# 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 .
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**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 :**

**Mass : The acting force increases by increasing the mass of the object .****Change in velocity : The acting force increases by increasing the change in velocity .****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 = ( m _{1 }a_{1} ÷ m_{2 }a_{2} ) . **

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

**F1 = m _{1 }a_{1} , F2 = m_{2 }a_{2 }, m_{2} = ½ m_{2}_{ }, a_{2} = 2 m_{1} **

**F2 = ½ m _{1 }× 2 a_{1} = m_{1} a_{1}_{ }**

**∴ F1 = F2**

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

**a _{1} = F1 / m _{1} , a_{2} = F2 / m _{2} , m_{2} = ½ m _{1} , F_{2} = 2 F_{1}**

**a _{2} = ( 2 F1 ÷ ½ m _{1}) = 4 ( F1 ÷ m _{1 })**

**∴ a _{2} = 4 a_{1}**

**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 : F _{1} = − F_{2} , ( 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 .
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** 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**

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