Hey dear students we have learnt in previous articles about Newton’s laws of motion. In second law we have learn that when momentum of object is changed force is acts on the object, whereas in third law we learnt that for every action there is equal and opposite reaction.
From 2nd law,
Let’s learn the law of conservation of linear momentum in detail…..!
Statement: If no external force acts on interacting bodies, their momentum remains conserved. Or total momentum of two colliding bodies before and after collision is constant.
Suppose a tennis ball (object-1) of mass ‘m’ is thrown on the wall (object-2) with velocity ‘v’ so that ball exerts force on the wall given as,
According to Newton’s third law, wall also exerts the same force but the velocity vector gets reversed during this, then the force exerted by wall on ball is then
∴ ∆P + ∆P = 0
i.e. linear momentum of colliding bodies remains conserved.
To illustrate this consider the following situation…!
Suppose that two spheres of masses m1 and m2 moving initial velocities u1 and u2 (u1 > u2 )along the same line as shown in fig. below,
Let the spheres has head on collision in time ‘t’ and gets separated with the velocities v1 and v2.
In this case, before collision, the total momentum of sphere A and B will be
P1= m1u1+ m2u2 …………………..(A)
After collision the momentum will be
P2= m1v1+m2v2 …………………..(B)
During to collision, sphere A exerts force F1 on sphere B; in return according to Newton’s 3rd law sphere B will also exert force F2 on sphere A in time ‘t’. These forces are equal in magnitude but opposite in direction, hence
i.e. total momentum before collsion = total momentum after collsion