The small and large pistons of an ideal hydraulic machine have areas 4 cm² and 100 cm², respectively. If the large piston rises by 4 cm, the small piston must move downward through N cm. Find N.
Physics · Fluid Mechanics · pascal law and buoyant force
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Question

The small and large pistons of an ideal hydraulic machine have areas 4 cm² and 100 cm², respectively. If the large piston rises by 4 cm, the small piston must move downward through N cm. Find N.

G1 Physics · Accepted Answer

For an incompressible hydraulic fluid, A(small)x(small) = A(large)x(large). Therefore, x(small) = A(large)x(large)/A(small). Substitute A(large) = 100 cm², x(large) = 4 cm, A(small) = 4 cm². Thus, x(small) = 100×4/4 = 100 cm. Hence, N = 100.