CLS-24

Work of a force

Constant-force work.

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GoverningWork of a force

Governing equation

W=F s\cos\theta

$th \in \left[0, 180\right]$

where

F: F (N)
s: s (m)
th: th (deg)
W: Work of a force (J)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

W=F s\cos\theta

$th \in \left[0, 180\right]$

$th = 0$ $W = 120$

Along the curve

②

Domain of the variable — blue

th_{\min} = 0,\quad th_{\max} = 180

$th \in \left[0, 180\right]$

$th = 0$ $th = 0$

Along the curve

③

Response curve — green

W=F s\cos\theta

$th \in \left[0, 180\right]$

$th = 0$ $W = 120$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}W}{\mathrm{d}th}

$th \in \left[0, 180\right]$

$th = 1.132$ $W^{\prime} = -0.041$

Along the curve

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-24 — Work of a force) is the form associated with Work of a force. Working symbols: $F$ , $s$ , $th$ $\rightarrow$ $W$ . Constant-force work. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

W

from

F

s

th

in Classical mechanics via

W=F s\cos\theta

Constant-force 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

F = 40.000\,\mathrm{N}

s = 3.000\,\mathrm{m}

th = 30.000\,\mathrm{deg}

, the governing relation

W=F s\cos\theta

yields

W = 103.923\,\mathrm{J}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

F F40 Ns s3 mth th30 deg

Outputs

Work of a force W103.923 J

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Constant-force work. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube