Final answer:
To calculate the force required on the smaller piston to obtain a force of 3200 N at the larger piston in a hydraulic press, we can use Pascal's law and the formula P1A1 = P2A2. By rearranging the formula and substituting the given values, we can calculate the force applied to the smaller piston.
Step-by-step explanation:
The force required on the smaller piston to obtain a force of 3200 N at the larger piston in a hydraulic press can be calculated using Pascal's law which states that the pressure applied to an enclosed fluid is transmitted undiminished to all parts of the fluid and to the walls of its container.
Pascal's law can be expressed as:
P1A1 = P2A2
Where P1 is the pressure at the smaller piston, A1 is the area of the smaller piston, P2 is the pressure at the larger piston, and A2 is the area of the larger piston.
Given that the diameter of the smaller piston is 2.0 cm and the diameter of the larger piston is 16.0 cm, we can calculate the areas of the pistons as:
A1 = π(r1^2) = π(1.0^2) = 3.14 cm^2
A2 = π(r2^2) = π(8.0^2) = 200.96 cm^2
Since P2 is given as 3200 N, we can rearrange the equation to solve for P1:
P1 = (P2A2) / A1
P1 = (3200 N * 200.96 cm^2) / 3.14 cm^2
P1 = 200,960 N/cm^2
Therefore, the force required on the smaller piston to obtain a force of 3200 N at the larger piston is:
Force = P1 * A1 = 200,960 N/cm^2 * 3.14 cm^2
Force = 631,446.4 N