The dimension of work is calculated as [M¹L²T⁻²]. This is derived from the fundamental dimensions of force and displacement.
Here's a breakdown of the calculation:
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Work Definition: Work is defined as the force applied to an object multiplied by the displacement of the object in the direction of the force.
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Formula: Work (W) = Force (F) × Displacement (d)
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Dimensions of Force: Force, according to Newton's second law, is mass times acceleration (F = ma).
- Mass (m) has the dimension of [M¹].
- Acceleration (a) is the rate of change of velocity, which is displacement (length) per time squared, thus having the dimension [L¹T⁻²].
- Therefore, the dimension of Force (F) = [M¹L¹T⁻²].
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Dimensions of Displacement: Displacement is a measure of length, so its dimension is [L¹].
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Calculation of Work's Dimension: Since Work = Force × Displacement, the dimension of work is the product of the dimensions of force and displacement.
- Dimension of Work = Dimension of Force × Dimension of Displacement
- Dimension of Work = [M¹L¹T⁻²] × [L¹]
- Dimension of Work = [M¹L²T⁻²]
Therefore, the dimension of work is [M¹L²T⁻²], representing mass times length squared times time to the power of -2. This corresponds to the SI unit of work, the Joule (J).
