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A force of magnitude 800. N is applied to the center cylinder in the figure, downward on its 7.50 cm- radius piston. The master piston is pushed 1.000 cm into the cylinder and the radii of the two identical slaves are 2.000 cm. 4) Calculate the pressure in the system as the force is applied.

A force of magnitude 800. N is applied to the center cylinder in the figure, downward on its 7.50 cm- radius piston. The master piston is pushed 1.000 cm into the cylinder and the radii of the two identical slaves are 2.000 cm. 4) Calculate the pressure in the system as the force is applied.

College Physics
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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**Problems 4-6 refer to the following figure** --- **Figure Explanation:** The figure illustrates a system with three connected cylinders. The central cylinder has a piston with a 7.50 cm radius, and an external force of magnitude 800 N is applied downward on this central piston. The master piston is pushed 1.000 cm into the cylinder. The two slave cylinders on either side are identical, with each having a piston radius of 2.000 cm. --- **Problem Statements:** 4) **Calculate the pressure in the system as the force is applied.** 5) **Calculate the magnitude of the force exerted upward on the left slave piston.** 6) **Calculate the distance the right slave piston travels.** --- **Detailed Instructions for Problems:** - **Problem 4:** Use the given force and the area of the master piston to compute the pressure in the system by applying the formula \( P = \frac{F}{A} \), where \( P \) is the pressure, \( F \) is the force applied (800 N), and \( A \) is the area of the piston \( (\pi r^2) \). - **Problem 5:** Once the pressure \( P \) in the system is determined from Problem 4, use it to calculate the force on one of the slave pistons using the formula \( F_{slave} = P \cdot A_{slave} \), where \( A_{slave} \) is the area of one of the slave pistons. - **Problem 6:** For fluid displacement, use the relationship between the volume displaced by the master piston and the volume displaced by the slave pistons. The volume displaced in the master piston must be equal to the total volume displaced by the slave pistons (considering there are two). --- **Note:** For visual learners, refer to the detailed 3D representation of the system, which shows the positions and dimensions of the master and slave pistons clearly.
Transcribed Image Text:**Problems 4-6 refer to the following figure** --- **Figure Explanation:** The figure illustrates a system with three connected cylinders. The central cylinder has a piston with a 7.50 cm radius, and an external force of magnitude 800 N is applied downward on this central piston. The master piston is pushed 1.000 cm into the cylinder. The two slave cylinders on either side are identical, with each having a piston radius of 2.000 cm. --- **Problem Statements:** 4) **Calculate the pressure in the system as the force is applied.** 5) **Calculate the magnitude of the force exerted upward on the left slave piston.** 6) **Calculate the distance the right slave piston travels.** --- **Detailed Instructions for Problems:** - **Problem 4:** Use the given force and the area of the master piston to compute the pressure in the system by applying the formula \( P = \frac{F}{A} \), where \( P \) is the pressure, \( F \) is the force applied (800 N), and \( A \) is the area of the piston \( (\pi r^2) \). - **Problem 5:** Once the pressure \( P \) in the system is determined from Problem 4, use it to calculate the force on one of the slave pistons using the formula \( F_{slave} = P \cdot A_{slave} \), where \( A_{slave} \) is the area of one of the slave pistons. - **Problem 6:** For fluid displacement, use the relationship between the volume displaced by the master piston and the volume displaced by the slave pistons. The volume displaced in the master piston must be equal to the total volume displaced by the slave pistons (considering there are two). --- **Note:** For visual learners, refer to the detailed 3D representation of the system, which shows the positions and dimensions of the master and slave pistons clearly.
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