Work & Energy
Energy transformations that drive every mechanical system.
Work & Energy – Quantifying Force Over Distance
Explore how forces do work, how energy is stored and released, and how quickly machines deliver power. Essential concepts for every mechanical engineer.
What is Work in Physics?
In physics, work is done when a force causes a displacement. The amount of work depends on the magnitude of the force, the distance moved, and the angle between the force and the displacement. Only the component of force along the direction of motion contributes to work. Work is measured in Joules (J) and is a scalar quantity.
Why is the Work-Energy Theorem Important?
The Work-Energy Theorem states that the net work done on an object equals its change in kinetic energy. This connects force analysis to energy analysis, providing two complementary ways to solve the same problem. Engineers use energy methods extensively because they bypass the need to know force directions — only magnitudes and displacements are needed.
Core Concepts You'll Learn Here:
- 📌 Work Done (W = F·d·cosθ) – Energy transferred by a force along a displacement.
- 📌 Kinetic Energy (KE = ½mv²) – Energy due to motion; increases with the square of velocity.
- 📌 Gravitational Potential Energy (PE = mgh) – Energy stored by height above a reference.
- 📌 Conservation of Energy – In a closed system, total mechanical energy (KE + PE) is conserved.
- 📌 Power (P = W/t or P = Fv) – The rate of energy transfer or work done per unit time.
- 📌 Efficiency – Ratio of useful output energy to total input energy.
- 📌 Unit Conversions – Joules, kilojoules, calories, kilocalories, and horsepower.
What You'll Find in This Section
This section provides four focused calculators: Work Done (with angle between force and displacement), Kinetic Energy, Gravitational Potential Energy, and Power (via both W/t and F·v formulas). Each calculator supports multiple unit systems and displays detailed step-by-step solutions formatted with LaTeX equations, making them ideal for both education and professional verification.
Work & Energy Calculators
Analyze energy transformations in mechanical systems. Calculate the work done by forces, the kinetic energy of moving bodies, gravitational potential energy stored by height, and the power output of machines.
Work Done (W = F·d·cosθ): Calculate the energy transferred when a force moves an object through a displacement, accounting for the angle between force and motion.
Kinetic Energy (KE = ½mv²): Quantify the energy of motion. Velocity has a squared relationship with KE — doubling speed quadruples energy.
Potential Energy (PE = mgh): Determine the gravitational energy stored in an object due to its position above a reference level.
Power (P = W/t or P = Fv): Measure how quickly work is done or energy is transferred over time.
Work Done Calculator
Work is done when a force causes a displacement in the direction of the force. When the force is applied at an angle θ to the motion, only the component of force along the displacement contributes.
Kinetic Energy Calculator
Kinetic energy is the energy an object possesses due to its motion. It depends on both the mass and the square of the velocity.
Gravitational Potential Energy Calculator
Gravitational potential energy is the energy stored in an object due to its height above a reference point. It is the work done against gravity to lift the object to that height.
Power Calculator
Power is the rate at which work is done or energy is transferred. It can be calculated from work and time, or directly from force and velocity for objects in constant motion.