A piston, A, has a diameter of 0.53 cm. A second piston, B, has a diameter of 3.5 cm.Determine the force, F, necessary to support the 500.0 N weight in the absence of friction.
The key relationship is that the Pressure at piston A (Pa) equals the pressure at piston B (Pb). Pa = Pb
Pressure equals force divided by area. P = F/A
So you have: Fa/Aa = Fb/Ab
The area of a circle is pi r^2.
The force on piston B is 500 N and the radius is 1.75 cm.
The force on piston A is unknown, and the radius is 0.275 cm
Substituting into the equation:
Fa/(pi* .275^2) = 500 /( pi*1.75^2)
Solve for Fa = .275^2/1.75^2 * 500
Fa = 12.35 N