Gravitational Potential Energy & Work Done Calculator

Energy and Work Guide

Energy Equations

Gravitational PE: Ep = mgh. Where m = mass (kg), g = gravitational field strength (9.81 m/s² on Earth), h = height above reference level (m). Kinetic energy: Ek = ½mv². Where v = speed (m/s). Work done: W = Fd cosθ. Where F = force (N), d = distance (m), θ = angle between force and direction of motion. If force and motion in same direction: W = Fd (θ = 0, cos 0 = 1). Work done against gravity = increase in GPE = mgh. Power: P = W/t = Fv.

Conservation of Energy

In the absence of friction and air resistance: total mechanical energy is conserved. At the top: Ep = mgh, Ek = 0 (if starting from rest). At the bottom: Ep = 0, Ek = ½mv². Therefore: mgh = ½mv². v = √(2gh). The mass cancels — the speed at the bottom is independent of mass. Example: ball dropped from 10m. v = √(2 × 9.81 × 10) = √196.2 = 14.0 m/s. Pendulum: swings to same height on both sides (conservation). Roller coaster: speed at any point can be calculated from height difference.

Work-Energy Theorem

Net work done on an object = change in kinetic energy. W_net = ΔEk = ½mv² − ½mu². If a 5kg object is pushed by 50N over 3m (from rest): W = 50 × 3 = 150J. v = √(2×150/5) = √60 = 7.75 m/s. Work done against friction = friction force × distance = heat generated. Energy dissipated by friction: if an object slides down a slope and is slower than the frictionless case, the difference is heat: Q_friction = mgh − ½mv².

Elastic and Gravitational PE

Elastic PE: Ee = ½kx². Where k = spring constant (N/m), x = extension (m). A spring with k = 500 N/m extended by 0.1m: Ee = ½ × 500 × 0.01 = 2.5J. At maximum extension (zero velocity): all KE → elastic PE. At natural length: all elastic PE → KE. Combined conservation: if a ball compresses a spring: KE lost = elastic PE gained. mgh = ½kx² (ball on spring from height h). Types of energy: kinetic, gravitational PE, elastic PE, thermal (heat), chemical, nuclear, electrical, sound, light. Energy is a