A hydraulic press has one piston of diameter 2.0 cm and the other piston of diameter 8.0 cm.What force must be applied to the smaller piston to obtain a force of 1600 N at the larger piston:
A)100 N
B)400 N
C)1600 N
D)6400 N
E)26000 N

Question

Quizplus · Accepted Answer

The force needed on the smaller piston can be found using the principle of hydraulic systems, which states that the pressure applied at one point is transmitted equally throughout the fluid. The pressure (P) is given by the force (F) divided by the area (A), so P = F/A. Since the pressure is the same on both pistons, F1/A1 = F2/A2, where F1 and F2 are the forces on the smaller and larger pistons, respectively, and A1 and A2 are their respective areas. The areas can be calculated using the formula for the area of a circle, A = πr^2, where r is the radius of the piston. Therefore, the force required on the smaller piston is calculated by rearranging the formula to F1 = (A1/A2) * F2. Substituting the given values and converting diameters to radii (1 cm for the smaller piston and 4 cm for the larger piston), we find that F1 = (π*(1^2)/π*(4^2)) * 1600 N = (1/16)*1600 N = 100 N.

A Hydraulic Press Has One Piston of Diameter 2