**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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Question
![**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 \( 5.98 \, \text{m}^2 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4275793-d0d9-4c18-8132-1bc68d69e927%2F025bfdaf-c04d-4f23-a14b-9e2a68c5570e%2Fiadkyf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**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 \( 5.98 \, \text{m}^2 \).
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