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Work in physics is the energy transferred to or from an object when a force acts on it over a displacement. Unlike everyday usage, the physics definition of work requires both a force and a movement in the direction of that force. A force applied perpendicular to the displacement does zero work, and a force opposing the motion does negative work. This fundamental concept connects force, energy, and motion in classical mechanics.
The Work Calculator computes the mechanical work done by a constant force applied at any angle to the displacement. It uses the scalar product formulation $$W = F \cdot d \cdot \cos\theta$$, where $$F$$ is the magnitude of the applied force in newtons, $$d$$ is the displacement in meters, and $$\theta$$ is the angle between the force vector and the displacement vector. This relationship is the foundation of the work-energy theorem, which states that the net work done on an object equals its change in kinetic energy. Understanding work is essential for solving problems in engineering, biomechanics, and thermodynamics.
The calculator evaluates the dot product of force and displacement vectors:
$$W = F \cdot d \cdot \cos\theta$$
where $$F$$ is the applied force (N), $$d$$ is the displacement (m), and $$\theta$$ is the angle between force and displacement. When $$\theta = 0°$$, the full force contributes to work ($$\cos 0° = 1$$). At $$\theta = 90°$$, the force is perpendicular and does no work ($$\cos 90° = 0$$). For $$\theta > 90°$$, work becomes negative, meaning the force opposes the motion. The result is given in joules (J), where 1 J = 1 N·m. The effective force component along the direction of motion is $$F_{\parallel} = F \cos\theta$$.
Positive work means energy is transferred to the object, increasing its kinetic energy. Negative work means energy is removed from the object, such as friction slowing it down. Zero work occurs when the force is perpendicular to displacement (e.g., centripetal force in circular motion). For reference, lifting a 1 kg mass by 1 meter against gravity requires about 9.81 J of work.
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A 50 N horizontal push over 10 m with θ = 0° yields W = 50 × 10 × cos(0°) = 500 J.
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A 200 N force at 30° over 15 m gives W = 200 × 15 × cos(30°) ≈ 2598 J. Only the horizontal component (173.2 N) does work.
The SI unit of work is the joule (J), defined as the work done when a force of one newton moves an object one meter in the direction of the force. 1 J = 1 N·m = 1 kg·m²/s².
Yes. Work is negative when the force has a component opposite to the displacement direction (angle θ > 90°). Friction always does negative work on a sliding object, removing kinetic energy and converting it to thermal energy.
Because $$\cos 90° = 0$$, so $$W = Fd\cos 90° = 0$$. The force changes the direction of motion but not the speed, so no energy is transferred. Centripetal force in circular motion is a classic example.
This formula applies to constant forces only. For variable forces, work must be calculated as an integral: $$W = \int \vec{F} \cdot d\vec{s}$$, which sums infinitesimal contributions over the path.
The work-energy theorem states that the net work done on an object equals its change in kinetic energy: $$W_{net} = \Delta KE = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2$$. This connects force and motion through energy.
Work is the process of transferring energy, while energy is a state property of a system. Both are measured in joules. Work is done when a force causes displacement; energy is the capacity to do work.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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