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Magazine Chapter 1: Problem 38
What SI units are used for measuring the following quantities? For derived units, express your answers in terms of the six fundamental units. (a) Mass (b) Length (c) Temperature (d) Volume (e) Energy (f) Density
Short Answer
Expert verified
(a) kg, (b) m, (c) K, (d) m鲁, (e) J (kg路m虏/s虏), (f) kg/m鲁.
Step by step solution
01
Identify the fundamental SI unit for mass
The fundamental SI unit for measuring mass is the kilogram (kg). Kilogram is one of the seven base units in the International System of Units (SI).
02
Identify the fundamental SI unit for length
The fundamental SI unit for measuring length is the meter (m). The meter is also one of the seven base units used to measure spatial dimensions.
03
Identify the fundamental SI unit for temperature
The fundamental SI unit for measuring temperature is the kelvin (K). It is the base unit of temperature in the International System of Units.
04
Determine the SI unit for volume as a derived unit
Volume, being a derived unit, is measured in cubic meters (m鲁). It is derived from the base unit of length (meter), with the formula for volume being length 脳 width 脳 height (m 脳 m 脳 m).
05
Determine the SI unit for energy as a derived unit
Energy is measured in joules (J). The joule is a derived unit calculated as: \( kg \, m^2 \, s^{-2} \), combining mass (kg), length (meter, m), and time (second, s).
06
Determine the SI unit for density as a derived unit
Density is measured in kilograms per cubic meter (kg/m鲁). It is calculated using mass (kg) divided by volume (m鲁), using the derived units for both properties.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Mass Measurement
Mass is one of the most fundamental quantities in the International System of Units (SI). It is measured using the unit called the kilogram (kg). Mass defines the amount of matter in an object. The kilogram is a universal unit used across various scientific disciplines, making it central to global consistency in measurements.
- The kilogram symbol is written as "kg".
- It was initially defined by a platinum-iridium cylinder kept in France but is now defined by a fundamental constant known as the Planck constant.
- When measuring mass, balance scales and electronic balances are common tools utilized in laboratories.
Length Measurement
Length measurements are essential in everyday life and scientific inquiry and are measured using the SI unit of meter (m). The meter helps describe the size or distance between objects, which is vital for both simple measurements and complex calculations.
The meter was initially derived based on the Earth's meridian but is now defined by the speed of light in a vacuum.
The meter was initially derived based on the Earth's meridian but is now defined by the speed of light in a vacuum.
- The symbol for a meter is "m".
- When you measure length, tools like rulers, measuring tapes, and laser range finders are often employed.
- In various scientific fields, precise length measurements are critical, whether in physics, engineering, or architecture.
Temperature Measurement
Temperature is a critical physical property measured in kelvins (K), an SI base unit. Measuring temperature involves understanding the thermal energy within a substance, ranging from absolute zero to much higher levels.
Kelvin is unique as it does not include the term "degree," unlike other temperature scales such as Celsius and Fahrenheit. It provides a platform for direct equations and scientific calculations.
Kelvin is unique as it does not include the term "degree," unlike other temperature scales such as Celsius and Fahrenheit. It provides a platform for direct equations and scientific calculations.
- The symbol for kelvin is "K," without the degree symbol.
- Kelvin is linked to the triple point of water, precisely defined as 273.16 K.
- Common devices to measure temperature include thermometers and thermocouples.
Derived Units
Derived units in the SI system arise from combinations of the seven fundamental base units to measure quantities that aren't covered directly. For example, volume and energy are derived units that rely on these base measures.
- Volume: Measured in cubic meters (m鲁), volume is derived by multiplying length dimensions (e.g., height 脳 width 脳 depth).
- Energy: Energy's unit is the joule (J), written as \( kg \, m^2 \, s^{-2} \), indicating its dependency on mass, length, and time.
- Understanding derived units helps in performing physics and engineering calculations.
Density Measurement
Density is a derived quantity that indicates how much mass exists in a given volume and is measured in kilograms per cubic meter (kg/m鲁). The formula for density is \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \), meaning it directly relies on mass and volume measurements.
- Mass: Measured in kilograms (kg), offering a measure of quantity within a substance.
- Volume: Measured in cubic meters (m鲁), giving a value for physical space occupied.
- Density plays a key role in material science, helping identify substances and understand buoyancy.
- Devices that measure density include densitometers and hydrometers.
