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The dimensional formula for force of elasticity (Hooke's law force) is [M L T⁻²], representing mass times length over time squared. This formula describes the fundamental physical dimensions of elastic force in any system of units.
The calculator uses the dimensional formula:
Where:
Explanation: The dimensional formula shows that force has dimensions of mass multiplied by length and divided by time squared, consistent with Newton's second law (F = ma).
Details: Dimensional analysis is crucial for verifying equations, converting between unit systems, and understanding the fundamental nature of physical quantities. The [M L T⁻²] formula confirms that elastic force follows the same dimensional pattern as all mechanical forces.
Tips: Enter mass in kilograms, length in meters, and time in seconds. All values must be positive numbers. The calculator will display both the dimensional formula and the calculated force value in Newtons.
Q1: What is the difference between dimensional formula and unit?
A: Dimensional formula describes the fundamental physical nature (e.g., [M L T⁻²]), while units are specific measurement systems (e.g., Newtons, dynes, pound-force).
Q2: Why is the dimensional formula for force [M L T⁻²]?
A: This comes from Newton's second law F = ma, where acceleration has dimensions [L T⁻²], so force becomes [M] × [L T⁻²] = [M L T⁻²].
Q3: Does this apply to all types of forces?
A: Yes, all mechanical forces (gravitational, electromagnetic, elastic) have the same dimensional formula [M L T⁻²], regardless of their specific nature.
Q4: How is Hooke's law related to this dimensional formula?
A: Hooke's law (F = -kx) must be dimensionally consistent, so spring constant k must have dimensions [M T⁻²] to make F have [M L T⁻²].
Q5: Can dimensional formulas be used for unit conversion?
A: Yes, dimensional formulas help convert between different unit systems while maintaining physical consistency.