A dentist's chair with a patient in it weighs 1880 N. The output plunger of a hydraulic system begins to lift the chair, when the dentist's foot applies a force of 71.5 N to the input piston. Neglect any height difference between the plunger and the piston. What is the ratio of the radius of the plunger to the radius of the piston? Output - plunger Input piston Number Units

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Chapter1: Units, Trigonometry. And Vectors
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**Hydraulic System Problem: Dentists Chair Lift**

A dentist's chair with a patient in it weighs 1880 N. The output plunger of a hydraulic system begins to lift the chair when the dentist's foot applies a force of 71.5 N to the input piston. Neglect any height difference between the plunger and the piston. What is the ratio of the radius of the plunger to the radius of the piston?

**Diagram Description:**
The diagram shows a simplified hydraulic system consisting of two main components – an input piston and an output plunger. 

- The output plunger is shown supporting a dentist's chair with a patient sitting in it.
- The input piston is depicted with the dentist applying a force using his foot.
- There is an arrow indicating the direction of the applied force by the dentist.
- The force is transmitted through the fluid from the input piston to the output plunger, resulting in the lifting of the chair.

**Calculation Field:**
A field is provided to input the numerical ratio of the radius of the plunger to the radius of the piston, with a text box labeled "Number" followed by an unlabeled units input. 

---

Note: To solve the problem, use Pascal’s principle in hydraulics, which states that pressure exerted anywhere in a confined incompressible fluid is transmitted equally in all directions throughout the fluid.
Transcribed Image Text:**Hydraulic System Problem: Dentists Chair Lift** A dentist's chair with a patient in it weighs 1880 N. The output plunger of a hydraulic system begins to lift the chair when the dentist's foot applies a force of 71.5 N to the input piston. Neglect any height difference between the plunger and the piston. What is the ratio of the radius of the plunger to the radius of the piston? **Diagram Description:** The diagram shows a simplified hydraulic system consisting of two main components – an input piston and an output plunger. - The output plunger is shown supporting a dentist's chair with a patient sitting in it. - The input piston is depicted with the dentist applying a force using his foot. - There is an arrow indicating the direction of the applied force by the dentist. - The force is transmitted through the fluid from the input piston to the output plunger, resulting in the lifting of the chair. **Calculation Field:** A field is provided to input the numerical ratio of the radius of the plunger to the radius of the piston, with a text box labeled "Number" followed by an unlabeled units input. --- Note: To solve the problem, use Pascal’s principle in hydraulics, which states that pressure exerted anywhere in a confined incompressible fluid is transmitted equally in all directions throughout the fluid.
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