Ch 05 - Work, Energy And Power11th Physics

Dimensional Formulas:

• Work & Energy: $[M^1 L^2 T^{-2}]$
• Power: $[M^1 L^2 T^{-3}]$

CGS Conversion:

• The CGS unit of work and energy is the Erg.
• $1 \text{ Joule} = 10^7 \text{ ergs}$

Derivation Note: Since $1 \text{ N} = 10^5 \text{ dynes}$ and $1 \text{ m} = 10^2 \text{ cm}$, multiplying them yields $10^7$.

Variables & Units:

• $\vec{A}, \vec{B}$ = Given vectors
• $A_x, A_y, A_z$ = x, y, and z components of Vector A
• $B_x, B_y, B_z$ = x, y, and z components of Vector B

Conditions/Notes:

• Based on the orthogonal unit vector rules: $\hat{i} \cdot \hat{i} = 1$ and $\hat{i} \cdot \hat{j} = 0$.

The scalar (dot) product yields a scalar quantity from two vectors.

• Geometrically: It represents the product of the magnitude of one vector and the projection of the second vector strictly along the first.
• Mathematically: It follows both the commutative law ($\vec{A} \cdot \vec{B} = \vec{B} \cdot \vec{A}$) and the distributive law ($\vec{A} \cdot (\vec{B} + \vec{C}) = \vec{A} \cdot \vec{B} + \vec{A} \cdot \vec{C}$).
• Orthogonality: If two non-zero vectors are strictly perpendicular, their dot product is exactly zero.