Question

Write down a conservation law that should always hold for collisions. What quantity should be the same before and after any collision? Express in proper mathematical notation.

Answer 1

IN collisions

we have two types of collisions , Ealstic and inealstic collisions

in Elastic collisions both the momentum and kinetic energy of the system conserved that the total momentum beforce collision equal to the after the collision same as the kinetic energy

but in the case of inealstic collision only conservation of momentum takes place but not the kientic energy , energy will be waste in the form of heat or sound etc

conservation of momentum of two masses m1,m2 with initial velcoities before collision u1,u2, final velocities after the collision is v1,v2 is

m1*u1+m2*u2 = m1*v1+m2*v2

for conservation of kinetic energy  

0.5*m1*u1^2+0.5*m2*u2 = 0.5*m1*v1^2+0.5*m2*v2^2