted upon by a net force. An object in
motion remains in motion, unless acted upon by a net force.
(An object will remain at rest or continue motion unless an external
unbalanced(net force) force acts on it)
E.g.: A carom ball will not move until someone hits on it.
Net force- The net force is the sum of the forces acting upon an object.
- F
R
Net force= F + (-F) = 0 Net force = F + (-F) + R = R

4. Newton’s Second Law
The change of momentum per second is proportional to the applied force
and the momentum change takes place in the direction of the force.
F α m × Change in velocity per second
F α ma ( a- acceleration= rate of change of velocity )
F = k .ma
When F = 1N, m = 1 kg , and a = 1 ms-2 , then k= 1,
Therefore, F = ma
Alternate proof:
Since, force is equal to the rate of change of momentum,
F = dP / dt . (Where P is the momentum)
Thus, F= d(mv) / dt. (P=mv , m-mass, V- velocity)
F= m dv/ dt.
F= ma.
F = ma

5. Newton’s Third Law
To every action, there’s an equal and opposite
reaction.
Consider a tennis ball hitting the racket. Here the force exerted
by the ball on the racket is equal to the force exerted on the
ball by the racket. Also the sum of momentums after and
before are equal and thus the system obeys the conservation
of linear momentum principle.
Force on the
racket exerted
by the ball Force on
the ball
exerted
by the
racketBefore Collision After Collision

6. Some key terms
Impulse- Impulse is the change of momentum in a collision
or the product of the force exerted and the time taken for
the collision
Thus, I= Ft= Δmv (Δmv- change of momentum)
Inertia- It is the tendency of an object to remain at a
constant velocity, or its resistance/reluctance of being
accelerated.
Terminal Velocity- It is the maximum velocity of an
object falling from a height or moving from rest through a
frictional medium. Thus, at terminal velocity, the total
resistance acting upon an object should be equal to the
gravitational attraction/force.

7. Types of forces
1. Weight
2. The normal force
W= mg
R The normal
force on an
object always
acts
perpendicular
to the plane in
which the
object is kept
The product of the
mass and the
gravitational
acceleration, the
weight, always acts
towards the center of
the earth regardless
of the object’s
position or inclination

8. 3. Friction
4. Tension
R
W
W
R1
R2

9. Friction
Friction is the force resisting the relative motion of an
object.
There are two types of friction(dry friction):
1. Static friction
2. Kinetic friction
Static friction- Static friction is the friction that occurs
between two solid surfaces that do not move relative
to each other.
Thus, the static frictional force should always be
greater than the applied force on an object.

10. Kinetic friction- Kinetic friction or the kinetic frictional force occurs
when the two surfaces start to move relative to each other.
Force exerted by an
external source
Static
frictional
force
exerted on
the object
by the
surface
Frictional force > Force by external source. Therefore the
object remains stationary.
Object moving in the
direction of applied forceKinetic
frictional
force on the
object
Frictional force < Force by external source. Therefore the object moves.
Object
does not
move

11. The frictional force increases with the applied
force and reaches a maximum level. The frictional
force exerted at this position is called the limiting
frictional force. It actually is the position of the
object beginning its motion or transition between
immobility and mobility. Once a greater force than
the limiting frictional force is exerted on the
object, the object will start to move. However, the
frictional force acting upon the object is now a
constant value and is always less than the limiting
frictional force.
These information can be summarized as follows:

12. Since, Kinetic frictional force is a constant value, it can be shown that,
F kinetic / Normal force on the object also takes a constant value. This
value varies according to the surface the object is placed in. That’s the
reason as to why we can push a box easily in a more slippery surface, as
the ratio is smaller, the frictional force is smaller and the force needed
to push the box is smaller in comparison to that in a rough surface
Kinetic frictional force is always
constant and is less than the limiting
frictional force. However, always
applied force > kinetic frictional force
Limiting frictional force
(Maximum frictional force)
Static frictional force gradually increases with the applied force.
However always, applied force < static frictional force
Frictional force
Applied force / Time the
force was applied

13. This ratio is called the coefficient of frictional force.
Thus, F kinetic / Normal force = μ k .
Therefore, F kinetic = μ k Normal force or F k = μ k N
However, the limiting frictional force can also be
expressed in a similar notation as the frictional force
is a constant at the applied force.
Thus, F limiting = μ N.

14. Linear Momentum, Impulse
Newton defined the force acting on an object as
the rate of change of its momentum.
Momentum (mass × velocity) is a vector quantity
and acts in the direction of the velocity.
Change of momentum = mv – mu
Therefore, F =
Therefore, F × t = mv – mu = momentum change
However, F × t = I (I-Impulse)
Therefore, I= mv – mu = Δmv
mv – mu
t
I = Δmv

15. Momentum can be due to-
1. Change in velocity
E.g.: A ball 10g in weight increases velocity from
10m/s to 20m/s on colliding with a wall causing a
momentum change of 0.3kgms-1
10m/s
20m/s
Ft= mv- mu = 10 × 0.01 – 20 × 0.01
= 0.3 kgms-1

16. 2. Change of mass (e.g.: A rocket moves upwards
into the air and losing mass as its fuel is burnt)
E.g.: 0.1 kg of sand is allowed to fall onto a belt
moving at 0.1m/s. The sand is subjected to
horizontal momentum change of 0.01Ns.
Particles
of sand Belt (Provides extra force
needed for the momentum as
required by the sand particles )
Mass = 0.1 kg
Velocity gained = Velocity of Belt= 0.1 m/s
Therefore, momentum change per second
horizontally = 0.01 N

17. F= mass ×
= × Velocity Change
F = Mass per second × Velocity Change
Velocity Change
Time
Mass

18. Principle of Conservation of Linear
Momentum(PCLM)
Principle-
If no external forces act on a system of colliding objects, the total
momentum of the objects in a given direction is a constant(That
means the total momentum of the objects before collision= total
momentum after collision)
Explanation-
From PCLM,
m1u1 + m2u2 = m1v1 + m2v2

19. E.g.: An object A of mass 5 kg is moving with a velocity of 2m/s.
This object collides head-on with an object B of mass 1 kg moving
in the opposite direction with a velocity of 4m/s. After collision,
the objects stick. Calculate the final velocity of the composite.
From PCLM, 5 × 2 + 1 × 4 = 5 × V
V = 1.2 ms-1
2ms-1
4ms-1
V ms-1
A B A + B

20. E.g.: A snooker ball X of mass 0.03 kg, moving with a velocity of
1m/s hits a stationary ball Y of mass 0.01kg. Y moves off with a
velocity of 2.5 m/s at 60° to the initial direction of X. Find the final
velocity of X and its direction.
PCLM : 0.03 × 1 = 0.01 × 2.5 + 0.02 × V Cos θ
0.02V Cosθ = .0.005 V Cosθ = 0.25 ①
PCLM : 0 = 0.01 × 2.5 Sin60° + 0.03V Sinθ
V Sinθ = 0.72 ②
X 1ms-1
Y
60°
θ
2.5ms-1
V ms-1

21. ② / ①
Tanθ = 0.72/ 0.25=2.88
θ = 70.85°
By substituting to ①, V= 0.25/ 0.32= 0.76ms-1
Final direction, 70.85° to the horizontal in the initial
direction.
V Cosθ = 0.25
V Sinθ = 0.72 V

22. Types of Collisions
Collisions can be divided into two groups based on whether the
total kinetic energy is conserved in the system. In both of these
two types, the system in which the collisions takes place obeys the
conservation of linear momentum.
1. Elastic Collisions
It’s the type of collision of two or more objects where the total kinetic
energy is conserved or total initial kinetic energy = total final kinetic
energy.
Also, in this type of collision, the kinetic energy does not get converted
to any other form of energy.
2. Inelastic Collisions
It’s the type of collision where the total kinetic energy of the system is
not conserved.

23. Coefficient of Restitution (COR)
When two objects collide directly, their relative
velocity after collision is in a constant ratio to their
relative velocity before collision and is in the opposite
direction.
That is , final velocity/initial velocity = -e ,
Where e is the coefficient of restitution.
For most of the collisions that take place in the real
world, 0 ≤ e ≤ 1. However, there could be incidents
where e < o or e > 1. That means there could be
incidents where there’s a total kinetic energy gain
after collision and a collision which has a negative COR
means that the separation velocities of the objects are
in the same direction as their approaching velocities.

24. However, collisions where,
1. e = 1 are said to be elastic collisions, meaning
both the kinetic energy and the momentum
are conserved.
2. 1> e > 0 are said to be inelastic collisions,
meaning only the momentum is conserved,
while there’s an kinetic energy loss.
3. e = 0 are said to be ‘stop’ at collision.

25. Work
Work is said to be done when a force displaces a
body such that the component of the force acting
along the displacement is not zero.
Considering the dot or scalar product of the two
vectors,
W = F Cosθ. S W= FS Cosθ
θ
F
S

26. However, if the force is,
Parallel or along the displacement, θ = 0. Thus,
the above expression could be simplified as
W = FS
F
S

27. Special Points
1. Since displacement is a vector quantity, a work
done in an opposite direction to an initial work
done will cause for the net work done to be
zero.
E.g.: If you lift a weight S m and then lower down it
to its initial position, the work done is zero.
S

28. 2. When a force is perpendicular to the direction
of an object’s motion, this force does no work on
the object (θ = 90°, W= FS Cos 90° W= 0 )
V
T
T is perpendicular to V.
Therefore, rope does no
work on the ball.

29. Energy
It’s the capacity of a body to do work. Thus, we
can say that the energy is an aid to do work or
work cannot stand alone.
Forms of energy-
There are many forms of energy and the most
common being
1. Potential Energy(It is the energy stored in a
body due to its configuration or position)
2. Kinetic Energy(It is the energy stored in a body
due to its movement in a plane)

30. Mechanical Energy
It’s the sum of the potential energy and the
kinetic energy in a system.
Δ KE = ½ mv2 , ΔPE = mgh
E = Δ KE + ΔPE = ½ mv2 + mgh
E = ½ mv2 + mgh

31. Power
The rate at which work is done or energy is
suspended is called power.
P= W/t and instantaneous power can be
described as P= dw/dt
Since, W= FS and P= W/t,
It can be concluded that,
P= W/t
P = FVP = FV

32. Principle of conservation of Energy
Principle-
The total energy in a closed system is always a
constant.
Derivation-
Any energy present in a closed system gets
converted to another form of energy. This type of
energy includes mechanical energy, sound energy,
light energy, thermal energy etc.
Thus there’s no total energy gain or loss in a closed
system and the sum of all energies at any moment is
equal to that at another moment.

33. Principle of conservation of
mechanical energy
Principle-
If mechanical energy(sum of kinetic energy and
potential energy) does not get converted to any
other form of energy the mechanical energy in a
closed system is conserved.
Derivation-
KE (initial) + PE(initial) = KE (final) + PE (final)
Thus any system that obeys the principle of
conservation of mechanical energy should also
obey the principle of conservation of energy