CLS-25

Power F·v

Instantaneous mechanical power.

Reading speed

GoverningPower F·v

Governing equation

P=F v

$v \in \left[0.1, 40\right]$

where

F: F (N)
v: v (m/s)
P: Power F·v (W)

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

P=F v

$v \in \left[0.1, 40\right]$

$v = 0.1$ $P = 4$

Along the curve

②

Domain of the variable — blue

v_{\min} = 0.1,\quad v_{\max} = 40

$v \in \left[0.1, 40\right]$

$v = 0.1$ $v = 0.1$

Along the curve

③

Response curve — green

P=F v

$v \in \left[0.1, 40\right]$

$v = 0.1$ $P = 4$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}P}{\mathrm{d}v}

$v \in \left[0.1, 40\right]$

$v = 0.351$ $P^{\prime} = 40$

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-25 — Power F·v) is the form associated with Power F·v. Working symbols: $F$ , $v$ $\rightarrow$ $P$ . Instantaneous mechanical power. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

P

from

F

v

in Classical mechanics via

P=F v

Instantaneous mechanical power. 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}

v = 8.000\,\mathrm{m/s}

, the governing relation

P=F v

yields

P = 320.000\,\mathrm{W}

. 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 Nv v8 m/s

Outputs

Power F·v P320.000 W

Reading speed

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Narration of this film

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

Instantaneous mechanical power. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube