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In the above figure, the master cylinder has a circular cross section and a radius of 1.000 m. The slave cylinder has a radius of 24.50 cm. 1) What force must be applied down on the piston of the master cylinder to attain a pressure of 1.600 × 10° Pa in the system?

In the above figure, the master cylinder has a circular cross section and a radius of 1.000 m. The slave cylinder has a radius of 24.50 cm. 1) What force must be applied down on the piston of the master cylinder to attain a pressure of 1.600 × 10° Pa in the system?

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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--- Remember for these problems that in calculating the results, I’m using the value of π found on the PRC. If you round π to 3.14 in your calculations there is potential for your answer to be taken out of tolerance for a solution that uses the correct method. For numeric entry problems, report more digits in your answer than are significant, convert to standard units if necessary, and do not include the unit in the answer field. Bb understands 1.2345 E4 with no spaces and the E capitalized to be 1.2345 × 10⁴ if you choose to enter numbers in scientific notation. ### Problems 1-3 refer to the following figure. ![Hydraulic System Diagram](image URL) In the above figure, the master cylinder has a circular cross section and a radius of 1.000 m. The slave cylinder has a radius of 24.50 cm. 1. **What force must be applied down on the piston of the master cylinder to attain a pressure of 1.600 × 10⁶ Pa in the system?** A) 3.0172 × 10⁵ N B) 3.0174 × 10⁵ N C) 3.0175 × 10⁵ N D) 3.0176 × 10⁵ N E) 5.0270 × 10⁶ N F) 5.0272 × 10⁶ N G) 5.0275 × 10⁶ N H) 5.0275 × 10⁶ N --- #### Explanation of Diagram The diagram represents a hydraulic system featuring two connected cylinders with pistons of different radii. The master cylinder, larger of the two, has a radius of 1.000 meter. The slave cylinder, which is smaller, has a radius of 24.50 centimeters. The pistons are interconnected, meaning force applied on the master cylinder's piston translates to pressure within the system, affecting the slave cylinder. This principle is commonly explained by Pascal's Law in fluid mechanics, where pressure applied to a confined fluid is transmitted undiminished throughout the fluid in all directions. ---
Transcribed Image Text:--- Remember for these problems that in calculating the results, I’m using the value of π found on the PRC. If you round π to 3.14 in your calculations there is potential for your answer to be taken out of tolerance for a solution that uses the correct method. For numeric entry problems, report more digits in your answer than are significant, convert to standard units if necessary, and do not include the unit in the answer field. Bb understands 1.2345 E4 with no spaces and the E capitalized to be 1.2345 × 10⁴ if you choose to enter numbers in scientific notation. ### Problems 1-3 refer to the following figure. ![Hydraulic System Diagram](image URL) In the above figure, the master cylinder has a circular cross section and a radius of 1.000 m. The slave cylinder has a radius of 24.50 cm. 1. **What force must be applied down on the piston of the master cylinder to attain a pressure of 1.600 × 10⁶ Pa in the system?** A) 3.0172 × 10⁵ N B) 3.0174 × 10⁵ N C) 3.0175 × 10⁵ N D) 3.0176 × 10⁵ N E) 5.0270 × 10⁶ N F) 5.0272 × 10⁶ N G) 5.0275 × 10⁶ N H) 5.0275 × 10⁶ N --- #### Explanation of Diagram The diagram represents a hydraulic system featuring two connected cylinders with pistons of different radii. The master cylinder, larger of the two, has a radius of 1.000 meter. The slave cylinder, which is smaller, has a radius of 24.50 centimeters. The pistons are interconnected, meaning force applied on the master cylinder's piston translates to pressure within the system, affecting the slave cylinder. This principle is commonly explained by Pascal's Law in fluid mechanics, where pressure applied to a confined fluid is transmitted undiminished throughout the fluid in all directions. ---
### Physics Problem Set on Hydraulic Systems **2) What magnitude force pushes up on the slave cylinder if the pressure in the system is 1.600 × 10⁶ Pa?** A) 3.0172 × 10⁵ N B) 3.0174 × 10⁵ N C) 3.0175 × 10⁵ N D) 3.0176 × 10⁵ N E) 5.0247 × 10⁵ N F) 5.0272 × 10⁵ N G) 5.0265 × 10⁵ N H) 5.0251 × 10⁵ N **3) If the piston of the slave cylinder is extended through a distance 45.00 cm, calculate the distance through which the piston of the master cylinder must be pushed to achieve this movement if friction in the system is negligible. You can assume the movement is done when the system is at a pressure of 1.600 × 10⁶ Pa, but this isn’t strictly necessary to do the problem.** **Problems 4-6 refer to the following figure:** ![Diagram of a hydraulic system](image/diagram.png) 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. 5) Calculate the magnitude of the force exerted upward on the left slave piston. 6) Calculate the distance the right slave piston travels.
Transcribed Image Text:### Physics Problem Set on Hydraulic Systems **2) What magnitude force pushes up on the slave cylinder if the pressure in the system is 1.600 × 10⁶ Pa?** A) 3.0172 × 10⁵ N B) 3.0174 × 10⁵ N C) 3.0175 × 10⁵ N D) 3.0176 × 10⁵ N E) 5.0247 × 10⁵ N F) 5.0272 × 10⁵ N G) 5.0265 × 10⁵ N H) 5.0251 × 10⁵ N **3) If the piston of the slave cylinder is extended through a distance 45.00 cm, calculate the distance through which the piston of the master cylinder must be pushed to achieve this movement if friction in the system is negligible. You can assume the movement is done when the system is at a pressure of 1.600 × 10⁶ Pa, but this isn’t strictly necessary to do the problem.** **Problems 4-6 refer to the following figure:** ![Diagram of a hydraulic system](image/diagram.png) 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. 5) Calculate the magnitude of the force exerted upward on the left slave piston. 6) Calculate the distance the right slave piston travels.
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