CLS-14

Mechanical energy

E = ½ m v² + m g h. Conserved when only gravity does work.

Reading speed

NewtonianWork–energy

Governing equation

E=\tfrac12 mv^2+mgh

where

m: Mass (kg)
v: Speed (m/s)
h: Height (m)
E: Energy (J)

Lecture brief

Historical brief

Newtonian mechanics (1687) plus energy, angular momentum, Kepler and the ballistic parabola remain the first language of motion. Every sheet here is a closed-form orbit, throw, spin or oscillator. This sheet (CLS-14 — Mechanical energy) is the form associated with Work–energy. Working symbols: $m$ , $v$ , $h$ $\rightarrow$ $E$ . Kinetic plus gravitational potential. Other potentials add their own terms.

Purpose

Purpose: compute

E

from

m

v

h

in Classical mechanics via

E=\tfrac12 mv^2+mgh

E = ½ m v² + m g h. Conserved when only gravity does work. Use it when a real classical mechanics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

m = 2.000\,\mathrm{kg}

v = 4.000\,\mathrm{m/s}

h = 3.000\,\mathrm{m}

, the governing relation

E=\tfrac12 mv^2+mgh

yields

E = 74.9\,\mathrm{J}

. A mass sliding a ramp, two energy bars. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Mass m2 kgSpeed v4 m/sHeight h3 m

Outputs

Energy E74.9 J

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

A mass sliding a ramp, two energy bars.

Kinetic plus gravitational potential. Other potentials add their own terms.

Reading speed

Watch on YouTube