If a dentist's chair weighs 1600 N and is raised by a large piston with cross sectional area 75.0 cm², what force must be exerted on a small piston of cross-sectional area 3.75 cm² to lift the chair?
If a dentist's chair weighs 1600 N and is raised by a large piston with cross sectional area 75.0 cm², what force must be exerted on a small piston of cross-sectional area 3.75 cm² to lift the chair?
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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![**Problem Statement:**
If a dentist’s chair weighs 1600 N and is raised by a large piston with a cross-sectional area of 75.0 cm², what force must be exerted on a small piston of cross-sectional area 3.75 cm² to lift the chair?
**Explanation:**
This physics problem is related to Pascal's Principle, which states that pressure applied to a confined fluid is transmitted undiminished in all directions throughout the fluid. By using pistons of different sizes, a small force can be transformed into a larger force.
To solve this, you can use the formula for pressure:
\[ \text{Pressure} (P) = \frac{\text{Force} (F)}{\text{Area} (A)} \]
Since the pressures are equal, you can equate the two:
\[ \frac{F_1}{A_1} = \frac{F_2}{A_2} \]
Where:
- \( F_1 \) is the force exerted by the smaller piston.
- \( A_1 \) is the area of the smaller piston (3.75 cm²).
- \( F_2 \) is the force exerted by the larger piston (1600 N).
- \( A_2 \) is the area of the larger piston (75.0 cm²).
Rearranging for \( F_1 \):
\[ F_1 = \frac{F_2 \times A_1}{A_2} \]
Plug in the given values to find the force needed on the small piston.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc463f08e-ec7e-4810-a9a2-5563bca4d00b%2F76551db0-555e-42ee-b3d1-3ea017e06101%2Fmvs9ozb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
If a dentist’s chair weighs 1600 N and is raised by a large piston with a cross-sectional area of 75.0 cm², what force must be exerted on a small piston of cross-sectional area 3.75 cm² to lift the chair?
**Explanation:**
This physics problem is related to Pascal's Principle, which states that pressure applied to a confined fluid is transmitted undiminished in all directions throughout the fluid. By using pistons of different sizes, a small force can be transformed into a larger force.
To solve this, you can use the formula for pressure:
\[ \text{Pressure} (P) = \frac{\text{Force} (F)}{\text{Area} (A)} \]
Since the pressures are equal, you can equate the two:
\[ \frac{F_1}{A_1} = \frac{F_2}{A_2} \]
Where:
- \( F_1 \) is the force exerted by the smaller piston.
- \( A_1 \) is the area of the smaller piston (3.75 cm²).
- \( F_2 \) is the force exerted by the larger piston (1600 N).
- \( A_2 \) is the area of the larger piston (75.0 cm²).
Rearranging for \( F_1 \):
\[ F_1 = \frac{F_2 \times A_1}{A_2} \]
Plug in the given values to find the force needed on the small piston.
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