Question

Find the law of conservation of linear momentum by using Newton’s third law of motion.

Answer 1

$F_{1}= \frac{dP_{1}}{dt}$
$F_{2}= \frac{dP_{2}}{dt}$
by 3rd law,
$F_{1}=-F_{2}$
$F_{1}+F_{2}=0$
$\frac{dP_{1}}{dt}+ \frac{dP_{2}}{dt}=0$
$\frac{d(P_{1}+P_{2})}{dt}=0$

$\frac{dP}{dt}=0$

where P=total linear momentum, as the derivative is zero, it is conserved

Answer 2

Conservation of momentum

Take three masses moving with forces F1 , F2 AND F3

F1 = m1a = m1 dv1/dt

F2 = m2a = m2 dv2/dt

F3 = m3a = m3 dv2/dt

reaction force = F1+F2+F3 ( if F=0)

m1 dv1/dt + m2 dv2/dt + m3 dv3/dt = 0

Intigrating above equation

m1v1 + m2v2 + m3v3 = constant

If net force on a system is zero than momentum will remain consatnt.