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Chapter 1: Problem 2

Explain what a "derived unit" of measure is.

Short Answer

Expert verified
Answer: A derived unit of measure is a unit that is derived from a set of fundamental or base units through algebraic operations like multiplication and division. Some common examples of derived units include area (square meter, m^2), volume (cubic meter, m^3), speed (meter per second, m/s), acceleration (meter per second squared, m/s^2), and force (newton, N). Derived units are used to measure physical quantities that are not covered by base units.

Step by step solution

01

Define a unit of measure

A unit of measure is a standardized quantity of a physical property such as length, mass, time, temperature, etc., used to express the value of that property in a specific measurement system (like the International System of Units, or SI).
02

Define derived units

Derived units are units of measure that are obtained by combining the base units through algebraic operations like multiplication and division. They are derived from a set of fundamental or base units and are used to measure physical quantities that are not covered by base units.
03

Give examples of derived units

Some examples of derived units are: 1. Area (square meter, m^2) - Derived from the base unit of length (meter, m) by multiplying it by itself: m x m = m^2. 2. Volume (cubic meter, m^3) - Similar to area, derived from the base unit of length (meter, m) by multiplying it by itself three times: m x m x m = m^3. 3. Speed (meter per second, m/s) - Derived from the base units of length (meter, m) and time (second, s). The speed is found by dividing the length unit by the time unit: m / s = m/s. 4. Acceleration (meter per second squared, m/s^2) - Derived by dividing a speed unit (m/s) by a time unit (s) again: (m/s) / s = m/s^2. 5. Force (newton, N) - Measured in units of mass (kilogram, kg), length (m), and time (s). It can be calculated by the formula: force = mass x acceleration. Thus, force has a derived unit, kilogram meter per second squared: kg m/s^2, also called a newton (N). These examples show how derived units are obtained from basic units and used to express other physical quantities.

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Key Concepts

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

International System of Units
The International System of Units, abbreviated as SI from its French phrase "Syst猫me International d'Unit茅s," is the world's most widely used system of measurement. It provides a standard framework for measuring various physical properties in science, industry, and everyday life. The SI system builds upon a foundation of seven base units that cover different dimensions:
  • Length - meter (m)
  • Mass - kilogram (kg)
  • Time - second (s)
  • Electric current - ampere (A)
  • Temperature - kelvin (K)
  • Amount of substance - mole (mol)
  • Luminous intensity - candela (cd)
These units help ensure consistency and reduce confusion when sharing scientific and technical information across borders. They serve as building blocks for creating derived units, used to measure more complex physical quantities.
Physical Quantities
Physical quantities are properties of materials and systems that can be quantified or measured. They include both fundamental properties like mass and length, and complex quantities like velocity and energy. Each physical quantity can be expressed in terms of a unit from a measurement system, like the International System of Units. Physical quantities are divided into two types: base quantities and derived quantities. Base quantities correspond to the base units such as meter and kilogram, representing simple, standalone aspects of reality.
  • Length and mass are examples of base quantities.
  • Velocity, force, and pressure are examples of derived quantities.
Understanding these quantities helps us describe the world around us, predict phenomena, and engineer new technologies.
Base Units
Base units are the fundamental building blocks of measurement systems like the SI. These units represent the simplest, most basic aspects of what we can measure. In the SI system, there are seven base units, each corresponding to a base quantity such as length, mass, or time. These base units are:
  • Meter (m) for length
  • Kilogram (kg) for mass
  • Second (s) for time
  • Ampere (A) for electric current
  • Kelvin (K) for temperature
  • Mole (mol) for the amount of substance
  • Candela (cd) for luminous intensity
Each base unit in the SI is precisely defined to provide a unique and consistent measurement method. They form the foundation for deriving other units, helping us measure a broader spectrum of physical quantities.
Algebraic Operations
Algebraic operations, including multiplication and division, play a crucial role in deriving new units from base units. By applying these operations, we create derived units to measure quantities like speed, area, and force.For example, when we want to measure area, we multiply the base unit of length (meter) by itself, resulting in the derived unit of square meters (\( m^2 \)). This shows how two length dimensions combine into an area unit.Similarly, speed is calculated by dividing the base unit of length by the base unit of time, delivering the derived unit of meters per second (\( m/s \)). By understanding algebraic operations on units, one can both comprehend and compute complex physical quantities within a systematic framework. This approach ensures accuracy and coherency in scientific measurements.

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Most popular questions from this chapter

A north wind is blowing (the air is moving towards the south). When a person is walking towards the north, is the relative speed of the wind that the person senses greater than, the same as, or less than the speed the person senses when not walking? How about when the person is walking towards the south?

How does the velocity of a freely falling body change with time? How does the distance it has fallen change? How about the acceleration?

The following are speeds and headings displayed on a GPS receiver. (Heading gives the direction of motion based on: north \(=0^{\circ}\), east = \(90^{\circ}\), south \(=180^{\circ}\), etc.) In each case, indicate whether the receiver was accelerating during the time between the displays, and if it was, describe in what way the receiver was accelerating. a) Initially: \(60 \mathrm{mph}, 70^{\circ} .5\) seconds later: \(50 \mathrm{mph}, 70^{\circ} .\) b) Initially: \(50 \mathrm{mph}, 70^{\circ} .5\) seconds later: \(70 \mathrm{mph}, 70^{\circ} .\) c) Initially: \(60 \mathrm{mph}, 70^{\circ} .5\) seconds later: \(60 \mathrm{mph}, 90^{\circ} .\)

If a ball is thrown straight up into the air, what is its acceleration as it moves upward? What is its acceleration when it reaches its highest point and is stopped at an instant?

Can the resultant of two velocities have zero magnitude? If so, give an example.
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