Data Source and Methodology
Authoritative Data Source: OpenStax College Physics, Chapter 7 “Work, Energy, and Energy Resources” (latest edition, 2016) — openstax.org/details/books/college-physics. Unit conversion constants are taken from the NIST Guide to the SI (2019) — physics.nist.gov/cuu/Units/.
All calculations are rigorously based on the formulas and data provided by these sources. Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
The Formula Explained
$W = \\vec{F} \\cdot \\vec{d} = F\\,d\\,\\cos(\\theta)$
Solving for each variable:
$F = \\dfrac{W}{d\\,\\cos(\\theta)}\\,,\\quad d = \\dfrac{W}{F\\,\\cos(\\theta)}\\,,\\quad \\theta = \\arccos\\!\\left(\\dfrac{W}{F\\,d}\\right)$
Glossary of Variables
-
- Work (W): Energy transferred by a force along a displacement; SI unit: joule (J).
- Force (F): Constant force magnitude; SI unit: newton (N). 1 lbf = 4.4482216152605 N.
- Displacement (d): Straight-line distance moved; SI unit: meter (m). 1 ft = 0.3048 m.
- Angle (θ): Angle between force direction and displacement; measured in degrees.
- ft·lbf: Foot-pound-force; 1 ft·lbf = 1.3558179483314 J.
- BTU: British thermal unit; 1 BTU = 1055.05585262 J.
How It Works: A Step-by-Step Example
Suppose a 50 N force acts through a displacement of 12 m at an angle of 30° to the direction of motion. The work done is:
$W = F\\,d\\,\\cos(\\theta) = 50\\,\\text{N} \\times 12\\,\\text{m} \\times \\cos(30^\\circ)$
$\\cos(30^\\circ) = \\sqrt{3}/2 \\approx 0.8660$
$W \\approx 600 \\times 0.8660 = 519.6\\,\\text{J}$
The sign of W indicates whether the force aids motion (positive) or opposes it (negative).
Frequently Asked Questions (FAQ)
Is this calculator for physics work or work hours?
It is exclusively for physics work (energy transfer), not for timecards or payroll.
What if the force is perpendicular to the motion?
At θ = 90°, cos(θ) = 0, so W = 0. No energy is transferred along the path.
Can I calculate the angle from known work, force, and distance?
Yes. The calculator uses θ = arccos(W / (F d)) if the ratio is between −1 and 1.
How are units converted?
Using NIST constants: 1 lbf = 4.4482216152605 N; 1 ft = 0.3048 m; 1 ft·lbf = 1.3558179483314 J; 1 BTU = 1055.05585262 J; 1 Wh = 3600 J; 1 kWh = 3.6×10^6 J.
Why is my result negative?
If θ > 90°, the force opposes the motion, leading to negative work.
Does this handle variable forces or curved paths?
No. It assumes constant force and straight-line displacement. For variable forces, use the line integral W = ∫ F · ds.
How many significant figures are shown?
Results are formatted for readability; use the raw value if you need more precision via the copy button.