Principle of Conservation of Linear Momentum and Newton Laws of Motion


 
 
Concept Explanation
 

Principle of Conservation of Linear Momentum and Newton Laws of Motion

The principle of conservation of linear momentum follows form the Newton's laws of motion. We will show it by an example.

Suppose two object A and B, of mass   m_1 and  m_2  are moving in the same direction with velocity u_1: and :u_2 respectively(u_1>u_2). Object A collides with object B and after time t both  moves in the original direction with velocity  v_1: and:v_2 respectively.

The change in momentum of object A is m_1v_1; -:m_1u_1

The force applied by B on A

          F_1:=:frac{change:in;momentum;of;A}{time}

or      F_1:=:frac{m_1v_1:-:m_1u_1}{t}

The change in momentum of object B is  m_2v_2:-m_2u_2

The force applied by A on B

   F_2:=:frac{change:in:momentum;of;B}{time} 

  F_2:=:frac{m_2v_2-m_2u_2}{t}

By Newton's third law that is for each and every action there is equal and opposite reaction

                                    F_1:=:-F_2

     Rightarrow frac{m_1v_1:-:m_1u_1}{t}= frac{m_2v_2:-:m_2u_2}{t}

     Rightarrow m_1v_1:-:m_1u_1:=:m_2u_2:-:m_2v_2

    Rightarrow m_1u_1:+:m_2u_2:=:m_1v_1:+m_2v_2

  Hence,      Initial momentum       =     Final momentum

Or we can say that momentum of a system is conserved.

Sample Questions
(More Questions for each concept available in Login)
Question : 1

A metal ball with the momentum mv strikes a wall and bounces back. The change in the ball's momentum is ideally  ________________

Right Option : D
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Question : 2

A 40 kg men, running at 3 ms^-^1, jumps onto a stationary 10 kg skateboard. The speed of the man and the skateboard is:

Right Option : B
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Question : 3

Working of Rocket is based on the principle of __________

Right Option : C
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Explanation
 
 


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