Newton’s Second Law of motion, Newton’s Third Law, Factors that affect the acting force & the acceleration

It is preferable to use air bags in the cars to protect the driver during accident , The colliding of a large truck with wall is more destructive than the colliding of a small truck because the acting force increases by the mass , Colliding car with a wall is a more destructive than colliding than colliding haystack .

If a person falls in water , he will not be harmed , while if he falls on the ground , he will be harmed , The severity of injury increases by increasing the height of falling because the change in velocity ( momentum ) , An egg will not break if it falls on a pillow , while it will break if it falls on the ground .

Newton’s Second Law of motion

There are two forms of Newton’s Second Law :

The resultant force affecting an object equals to the rate of change in the object’s momentum ( motion amount ) .

F = Δ p / Δ t = Δ m v / Δ t = ( Δ m v_f − Δ m v_i ) / Δ t

F = m ( v_f − v_i ) /Δ t = m ( Δ v / Δ t ) = m a

F = m a    →    a = F / m

From Newton’s Second Law : The change in momentum depends on the time of this change and the acting force :

Δ m v = F Δ t

The other form of Newton’s Second Law of motion :

When a resultant force affects an object , The object acquires an acceleration that is directly proportional to the resultant force and it is inversely proportional to the object mass .

Explanation of Newton’s Second Law :

When a resultant force acts on a car during an interval of time , its velocity increases and acquires an acceleration .

If two cars of equal masses are affected by two forces 20 N and 5 N , the acceleration of the first car motion will be greater than the acceleration of the second car motion .

Acceleration is directly proportional to the resultant force acting on the object at constant mass ( a ∝ F ) .

If two cars are affected by equal forces but the mass of the first car is greater than the mass of the second car , the acceleration of the first car motion will be less than the acceleration of the second car motion .

Acceleration is inversely proportional to the object mass at constant force ( a ∝ 1 / m ) .

The mathematical formula that expresses Newton’s Second Law :

a = ∑ F / m            or  ∑ F = m a

The force ( F ) is a vector quantity since it is the product of a scalar quantity ( mass ) and a vector quantity ( acceleration ) .

The unit of measuring force is kg.m/s² which is equivalent to the Newton ( N ) and its dimensions are MLT⁻² .

The Newton : It is the force that when acts on an object of mass 1 kg accelerates it at 1 m/s² in the same direction .

When the resultant force acts on a body = 20 N , It means that it is the product of the mass of the body and its acceleration = 20 kg.m/s² .

Factors that affect the acting force :

1. Mass : The acting force increases by increasing the mass of the object .
2. Change in velocity : The acting force increases by increasing the change in velocity .
3. The time of impact : The acting force decreases by increasing the time of impact .

F = m Δ v / Δ t

If the change in momentum occurs in short time interval , the effect of impact will be larger , If the change in momentum occurs in long time interval , the effect of impact will be smaller .

Factors that affect the acceleration :

The resultant force : The acceleration is directly proportional to the resultant force acting on the constant mass , Slope = a / F = 1 / m .

The object mass : The acceleration is inversely proportional to the object mass at constant resultant force , Slope = m a = F .

Guidelines to solve problems

Use the law , F = m a

If we compare between two resultant forces which affect on two different objects , they move with uniform acceleration : F1 ÷ F2 = ( m₁ a₁ ÷ m₂ a₂ ) . 

If the object mass decreases to half and the acquired acceleration increases to double , the resultant force remains unchanged .

F1 = m₁ a₁    ,  F2 = m₂ a₂  ,   m₂ = ½ m₂  ,   a₂ = 2 m₁

F2 =  ½ m₁ ×  2 a₁ = m₁ a₁  

∴  F1 = F2

If the object mass decreases to half and the resultant force increases to double , the acquired acceleration increases to four times .

a₁ = F1 / m ₁ ,   a₂ = F2 / m ₂   ,  m₂ = ½ m ₁   , F₂ = 2 F₁

a₂ = ( 2 F1 ÷ ½ m ₁) = 4 (  F1 ÷ m ₁ )

∴ a₂ = 4 a₁

If there is a friction force ( F_friction ) between the surface and the body , the body moves due to acting force ( F_acting ) :

F_moving = ∑ F = F_acting + ( − F_friction )

Negative sign indicates that friction force acts in opposite direction .

In case of more than one force acts on the body , then

∑ F = F_moving = F1 + F2 + F3 + …… , where the forces acting in opposite direction such as friction force take negative sign .

Newton’s Third Law

When the object acts on another object by a force , the second object reacts with an equal force on the first object in a direction opposite to that of the action or for every action there is a reaction equal in the magnitude and opposite in the direction .

Explanation of Newton’s Third Law :

This law is related to two mutual forces between two different bodies , If we considered the first force as an action , the second force is considered as a reaction in the opposite direction .

The mathematical formula that expresses the law : F₁ = − F₂ , ( The negative sign indicates that the two forces act in opposite direction ) .

Action and reaction are paired , Originate and vanish together , This means that no single force can exist in the universe , Although they are equal , It is not a must that action and reaction are equilibrium since they act on different bodies , Action and reaction are of the same type , if the reaction is a gravitational force , reaction is a gravitational force , as well .

Applications of Newton’s Third Law

Launching a rocket is based on Newton’s Third Law of motion , A huge amount of burning gases rush down the rocket to generate a reaction pushing the rocket upwards , When a bullet is fired ( action ) , the rifle recoils backwards ( reaction ) , because of this a soldier should mount the rifle back firmly to his shoulder .

When a man jumps from a boat to the reef ( action ) , the boat shifts backwards ( reaction ) , When a person setting on a moving chair , pushes the wall ( action ) , the chair moves backwards ( reaction ) , When blowing a balloon and leaving it free , the trapped air pushes out the open end , causing the balloon to move forward .

 Laws of Circular motion & Types of centripetal force

Fundamental Forces in nature, Gravitational forces, Electromagnetic forces & Nuclear forces

Acceleration types, units, importance & Graphic representation of moving in a straight line