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For a material to float on the surface of water, the material must have a density less than that of water $(1.0 \mathrm{~g} / \mathrm{mL})$ and must not react with the water or dissolve in it. A spherical ball has a radius of $0.50 \mathrm{~cm}$ and weighs $2.0 \mathrm{~g}$. Will this ball float or sink when placed in water? (Note: Volume of a sphere $=\frac{4}{3} \pi r^{3}$.)

Name: Problem 60, Chapter 1: Chemistry
Uploaded: 2020-06-13T23:15:33-08:00
Duration: 2 min 10 s
Channel: Asma Hafiz
Description: For a material to float on the surface of water, the material must have a density less than that of water (1.0 g / mL) and must not react with the water or dissolve in it. A spherical ball has a radius of 0.50 cm and weighs 2.0 g. Will this ball float or sink when placed in water? (Note: Volume of a sphere =(4)/(3) πr^3.)

   For a material to float on the surface of water, the material must have a density less than that of water $(1.0 \mathrm{~g} / \mathrm{mL})$ and must not react with the water or dissolve in it. A spherical ball has a radius of $0.50 \mathrm{~cm}$ and weighs $2.0 \mathrm{~g}$. Will this ball float or sink when placed in water? (Note: Volume of a sphere $=\frac{4}{3} \pi r^{3}$.)

Chemistry

Steven S. Zumdahl,… 8th Edition

Chapter 1, Problem 60

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Solved by Expert Asma Hafiz

06/13/2020

Step 1

Volume = (4/3) * π * r^3 Volume = (4/3) * π * (0.50 cm)^3 Volume ≈ 0.52 cm³ Show more…

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For a material to float on the surface of water, the material must have a density less than that of water $(1.0 \mathrm{~g} / \mathrm{mL})$ and must not react with the water or dissolve in it. A spherical ball has a radius of $0.50 \mathrm{~cm}$ and weighs $2.0 \mathrm{~g}$. Will this ball float or sink when placed in water? (Note: Volume of a sphere $=\frac{4}{3} \pi r^{3}$.)

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Key Concepts

Volume of a Sphere

The volume of a sphere is determined using the formula 4/3 ? r³, where r is the radius of the sphere. This calculation helps in determining the amount of space the object occupies, which is crucial for finding its density by comparing its mass to its volume.

Buoyancy

Buoyancy is the upward force exerted by a fluid on an object immersed in it. According to Archimedes' principle, an object will float if the buoyant force (which depends on the volume of fluid displaced) is equal to or greater than its weight. This principle is key to understanding why an object floats or sinks in a fluid based on its density relative to that fluid.

Density

Density is a measure of how much mass is contained in a given volume. It is calculated by dividing the mass of an object by its volume. This concept is essential in buoyancy problems as an object will float in a fluid if its density is lower than that of the fluid, and sink if it is higher.

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