Study Guides/Physics/Dimension of Force

Study Guide · Physics

What is the Dimensional Formula of Force?

In physics, Dimensional Analysis is used to express any complex derived physical quantity purely in terms of the seven fundamental base units: Mass [M], Length [L], and Time [T]. One of the most foundational derived quantities in mechanics is Force.

The dimensional formula of Force is [M¹ L¹ T⁻²].

Question (Click to Flip)

What is the dimensional formula of force?

Answer

The dimensional formula of force is [M L T⁻²].

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Key Facts

Quantity: Force (F).

Formula Used: Newton's Second Law (F = ma).

Dimensional Formula: [M¹ L¹ T⁻²].

SI Unit: Newton (N).

Base Unit Breakdown: 1 Newton = 1 kg·m/s².

Step-by-Step Derivation

To find the dimension of any quantity, you must start with its fundamental mathematical formula. According to Newton's Second Law of Motion, the formula for Force is: Force = Mass × Acceleration (F = ma)

Let's break this down into base dimensions:

Mass is a fundamental quantity. Its dimension is simply [M].
Acceleration is defined as (Velocity / Time). Velocity is (Distance / Time). Therefore, Acceleration = Distance / (Time × Time). The dimension of Distance is [L]. The dimension of Time is [T]. So, the dimension of Acceleration = [L] / [T²] = [L T⁻²].

Now, multiply them together: Force = [M] × [L T⁻²] Force = [M¹ L¹ T⁻²]

Understanding the SI Unit

The standard SI unit of Force is the Newton (N). If we look at our derived dimension [M¹ L¹ T⁻²], we can easily see exactly what a Newton is made of:

Mass [M] = kilograms (kg)
Length [L] = meters (m)
Time [T⁻²] = seconds squared (s²) Therefore, 1 Newton is exactly equal to 1 kg·m/s².

Questions and Answers

What is the dimensional formula of force?+

The dimensional formula of force is [M L T⁻²].

How is the dimension of force derived?+

It is derived using the formula F = ma. We multiply the base dimension of Mass [M] by the derived dimension of Acceleration [L T⁻²] to get [M L T⁻²].

What are the fundamental dimensions used in mechanics?+

In classical mechanics, all formulas are broken down into three fundamental base dimensions: Mass [M], Length [L], and Time [T].

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