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Difficulty: EasyFundamental and Derived Units

The derived SI unit of force is the newton (N\text{N}), which can be expressed in terms of fundamental SI base units as kg⋅m⋅sx\text{kg}\cdot\text{m}\cdot\text{s}^{x}. What is the numerical value of the exponent xx?

Answer: -2

Answer

The numerical value of the exponent xx for time in the base SI expression of the newton is −2-2.
Force is defined by Newton's second law as mass times acceleration (F=maF = ma). In SI fundamental units, mass is measured in kilograms (kg\text{kg}) and acceleration in meters per second squared (m⋅s−2\text{m}\cdot\text{s}^{-2}). Combining these yields 1 N=1 kg⋅m⋅s−2\text{1\ N} = \text{1\ kg}\cdot\text{m}\cdot\text{s}^{-2}. Therefore, the power of time in seconds (xx) is −2-2.

Step-by-Step Solution

1
Identify the relationship between force and fundamental quantities
Force is defined as mass multiplied by acceleration (F=maF = ma)
This relates force to fundamental quantities of mass, length, and time.
2
Substitute the SI base units of mass and acceleration
Mass unit is kg\text{kg}; acceleration unit is m⋅s−2\text{m}\cdot\text{s}^{-2}
Kilogram, meter, and second are standard fundamental SI units.
3
Determine the exponent of seconds
The combined base unit expression is kg⋅m⋅s−2\text{kg}\cdot\text{m}\cdot\text{s}^{-2}, giving x=−2x = -2
Equating the powers of seconds gives x=−2x = -2.

Key Concept

Expressing derived units in terms of fundamental SI base units
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Topics

Fundamental and Derived Units

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