Work and Energy Physics Notes

Definition and Conditions of Work

• Definition: Work is done when a force acts on an object and moves it through a distance. It is defined as the product of the magnitude of force and the distance covered in the direction of force:     $W = F \times S$

• Zero Work Conditions:

  • If displacement $S = 0$ (e.g., pushing fixed wall).

  • If force $F = 0$ while moving with uniform velocity.

• Scalar Nature: Work does not convey directional information and is a scalar quantity.

Work at an Angle and Graphical Calculation

• Force at an Angle: When force $F$ acts at an angle $\theta$ with the direction of motion, work is done by the component acting along the direction of motion:     $W = F S \cos(\theta)$

  • Parallel ($\theta = 0^\circ$): $\cos(0^\circ) = 1 \implies W = F S$

  • Perpendicular ($\theta = 90^\circ$): $\cos(90^\circ) = 0 \implies W = 0$ (e.g., carrying a load horizontally where the upward force is perpendicular to displacement).

• Graphical Representation: The area under a force-distance curve represents the work done by that force.

Units and Sample Calculations of Work

• SI Unit: The SI unit of work is the joule ($\text{J}$). One joule of work is done when a force of $1\,\text{N}$ moves a body through a distance of $1\,\text{m}$ in its direction:     $1\,\text{J} = 1\,\text{N} \times 1\,\text{m} = 1\,\text{N\,m}$

• Larger Units: $1\,\text{kJ} = 10^3\,\text{J}$, $1\,\text{MJ} = 10^6\,\text{J}$.

• Worked Examples:

  • $200\,\text{J}$ of work pushing a carton $5\,\text{m}$ requires a force of $F = \frac{200\,\text{J}}{5\,\text{m}} = 40\,\text{N}$.

  • A $65\,\text{N}$ force pulling a suitcase for $20\,\text{m}$ at $\theta = 30^\circ$ does work $W = 65\,\text{N} \times 20\,\text{m} \times \cos(30^\circ) = 1125.8\,\text{J}$.

Concept and Forms of Energy

• Definition: Energy is the ability of a body to do work. It is a scalar quantity measured in joules ($\text{J}$).

• Energy Transfer: Performing $1\,\text{J}$ of work spends $1\,\text{J}$ of energy transferred from one system to another.

• Basic Mechanical Energy: Mechanical energy consists of:

  • Kinetic energy

  • Potential energy

• Notable Quantities:

  • Work done by a single beat of the human heart: $0.5\,\text{J}$

  • Energy of the nuclear bomb dropped on Hiroshima, Japan, in the second world war: $8.0 \times 10^{13}\,\text{J}$

  • Annual energy output of a power station: $10^{16}\,\text{J}$

Kinetic Energy

• Definition: Energy possessed by a body by virtue of its motion:     $E_k = \frac{1}{2} m v^2$

• Derivation Summary: Calculated from work done to bring a body of mass $m$ moving at velocity $v$ to rest via opposing force $F$ across distance $S$, using average velocity $S = \frac{v t}{2}$ and acceleration slope $a = \frac{v}{t}$.

• Example Calculation: A truck of mass $m = 3000\,\text{kg}$ moving at $v = 54\,\text{km\,h}^{-1} = 15\,\text{m\,s}^{-1}$ has kinetic energy:     $E_k = \frac{1}{2} \times 3000\,\text{kg} \times (15\,\text{m\,s}^{-1})^2 = 337500\,\text{J} = 337.5\,\text{kJ}$

Potential Energy

• Definition: Energy possessed by a body by virtue of its position or deformation.

• Gravitational Potential Energy: Energy stored in an object due to its position relative to the Earth.