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Chapter 2: Problem 6

Compare a base unit and a derived unit, and list the derived units used for density and volume

Short Answer

Expert verified
A base unit is a fundamental unit of measurement that cannot be derived from or expressed in terms of other base units, while a derived unit is formed using base units through mathematical relationships or formulas. The SI derived unit for density is kilogram per cubic meter (kg/m^3), as density is mass per unit volume. The SI derived unit for volume is cubic meter (m^3), which is obtained by raising the base unit for length (m) to the power of 3.

Step by step solution

01

Define Base Units

Base units are the fundamental units of measurement in a system. These units are independent and cannot be derived from or expressed in terms of other base units. They form the foundation of the system of units. For example, in the International System of Units (SI), there are seven base units: kilogram (kg) for mass, meter (m) for length, second (s) for time, ampere (A) for electric current, kelvin (K) for thermodynamic temperature, mole (mol) for amount of substance, and candela (cd) for luminous intensity.
02

Define Derived Units

Derived units are the units that are derived from the base units using mathematical relationships or formulas. They are combinations of base units, usually obtained by multiplication and division operations. Examples of derived units include area, volume, speed, acceleration, and density.
03

Compare Base Units and Derived Units

Here are the key differences between base units and derived units: 1. Base units are the fundamental units, while derived units are formed using base units. 2. Base units cannot be expressed in terms of other units, while derived units can be expressed in terms of base units. 3. The number of base units is limited, while there are numerous derived units depending on the physical quantities being measured.
04

Identify Derived Units for Density and Volume

Density is defined as mass per unit volume. Therefore, the derived unit for density can be obtained by dividing the base unit for mass (kg) by the derived unit for volume (m^3). The SI derived unit for density is thus kilogram per cubic meter (kg/m^3). Volume, on the other hand, is the measure of space occupied by a substance. The derived unit for volume can be obtained by raising the base unit for length (m) to the power of 3 (i.e., cubing it). The SI derived unit for volume is thus cubic meter (m^3).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Base Units
Base units form the cornerstone of the International System of Units (SI). These units are the fundamental building blocks of measurement systems. They are independent and cannot be broken down into or described using other units. In SI, there are seven base units:
  • Kilogram (kg): The unit for mass.
  • Meter (m): The unit for length.
  • Second (s): The unit for time.
  • Ampere (A): The unit for electric current.
  • Kelvin (K): The unit for thermodynamic temperature.
  • Mole (mol): The unit for amount of substance.
  • Candela (cd): The unit for luminous intensity.
These base units provide a foundation for forming other complex units, known as derived units. Remember, these are the essential, unmixed entities of measurement.
Derived Units
Derived units are created by combining base units through mathematical operations like multiplication or division. They offer a way to measure more complex physical quantities:
  • Area: Formed by squaring length (m2).
  • Volume: Formed by cubing length (m3).
  • Speed: Formed by dividing distance by time (m/s).
  • Acceleration: Formed by dividing speed by time (m/s2).
  • Density: Formed by dividing mass by volume (kg/m3).
Derived units extend the functionality of base units, allowing us to express a wide range of physical properties. They serve as a bridge between simple base measures and the complex realities we observe.
Density
Density is a derived unit that represents mass per unit volume. It helps in understanding how compact or concentrated a substance is. To find the density of a material, you use the formula:
  • \[\text{Density} = \frac{\text{Mass}}{\text{Volume}}\]
Using SI units, this becomes kilograms per cubic meter (kg/m3). Knowing a substance's density can tell you how much of it is crammed into a given space. This measurement is vital for many scientific and engineering applications, like determining whether an object will float or sink in water.
Volume
Volume measures the amount of space an object occupies. It is a derived unit obtained by raising the base unit of length, the meter, to the third power (m3). Commonly in everyday contexts, you might hear of volume in liters or milliliters, but in scientific contexts, cubic meters are standard.
  • It is crucial in various fields:
  • Helps in computing the capacity of containers.
  • Important in chemistry for measuring the amount of fluids.
  • Vital in construction and architecture for assessing materials needed.
Mastering how to measure and calculate volume allows for better understanding and manipulation of physical spaces and resources efficiently.

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