Linear momentum is a vector quantity defined as the product of an object's mass, m, and its velocity, v. Linear momentum is denoted by the letter p and is called momentum for short. Note that a body's momentum is always in the same direction as its velocity vector. The unit of momentum are kg. m/s. p=mv
Conservation of Linear Momentum
Conservation of linear momentum expresses the fact that a body or system of bodies in motion retains its total momentum, the product of mass and vector velocity, unless an external force is applied to it. In an isolated system (such as the universe), there are no external forces so momentum is always conserved.
F=dtdp Since F=0 Therefore p= constant
Explanation of Physical Phenomena using principle of conservation of Momentum
Example: Two balls of equal masses are thrown upwards along the same vertical line at an interval of 2 seconds with the same initial velocity of 39.2ms−1. Find the total time of flight of each ball, if they collide at a certain height, and the collision is perfectly inelastic.
Solution: When the particles collide the height of both particles will be same, For first particle time will be t and for second particle time will be t−2 h=ut−21gt2=u(t−2)−21g(t−2)2 ut−21gt2=ut−2u−21g(t2−4t+4) 0=−2u+2gt−2g t=gu+1 t=5s By solving the quadratic equation in t we get the time of first collision to be 5s. h=39.2×5−21g×52=20g−12.5g=7.5gmeter Now by momentum conservation, velocity of particles after collision
m(u−gt)+m(u−g(t−2))=mv′ mu−5mg+mu−3mg=mv′ v′=2u−8g=0m/s a=−g Now for collision with ground let time taken be t2 h=21gt22⇒t=g2h=g2×7.5g=15 Thus, times of total time of flights will be 5+15s and 3+15s
Law of conservation of linear momentum
The law of conservation of linear momentum states that if no external forces act on a system, then the linear momentum of the system remains constant.