Question

state and prove law of conservation of momentum

Answer 1

AnsweR ⬇⬇⬇

➡conservation of momentum ⤵

⭐A conservation law stating that the total linear momentum of a closed system remains constant through time, regardless of other possible changes within the system.

↪Explanation↩ ⬇⬇

Law of conservation of linear momentum :- when there is no any external force applied on a system of particles then , momentum of system of particles will be conserved or you can say that if external force is zero. Then momentum of system of particles in intially = momentum of system of particles in finally.

Mathematically,

From Newton's second law,

Fext = dP/dt

If Fext = 0, ∫ dP =∫ 0.dt

Means dP = 0

e.g., Pi = Pf

{F_=0}{P_i=P_f}

Let two bodies A and B of masses m₁ and m₂ are moving with velocities u₁ and u₂ , after collision velocities of bodies are v₁ and v₂ respectively.

Then, initial momentum of bodies ,Pi= m₁u₁ + m₂u₂

Final momentum of bodies, Pf = m₁v₁ + m₂v₂

Because external force doesn't apply here, so, linear momentum will be conserved .

e.g., Pi = Pf

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

[Note :- here doesn't include sign of velocity , but when you will solve question include direction of velocity as you know velocity is vector quantity]

Answer 2

⏯️⏯️when two or more body act on another, there total momentum remain constant or conserved provide no external force acting on it.

⏯️⏯️ let us now consider two bodies a truck and a car moving on a straight line with initial velocity u1 and u2 having mass M1 and M2 respectively . suppose ( a) u1 > u2.
at the time of collision the truck exert a force F1 on the car. hence, the velocity of car changes from v1 to V2.

hence acceleration produced in car will be equal to
$\frac{v2 - u2}{t \: } = a2$

force F1 exerted by truck on car will be

$f1 = m2 \times a2 \\ \\ = m2 \times \frac{v2 - u2}{t} \\ \\ this \: is \: equation \: (1)$

at the same time car also exert a force f 2 on the truck

$hence \: v = u + at \\ \\ v1 = u1 + a1t \\ \\ \frac{v1 - u1}{t} = a1 \\ \\ f2 = m1 \times a1 \\ \\ m1 \times ( \frac{v1 - u1}{t} ) \\ \\ this \: is \: equation \: 2$

according to Newton's third law of motion

F1 = -F2

$m2( \frac{v2 - u2}{t} ) = - m1( \frac{v1 - u1}{t} )$

$m2v2 - m2u2 = - m1v1 + m1u1$

$m1v1 + m2v2 = m1u1 + m2u2$

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