Lignum vitae is a hard, durable, and extremely dense wood used to make ship bearings. A sphere of this wood with a diameter of 7.60 cm has a mass of 313 g. (a) What is the density of the lignum vitae sphere? (b) Will the sphere float or sink in water? (c) Will the sphere float or sink in chloroform? (The density of chloroform is 1.48 g/mL.)

Key Concepts

Density

Density is defined as mass per unit volume, typically expressed in grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). It is a crucial property that helps determine whether an object will float or sink in a fluid. The formula for density is D = m/V, where D is density, m is mass, and V is volume. Understanding how to calculate density is essential for solving the problem regarding the lignum vitae sphere.

Buoyancy

Buoyancy refers to the ability of an object to float in a fluid, which is determined by the relationship between the object's density and the density of the fluid. An object will float if its density is less than that of the fluid and sink if its density is greater. This principle is governed by Archimedes' principle, which states that the upward buoyant force on an object is equal to the weight of the fluid displaced by the object. Understanding buoyancy is key to answering whether the sphere will float or sink in water and chloroform.

Volume of a Sphere

The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius of the sphere. This calculation is necessary to determine the volume of the lignum vitae sphere, which is essential for calculating its density. Knowing how to derive the volume from the diameter is important for solving part (a) of the question, as it directly impacts the density calculation.