Question

prove the principle of conservation of linear momentum for two bodies moving along the same line and colliding​

Answer 1

LAW OF CONSERVATION OF LINEAR MOMENTUM

= This law state that total momentum of

system remain conserved in the absence of

external force

PROOF

consider a body of mass M1 moving with

velocity U1 strike against another body of

mass M2 with velocity U2

Let two body remain in contact with small

time interval ∆t

Let F12 be the average force exerted by mass

M1 on M2

Let F21 be the Average force of M2 due to M1

Let V1 and V2 are two velocity

Momentum of mass M1 before collision = M1U1

Momentum of mass M2 after collision = M2U2

Momentum of mass M1 after collision = M1V1

By using the definition of Impulse change in momentum of mass M1 is

F12∆t = M1V1 - M1U1....... (1)

change in momentum of mass M2 is

F21∆t = M2V2 - M2U2....... (2)

Adding equation (1) and (2) we get

F12 + F21 = 0

Thus (M1V1 + M2V2) = (M1U1 - M2U2)

Momentum after collision =

momentum before collision

Hence, momentum of isolated system

is conserved

Answer 2

Law of conservation of momentum states that total momentum of system remains conserved in the absence of external force.

Proof:

Consider a body of mass m1 moving with velocity U1, striking against another body of mass m2 moving with velocity U2.

Let the two bodies remain in contact with each other for a small interval "delta t".

Let F12 be the average force exerted by mass m1 on m2, and let F21 be the force on m2 due to m1.

Let v1 and v2 be the velcoities of two bodies after collision.

Momentum of mass m1 before collision=m1u1

Momentum of mass m2 after collision=m2u2

Momentum of mass m1 after collision=m1v1

By using the definition of impulse, change in momentum of mass m1 is,

(refer figure).

solution