A hydraulic press has one piston of diameter 2.0 cm and the other piston of diameter 16.0 cm. What force must be applied to the smaller piston to obtain a force of 3200 N at the larger piston?

The force applied to the smaller piston = 2512 N

Explanation:

Hydraulic press: A hydraulic press is a device used to produce a very large force. A hydraulic force operates based on pascal's principle.

F/f = A/a ... Equation 1

making f the subject of the equation above

f = (F*a) / A ... Equation 2

Where F = Force on the larger piston, f = force on the smaller piston, A = area of the larger piston, a = area of the smaller piston.

Given: F = 3200 N, and

Area (A) = πD²/4 where D = 16.0 cm = 0.16 m

A = 3.143 * (0.16) ²/4 = 0.02 m²

Also

a = πd²/4 where d = 2 cm = 0.02 cm

a = 3.143 * (0.02) ²/4

a = 0.0157 m²

Substituting these values into equation 2

f = (3200*0.0157) / 0.02

f = 2512 N

The force applied to the smaller piston = 2512 N