Topic: Find the Relation Between A₁ and A₂

In many physics problems, especially involving pulleys, hydraulics, and fluid systems, we encounter two cross-sectional areas: A₁ and A₂. To find the relation between them, we use the principle of continuity of flow or mechanical equilibrium.

For Hydraulics (Pascal’s Law):
If force is applied on one piston with area A₁ and transferred to another piston with area A₂,

F1A1=F2A2
A
1
​

F
1
​

​

=
A
2
​

F
2
​

​


This means the pressure is constant throughout the fluid.

For Fluid Flow (Continuity Equation):
If a fluid flows through two sections of a pipe,

A1v1=A2v2
A
1
​

v
1
​

=A
2
​

v
2
​


Here, the product of area and velocity remains constant (conservation of mass).

For Pulleys (Rope Systems):
Areas A₁ and A₂ may represent displacements or loop segments where the relation depends on the geometry of the pulley system.

Thus, the relation between A₁ and A₂ depends on the physical situation, but it always arises from a conservation principle: either pressure, mass flow, or mechanical advantage.
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