A tin can has a total volume of 1200 cm^3 and a mass of 130 g. How many grams of lead shot of

step 1 And this problem, we have a tin can floating in water. We're told that it has a volume of 1 ,200

A tin can has a total volume of 1200 cm^3 and a mass of 130...

A tin can has a total volume of $1200 \mathrm{~cm}^{3}$ and a mass of $130 \mathrm{~g}$. How many grams of lead shot of density $11.4 \mathrm{~g} / \mathrm{cm}^{3}$ could it carry without sinking in water?

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Key Concepts

Archimedes' Principle

This principle states that any object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. In equilibrium (i.e., floating), the weight of the object is balanced by the buoyant force, which is central to determining the conditions under which an object will remain afloat.

Buoyancy Condition

The buoyancy condition for floating requires that the total weight of an object (including any additional mass it carries) must not exceed the weight of the fluid displaced by its external volume. This concept is used to calculate the maximum extra mass that can be added to an object before it sinks.

Density and Mass-Volume Relationship

Density, defined as mass per unit volume, links an object's mass to the space it occupies. Understanding this relationship allows for conversion between mass and volume, an essential step when dealing with different materials and assessing whether the volume displacement is sufficient to support a given mass in fluids.

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