Dimensional Formula Of Force And Work

Dimensional Formulas:

\[ \text{Force} = [M L T^{-2}] \] \[ \text{Work} = [M L^2 T^{-2}] \]

Force Dimension:

Work Dimension:

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1. What is Dimensional Formula of Force and Work?

Definition: Dimensional formulas express physical quantities in terms of fundamental dimensions (Mass, Length, Time).

Purpose: They help in checking the correctness of equations and performing unit conversions.

2. How Are These Formulas Derived?

The dimensional formulas are:

\[ \text{Force} = [M L T^{-2}] \] \[ \text{Work} = [M L^2 T^{-2}] \]

Where:

\( M \) — Mass (kg)
\( L \) — Length (m)
\( T \) — Time (s)

Explanation:

Force = mass × acceleration → [M] × [L T⁻²] = [M L T⁻²]
Work = force × distance → [M L T⁻²] × [L] = [M L² T⁻²]

3. Importance of Dimensional Analysis

Details: Dimensional formulas help verify equations, convert units, and understand relationships between physical quantities.

4. Using the Calculator

Tips: Enter values for mass (kg), length (m), and time (s) to see how they combine in force and work dimensions.

5. Frequently Asked Questions (FAQ)

Q1: Why is time squared in these formulas?
A: Because acceleration (in force) has time squared in denominator (m/s²), which carries through to work.

Q2: What's the SI unit for force and work?
A: Force is Newtons (kg·m/s²), Work is Joules (kg·m²/s²).

Q3: Can I use different units?
A: Yes, but maintain consistency (e.g., if using cm for length, use cm throughout).

Q4: How does this relate to energy?
A: Work and energy share the same dimensional formula [M L² T⁻²].

Q5: What about other physical quantities?
A: Each physical quantity has its own dimensional formula based on its definition.