The spring of the pressure gauge shown in Figure P14.7 has a...

Name: Problem 7, Chapter 14: Physics for Scientists and Engineers with Modern Physics
Uploaded: 2021-08-26T01:31:43-08:00
Duration: 4 min 46 s
Channel: Eduard Sanchez
Description: The spring of the pressure gauge shown in Figure P14.7 has a force constant of 1 250 N/m, and the piston has a diameter of 1.20 cm. As the gauge is lowered into water in a lake, what change in depth causes the piston to move in by 0.750 cm?

The spring of the pressure gauge shown in Figure P14.7 has a force constant of 1 250 N/m, and the piston has a diameter of 1.20 cm. As the gauge is lowered into water in a lake, what change in depth causes the piston to move in by 0.750 cm?

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Key Concepts

Hooke's Law

Hooke's Law describes the direct proportionality between the force applied to a spring and its resulting displacement, expressed as F = kx, where k is the spring constant and x is the displacement. This concept is crucial for determining how much force is required to compress or extend the spring by a given distance.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the gravitational force acting on it, calculated as P = ?gh, where ? is the fluid density, g is the acceleration due to gravity, and h is the depth. This principle explains how pressure increases with depth in a fluid such as water.

Pressure Acting on a Surface

The force exerted by a fluid on a surface is determined by the pressure of the fluid and the area over which it acts, using the relationship F = PA. This concept is key in relating the pressure increase due to depth with the force applied on the piston of the gauge.

Area Calculation for a Circular Piston

The area of a circular piston is found using the formula A = ?r², or equivalently A = (?d²)/4, where r is the radius and d is the diameter. This calculation is necessary for determining the surface area on which the fluid’s pressure exerts force, linking the geometric properties of the piston to the resultant force in the system.

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