An ore sample weighs 17.50 N in air. When the sample is suspended by a light cord and totally im

step 1 Okay, in this problem, what the tension reads is the difference between the gravitational force

An ore sample weighs 17.50 N in air. When the sample is...

An ore sample weighs 17.50 $\mathrm{N}$ in air. When the sample is suspended by a light cord and totally immersed in water, the tension in the cord is 11.20 $\mathrm{N}$ . Find the total volume and the density of the sample.

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Key Concepts

Archimedes' Principle

Archimedes' Principle states that any object fully or partially immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced. This principle is crucial when determining how a submerged object's apparent weight changes relative to its true weight in air.

Buoyant Force

Buoyant force is the upward force exerted by a fluid that opposes the weight of an immersed object. It is determined by the volume of the fluid displaced and the density of the fluid, which in turn affects the net force experienced by the object when submerged.

Apparent Weight

Apparent weight refers to the weight of an object as measured when it is submerged in a fluid. Since the fluid provides an upward buoyant force, the apparent weight is less than the true weight measured in air. The difference between these weights can be used to calculate properties such as volume and density.

Volume and Density Relationship

The relationship between an object's volume, density, and weight is fundamental in physics. Density is defined as mass divided by volume, and weight is the product of mass and gravitational acceleration. By determining the volume of displaced fluid (using the buoyant force) and knowing the true weight of the object, one can calculate the object's density.

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