Question

drive an equations for law of conservation



ans it. ಠ‿ಠ​

Answer 1

$\huge \mathfrak\red{Answer:-}$

The law of conservation of momentum is one of the most prominent laws in physics. The principle of conservation of momentum law tells us that the total momentum of a system is always conserved.

Momentum Conservation Principle

Momentum Conservation PrincipleLaw of conservation of momentum states that

For two or more bodies in an isolated system acting upon each other, their total momentum remains constant unless an external force is applied. Therefore, momentum can neither be created nor destroyed.

Newton’s third law states that for a force applied by an object A on object B, object B exerts back an equal force in magnitude, but opposite in direction. This idea was used by Newton to derive the law of conservation of momentum.

Consider two colliding particles A and B whose masses are m_1 and m_2 with initial and final velocities as u_1 and v_1 of A and u_2 and v_2 of B. The time of contact between two particles is given as t.

$\sf{A=m_1(v_1−u_1)}$ (change in momentum of particle A)

$\sf{B=m_2(v_2−u_2) }$(change in momentum of particle B)

FBA=−FAB (from third law of motion)

FBA=m2∗a2=m2(v2−u2)t

FAB=m1∗a1=m1(v1−u1)t

$\sf{m_2(v_2−u_2)t=−m_1(v_1−u_1)t</p><p>m1_u_1+m2u2=m1v1+m2v2}$

Therefore, above is the equation of law of conservation of momentum where m1u1+m2u2 is the representation of total momentum of particles A and B before the collision and m1v1+m2v2 is the representation of total momentum of particles A and B after the collision.

Answer 2

Answer:

GIVEN EQUATION IS

$\bold{\boxed{\boxed{ ❲\frac{4x - 3}{2x + 1}❳ - 10 (\frac{2x + 1}{4x - 3} ) = 3}}}$

$❲ 2x+14x−3 ❳−10( 4x−3 2x+1)=3$

$\bold{( \frac{4x - 3}{2x + 1} ) - 10 (\frac{2x + 1}{4x - 3} ) = 3}</p><p>⟹( 2x+14x−3)−10( 4x−32x+1 )=3$

⟹$\bold{\frac{ {(4x - 3)}^{2} - 10 {(2x + 1)}^{2} }{(2x + 1)(4x - 3)} = 3}⟹ (2x+1)(4x−3)(4x−3) 2−10(2x+1) 2 =3$

$\bold⟹(16 {x}^{2} - 24x + 9) - 10(4 {x^{2} + 4x + 1)}$

$⟹(16x 2 −24x+9)−10(4x2 +4x+1)$

$\bold{= 3(8 {x}^{2} - 6x + 4x - 3)}=3(8x </p><p>2−6x+4x−3)$

$\bold{16 {x}^{2} - 24x + 9 - 40 {x}^{2} - 40x - 10}16x 2 −24x+9−40x 2−40x−10$

$\bold{ = 24 {x}^{2} - 18x + 12x - 9}=24x </p><p>2−18x+12x−9$

$\bold{⟹- 24 {x}^{2} - 64x - 1 = 24 {x}^{2} - 6x - 9}⟹−24x 2 −64x−1=24x 2 −6x−9$

$⟹\bold{- 24 {x}^{2} - 24 {x}^{2} - 64x + 6x - 1 + 9 = 0}⟹−24x 2−24x 2−64x+6x−1+9=0$

$⟹\bold{- 48 {x}^{2} - 58x + 8 = 0}$

$⟹−48x 2−58x+8=0$

$⟹\bold{24 {x}^{2} + 29x - 4 = 0}⟹24x </p><p>2+29x−4=0$

$⟹\bold{24 {x}^{2} + 32x - 3x - 4 = 0}$

⟹24x 2 +32x−3x−4=0

$⟹\bold{8x(3x + 4) - 1(3x + 4) = 0}$

⟹8x(3x+4)−1(3x+4)=0

$⟹\bold{(3x + 4)(8x - 1) = 0}$

⟹(3x+4)(8x−1)=0

$⟹\bold{3x + 4 = 0}⟹3x+4=0$

$⟹\bold{8x - 1 = 0}⟹8x−1=0$

$\bold{\boxed{\red{x = - \frac{4}{3} }}}$

x=−3/4