Which expression correctly describes energy using SI units?
A. [tex]1 \, J = 1 \, kg \cdot m^2 / s[/tex] B. [tex]1 \, J = 1 \, kg \cdot m / s[/tex] C. [tex]1 \, J = 1 \, kg \cdot m^2 / s^2[/tex] D. [tex]1 \, J = 1 \, kg \cdot m / s^2[/tex]
To determine the correct expression that describes energy using SI (International System of Units), let's break down the definition and unit of energy.
### Step-by-Step Solution:
1. Understanding Energy and Joule: - The SI unit of energy is the Joule (J). - A Joule is defined based on Newton's laws of motion and work-energy principles.
2. Work Done Formula: - Energy can be defined as the work done by a force. - The work done [tex]\( W \)[/tex] by a force [tex]\( F \)[/tex] to move an object through a distance [tex]\( d \)[/tex] is: [tex]\[
W = F \times d
\][/tex] - Work ([tex]\( W \)[/tex]) has the same units as energy.
3. Force Definition: - According to Newton's second law, force ([tex]\( F \)[/tex]) is the product of mass ([tex]\( m \)[/tex]) and acceleration ([tex]\( a \)[/tex]): [tex]\[
F = m \times a
\][/tex]
4. Units for Force: - The SI unit of mass ([tex]\( m \)[/tex]) is the kilogram (kg). - The SI unit of acceleration ([tex]\( a \)[/tex]) is meters per second squared (m/s[tex]\(^2\)[/tex]): [tex]\[
F = kg \times m/s^2
\][/tex]
5. Combining Units for Work: - Substituting the unit of force into the work done equation: [tex]\[
W = (kg \times m/s^2) \times m
\][/tex] - Simplifying, we get: [tex]\[
W = kg \times m^2 / s^2
\][/tex]
6. Conclusion: - The correct expression for energy using SI units is: [tex]\[
1 \, \text{J} = 1 \, \text{kg} \cdot \text{m}^2 / \text{s}^2
\][/tex]
