Final answer:
Using Pascal's principle to calculate pressure transmission in a hydraulic press, the force generated by the press (F²) is found to be 100 N when the applied force (F¹) is 25 N and the areas involved are 0.5 m² and 2 m² respectively.
Step-by-step explanation:
To calculate the force generated by a hydraulic press (F²) when given F¹ = 25 N, A¹ = 0.5 m², and A² = 2 m², we use Pascal's principle which states that pressure is transmitted undiminished in an enclosed static fluid. We assume the hydraulic press is an ideal system, so the pressure (P) exerted by F¹ on A¹ must equal the pressure exerted by F² on A². The formula to calculate the pressure is P = F/A, so:
P¹=P²
(F¹/A¹)=(F²/A²)
(25 N/0.5 m²) = (F²/2 m²)
50 N/m² = (F²/2 m²)
F² = 100 N
To calculate the force generated by a hydraulic press, you can use the formula F² = F¹ * A² / A¹, where F¹ is the initial force, A¹ is the initial area, A² is the final area, and F² is the final force. Substituting the given values, we have F² = 25 N * 2 m² / 0.5 m² = 100 N. Therefore, the force generated by the hydraulic press is 100 N.
This shows that option (b) 100 N is the correct force generated by the hydraulic press.