Momentum And Its Conservation Formula-Solved Examples

Momentum is the tendency of the object to be in motion and therefore is a vector quantity. It is determined by the product of the mass of the object and its velocity. If both the objects are not experiencing any external forces, then the total momentum of the objects before and after the interaction is the same. This relation under the fundamental law of physics is known as the conservation of momentum.

This fundamental law of physics can be applied to explain the phenomenon of collision and explosion. The momentum formula is given by,

Momentum (P) = mass (m) x velocity (v)

Conservation of momentum can be described by

P1 (before) + P2 (before) = P1 (after) + P2 (after)  

This equation is valid for the object that undergoes collision.

Example 1

A ball of 1 kg is moving at a speed of 5 m / s collides with a cricket bat of 2.5 Kg swung at a speed of 1.5 m / s. right after the collision the cricket bat swings at a speed of 1.5 m / s. Calculate the magnitude and the velocity of the cricket ball.

Solution:

Given:

m1 = 1 kg

m2 = 2.5 kg

v1 = 5 m/s

v2 = 1.5 m/s

The relation between the colliding bodies is given by,

P1 (before) + P2 (before ) = P1 ( after ) + P2 ( after )

The momentum relation is expressed by,

(m1 v1) before + ( m2 v2 ) before = ( m1 v1 ) after + ( m2 v2 ) after

v1 (after) = [(m1v1)before+(m2v2)before−(m2v2)after] / (m1)after

                             = 1 x 5 + 2.5 x -1.5 – 2.5 x 1.5 / 1

                             = -2.5

Therefore, v1 (after) = – 2.5 m/s

The negative sign shows that it travels in the opposite direction.

Er. Neeraj K.Anand is a freelance mentor and writer who specializes in Engineering & Science subjects. Neeraj Anand received a B.Tech degree in Electronics and Communication Engineering from N.I.T Warangal & M.Tech Post Graduation from IETE, New Delhi. He has over 30 years of teaching experience and serves as the Head of Department of ANAND CLASSES. He concentrated all his energy and experiences in academics and subsequently grew up as one of the best mentors in the country for students aspiring for success in competitive examinations. In parallel, he started a Technical Publication "ANAND TECHNICAL PUBLISHERS" in 2002 and Educational Newspaper "NATIONAL EDUCATION NEWS" in 2014 at Jalandhar. Now he is a Director of leading publication "ANAND TECHNICAL PUBLISHERS", "ANAND CLASSES" and "NATIONAL EDUCATION NEWS". He has published more than hundred books in the field of Physics, Mathematics, Computers and Information Technology. Besides this he has written many books to help students prepare for IIT-JEE and AIPMT entrance exams. He is an executive member of the IEEE (Institute of Electrical & Electronics Engineers. USA) and honorary member of many Indian scientific societies such as Institution of Electronics & Telecommunication Engineers, Aeronautical Society of India, Bioinformatics Institute of India, Institution of Engineers. He has got award from American Biographical Institute Board of International Research in the year 2005.