Force and laws of motion : Class 9th Notes

Force and laws of motion

Force :- force is an external effort in the the form of push or pull

1. Produce or tries to produce motion in a body at rest.

2. Stops or tries to stops a moving body.

3. Change or try to change the direction of moving body.

Types of forces :- 

1. Contact force :- the force acting between two bodies when both bodies are in physical contact.

Example :- normal force 

2. Non contact force :- the force acting between two bodies when both bodies are not in physical contact.

Example :- gravitational force, electrostatic force, magnetic force etc.

Normal force :- If contact force between the bodies is perpendicular to the surface in contact, the force is known as normal force.

Balanced force :- When several forces act on a body simultaneously, their effects can compensate one another with the result there is no change in the state of rest or uniform motion is called balanced force.

• The net force acting on the body is zero for balanced force. 

• In case of balanced force the body as a whole either remains at constant or uniform motion.

Unbalanced force :- When several forces act on a body and their net effect is not zero then it is called unbalanced force.

• Unbalanced force produce non-uniform motion in the body.

• Unbalanced force accelerates the body.

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Components of a force :- 

Unit  of forces

SI unit of force is Newton.

1 N = 1 kg 1ms^-2

1 N = 1 kg ms^-2

C.G.S unit of force is dyne

1 dyne = 1gcms^-2

Relation between newton and dyne.

1 N = 1kg ms^-2

1 N = 1000g × 100 cms^-2

1 N = 10⁵ g cms^-2

1 N = 10⁵ dyne

1 kgf = 9.8 N.

F = 1 kgf

m = 1 kg, a = 9.8 m/s²

F = 1 kg × 9.8 m/s²

   =  9.8 kg m/s2

1 kgf = 9.8 N

Linear momentum :- 

Linear momentum of a body is the quantity of motion contained in a body.

• Momentum of a body is measured by the force required to stop the force in unit time.

      Momentum = force × time

• Force required to stop a moving body depends upon

1. Mass of the body :- larger the mass of a body, greater is its linear momentum.

2. Velocity of the body :- larger the velocity of a body greater is its linear momentum.

The product of the mass of the body and its velocity is called momentum.

       Momentum = mass*velocity 

                         P = mv

• SI unit = kgm/s

• CGS unit = gcm/s

• Other unit = kg m/s2 .s = N.s

• It is a vector quantity and its direction is same as the direction of velocity

•  When two bodies of unequal masses m₁, m₂ and its velocity V₁ and V₂ respectively have the same linear momentum.

P₁ = P₂

m₁v₁ = m₂v₂

m₁/m₂ = v₂/v₁

• Velocities of the body is having equal linear momentum varrise is inversely as their masses 

Or

The heavier body have  smaller velocity and the lighter body have larger velocity.

Newton's law of motion :- 

Newton's first law of motion :- A body continues to be in its state of rest or of uniform motion along a straight line unless it is acted upon by some external force to change the state.

• Newton's first law give qualitative definition of force.

• Newton's first law defines inertia.

Inertia :- The inability of a body to change by itself its a state of rest or state of uniform motion along a straight line is called the inertia of the body.

• Newton's first law is also called law of inertia.

Quantitative inertia of a body is measured by the mass of the body. 

• Heavier the body, greater is the force required to change its state and hence greater is its inertia.

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Types of inertia :- 

Inertia of a body is of three type :-

1. Inertia of rest

2. Inertia of motion

3. Inertia of direction

1. Inertia of rest :- It is the inability of a body to change by itself its state of rest.

• this means a body at rest remains at rest and cannot start moving on its own.

2. Inertia of motion :- It is inability of a body to change by it self it's  state of uniform motion.

• A body in uniform motion can neither accelerate nor retarded on its own and come rest .

3. Inertia of direction :- It is the inability of a body to change by it self its direction of motion.

Newton's second law :- 

The rate of change of linear momentum of a body is directly proportional to the external force applied on the body and this change Takes place always in the direction of applied force.

Let a body of mass " m" moving with velocity "u" a force "f" is applied on the body and after time "t" its velocity becomes "v" 

Initial momentum of a body Pi = mu

Final momentum of a body Pf = mv

Force ∝ rate of change of momentum.

F ∝ (Pi - Pf) / t

F ∝ (mv - mu) / t

F ∝ m(v - u) / t

F ∝ ma

F = Kma

K = Proportionality constant

K = 1 (for all unit)

F = ma

• The absolute value of force on SI is Newton.

• 

1N = 1 Newton force is that force which produces an acceleration of 1m/s² in a body of mass 1kg .

                     1N = 1kg × 1m/s² 

• The absolute of force on CGS system is dyne.

1dyne = 1 dyne force is that force which produces an acceleration of 1cm/s² in a body of mass 1g.

                 1 dyne = 1g × 1cm/s²

                 1N = 10⁵ dyne 

Gravitational unit :- 

Gravitational unit of force on SI is 1 kgwt aur 1 kilogram force (kgf) 

It is that force which produces an acceleration of 9.8m/s² in a body of mass 1 kg.

       1 kgwt or 1 kgf =  1 kg × 9.8m/s²

       1 kgwt or 1 kgf = 9.8 kgm/s² 

                                  = 9.8 N

The gravitational unit of force on CGS system is 1gwt or 1 gram force (gf)

It is that force which produces an acceleration of 980 gcm/s² in a body of mass 1 gram.

        1gwt or 1 gf = 1g × 980 cm/s²

                              = 980 gcm/s² = 980 dyne

Importance of Newton's second law of motion.

1. No force is required to move a body uniformly along a straight line, that means no external force is required 

                  F = ma = 0

2. Accelerated motion is always due to external force.

• Speed of a body may change :- for this force has to be applied in a direction of motion or in a direction opposite to that of motion.

• Direction of motion of a body may change :- for this force has to be applied in the direction perpendicular to the direction of motion of the body.

• Velocity of a body may changed :- for this force has to be applied in an incline direction so that tangential component of force changes the speed and the normal component of the force changes the direction of motion of body.

Newton's third law 

To every action there is always an equal and opposite reaction.

• Newton's third law is contained in the Newton 2nd law.

Consider an isolated system of two bodies "a" and "b" let them collide during collision let the body "a" exert a force F₁ (action) on body b for time Δt let  the body a b exerts a force  F₂ (reaction) on body a for the same time Δt

According to Newton's second law 

Force = change in momentum/time

Change in momentum = force*time 

For body A

Change in momentum =  F₂ × Δt

For body B

Change in momentum = F₁ × Δt

Total change in momentum = F₂Δt + F₁Δt

If no external force is acting on the system then the total change in linear momentum of the system is zero.

      By Newton's second law

F₁Δt + F₂Δt = 0

F₁Δt = F₂Δt

F₁ = -F₂

Action  = -reaction

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Conservation of momentum (principle) 

In an isolated system the vector sum of the linear momentum of all the body of all the system is conserved and is not affected due to their mutual action and reaction.

Isolated system :- A system of body is which is free from the influence of any external forces.

Supposed to objects A and B of mass M₁ and M₂ are moving in the same direction with velocity U₁ and U₂ respectively (U₁>U₂) object A collide with object B and after time t both moves in original direction with velocity V₁ and V₂ respectively.

Friction 

Friction is a resistance to the relative motion between two objects in contact or the body and its surrounding.

• When two objects are kept in contact a reaction force "R" acts between the two object.

Force "R" has two component - f along the surface and N perpendicular to the surface. The force f which acts along the surface is called the force of friction.

The component of force which is perpendicular to the surface is normal reaction.

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• The magnitude of the frictional force is just sufficient to prevent movement and increases as the tendency as to move increases, up to limiting value. When the limiting value is reached, the frictional force cannot increases in any further and motion is about to begin.

• The frictional force is directly proportional to normal reaction (N)

F ∝ N

F = μN (at limiting equilibrium)

μ = coefficient of friction 

μ = F/N

In general, F ≤ μN

Types of friction :- 

1. Static frictional force

When there is no relative motion between the contact surface, the frictional force is called a static frictional force.

            f_s ≤ μ_sN

2. Limiting frictional force 

The frictional force acts when the body is about to move.

• This is the maximum frictional force that can exist at the contact surface.

3. Kinetic fictional force 

Once relative motion starts between the surface in contact, the frictional force is called Kinetic frictional force.

• The magnitude of kinetic fictional force is also proportional to normal force.

f_k ∝ N 

f_k = μ_kN

Note :- μ_k < μ_s

Angle of friction :- 

The angle between resultant (R) and normal force (N) is called angle of friction.

Tan λ = μN / N = μ

Tan λ = μ = coefficient of friction.

Graph between static friction, kinetic friction and limiting friction.

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