What Is Work in Physics?
In physics, work is done when a force causes an object to move through a displacement. Unlike everyday usage, “doing work” in physics requires both force and displacement in the same direction. The SI unit of work is the joule (J), equal to one newton-metre.
W = Fd (Force Parallel to Displacement)
The simplest case: when force is applied in the same direction as the displacement. Force in newtons, displacement in metres, gives work in joules.
W = Fd cos(\u03B8) (General Case)
When force is applied at angle θ to the displacement, only the component along the displacement does work. At 0° all force does work; at 90° no work is done; at 180° the force does maximum negative work.
Work–Energy Theorem
The net work done on an object equals the change in its kinetic energy. This powerful theorem connects force, displacement, and speed change without needing to know acceleration explicitly.
W = Pt (Work from Power and Time)
When power is constant, work equals power times time. P in watts and t in seconds gives W in joules.
W = mgh (Work Against Gravity)
Lifting mass m by height h against gravitational acceleration g requires work W = mgh. This equals the gravitational potential energy gained.
How to Use the Calculator
- Choose a calculation mode matching your known values.
- Enter values with units.
- Click Calculate.
- Review the result, formula steps, and interpretation.
Example Calculations
50 N \u00D7 10 m (parallel)
W = 50 × 10 = 500 J
100 N, 5 m, 30°
W = 100 × 5 × cos(30°) = 433 J
Work–energy: 2 kg, 0 to 10 m/s
W = ½ × 2 × (10² − 0²) = 100 J
2 kW for 1 hour
W = 2000 × 3600 = 7 200 000 J = 7.2 MJ
Common Mistakes
- Forgetting to use the component of force along the displacement.
- Using degrees with cos() in a calculator set to radians.
- Treating work as always positive (it can be negative or zero).
- Confusing weight (N) with mass (kg) in W = mgh.
- Using total distance instead of displacement.
Accuracy and Limitations
These formulas assume constant force during the displacement. For variable forces, integration is required. Friction, air resistance, and real-world inefficiencies are not automatically included. W = mgh assumes constant gravity near a surface. This tool is educational and should not replace engineering calculations.
FAQ
What is work in physics?›
Work is the transfer of energy by a force acting through a displacement. W = Fd cos(θ), measured in joules.
Can work be negative?›
Yes. When the force opposes the displacement (angle > 90°), work is negative. Friction always does negative work.
When is work zero?›
When force is perpendicular to displacement (θ = 90°), or when displacement is zero.
What is the work–energy theorem?›
The net work done on an object equals the change in its kinetic energy: W_net = KE_final − KE_initial.
Is work a scalar or vector?›
Work is a scalar quantity (no direction), even though it is calculated from two vectors (force and displacement).
What is the difference between work and energy?›
Work is the process of transferring energy. Energy is the capacity to do work. Both are measured in joules.
How does W = mgh relate to W = Fd?›
Lifting an object against gravity: F = mg and d = h, so W = Fd = mgh.
How does W = Pt relate to W = Fd?›
Power P = W/t, so W = Pt. This is useful when you know how long a constant power output is maintained.
Sources
Author & technical reviewer
Manish Kumar
PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.
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