**Problem Statement:** 2. If 34 N of force, applied to a piston with an area of 0.3 m², is sufficient to lift 678 N, calculate the area of the output piston. **Explanation:** This problem involves the principles of Pascal's Law, which states that pressure applied at any point to a confined fluid is transmitted undiminished throughout the fluid. This is often used in hydraulic systems. Let: - \( F_1 = 34 \, \text{N} \) (force applied to the input piston) - \( A_1 = 0.3 \, \text{m}^2 \) (area of the input piston) - \( F_2 = 678 \, \text{N} \) (force lifted by the output piston) - \( A_2 \) (unknown area of the output piston to be calculated) According to Pascal's Law: \[ \frac{F_1}{A_1} = \frac{F_2}{A_2} \] Substituting the known values to find \( A_2 \): \[ \frac{34 \, \text{N}}{0.3 \, \text{m}^2} = \frac{678 \, \text{N}}{A_2} \] Solving for \( A_2 \): \[ A_2 = \frac{678 \, \text{N} \times 0.3 \, \text{m}^2}{34 \, \text{N}} \] Calculating gives: \[ A_2 = \frac{203.4 \, \text{Nm}^2}{34 \, \text{N}} \approx 5.98 \, \text{m}^2 \] Therefore, the area of the output piston is approximately \( 5.98 \, \text{m}^2 \).

Problem Statement: 2. If 34 N of force, applied to a piston with an area of 0.3 m², is sufficient to lift 678 N, calculate the area of the output piston. Explanation: This problem involves the principles of Pascal's Law, which states that pressure applied at any point to a confined fluid is transmitted undiminished throughout the fluid. This is often used in hydraulic systems. Let: - \( F_1 = 34 \, \text{N} \) (force applied to the input piston) - \( A_1 = 0.3 \, \text{m}^2 \) (area of the input piston) - \( F_2 = 678 \, \text{N} \) (force lifted by the output piston) - \( A_2 \) (unknown area of the output piston to be calculated) According to Pascal's Law: \[ \frac{F_1}{A_1} = \frac{F_2}{A_2} \] Substituting the known values to find \( A_2 \): \[ \frac{34 \, \text{N}}{0.3 \, \text{m}^2} = \frac{678 \, \text{N}}{A_2} \] Solving for \( A_2 \): \[ A_2 = \frac{678 \, \text{N} \times 0.3 \, \text{m}^2}{34 \, \text{N}} \] Calculating gives: \[ A_2 = \frac{203.4 \, \text{Nm}^2}{34 \, \text{N}} \approx 5.98 \, \text{m}^2 \] Therefore, the area of the output piston is approximately \( 5.98 \, \text{m}^2 \).

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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