(a) Find the force P that must be applied to a piston of area 11.60 cm2 to produce sufficient fluid pressure to support a car weighing 10,001 N by means of a column of fluid of cross sectional area 285 cm2 as seen in the figure below. (b) Find the increase in the car's gravitational potential energy when it is raised 1.00 m. (c) How far must the smaller piston move in order for the larger one to move 1.00 m?

Physics for Scientists and Engineers: Foundations and Connections
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Author:Katz, Debora M.
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Chapter15: Fluids
Section: Chapter Questions
Problem 57PQ: Water flows through a pipe that gradually descends from a height of 6.78 m to the ground. Near the...
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(a) Find the force P that must be applied to a piston of area 11.60 cm2 to produce sufficient fluid pressure to support a car weighing 10,001 N by means of a column of fluid of cross sectional area 285 cm2 as seen in the figure below.


(b) Find the increase in the car's gravitational potential energy when it is raised 1.00 m.


(c) How far must the smaller piston move in order for the larger one to move 1.00 m?


(d) Calculate the work done by P in moving the smaller piston.
The image illustrates a hydraulic lift system using Pascal's principle. It shows a car placed on a large piston connected to a narrow, horizontal tube containing fluid. On the left, another narrow vertical piston is marked with a downward arrow labeled "P," indicating applied pressure.

### Explanation:

1. **Hydraulic System:**
   - The system consists of two pistons of different sizes connected by a fluid-filled chamber.
   
2. **Pressure Application (P):**
   - Pressure is applied to the smaller piston on the left. According to Pascal's principle, any change in pressure applied to an enclosed fluid is transmitted undiminished throughout the fluid.

3. **Lifting Mechanism:**
   - The large piston on the right supports the car. When pressure is applied to the small piston, it is transmitted through the fluid, creating an upward force that lifts the car.

4. **Principle of Operation:**
   - The system demonstrates how hydraulic lifts can magnify force. Since pressure is constant throughout the fluid, a small force applied to the smaller piston results in a larger force on the larger piston, enabling it to lift heavy objects like cars.

This setup is commonly used in car workshops for the underbody maintenance of vehicles.
Transcribed Image Text:The image illustrates a hydraulic lift system using Pascal's principle. It shows a car placed on a large piston connected to a narrow, horizontal tube containing fluid. On the left, another narrow vertical piston is marked with a downward arrow labeled "P," indicating applied pressure. ### Explanation: 1. **Hydraulic System:** - The system consists of two pistons of different sizes connected by a fluid-filled chamber. 2. **Pressure Application (P):** - Pressure is applied to the smaller piston on the left. According to Pascal's principle, any change in pressure applied to an enclosed fluid is transmitted undiminished throughout the fluid. 3. **Lifting Mechanism:** - The large piston on the right supports the car. When pressure is applied to the small piston, it is transmitted through the fluid, creating an upward force that lifts the car. 4. **Principle of Operation:** - The system demonstrates how hydraulic lifts can magnify force. Since pressure is constant throughout the fluid, a small force applied to the smaller piston results in a larger force on the larger piston, enabling it to lift heavy objects like cars. This setup is commonly used in car workshops for the underbody maintenance of vehicles.
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