What is the work-energy theorem?
The work-energy theorem states that the net work done on an object equals the change in its kinetic energy: W_net = ΔKE = ½m·v_f² − ½m·v_i². If the net work is positive, the object speeds up; if negative, it slows down. See also our find Heat Generated (Q) with Joule Heating Calculator.
How do I calculate work done by a force?
Work done by a constant force is calculated as W = F·d·cos(θ), where F is the applied force in newtons, d is the displacement in metres, and θ is the angle between the force and the direction of motion. When the force is parallel to the motion (θ = 0°), cos(θ) = 1 and the formula simplifies to W = F·d.
What units are used in the work-energy theorem?
The SI unit for both work and energy is the joule (J), where 1 J = 1 N·m = 1 kg·m²/s². Force is measured in newtons (N), mass in kilograms (kg), velocity in metres per second (m/s), and displacement in metres (m).
Under what conditions is work done zero?
Work is zero when: (1) no displacement occurs, (2) the force is perpendicular to the displacement (θ = 90°, so cos 90° = 0), or (3) the applied force is zero. For example, carrying a box horizontally while the gravitational force acts downward does zero work against gravity. You might also find our calculate Impact Energy useful.
Can work be negative?
Yes. When the force component acts opposite to the direction of motion (θ > 90°), the work done is negative. Friction is a classic example — it always does negative work on a sliding object, removing kinetic energy and slowing it down.
How does a work-energy theorem calculator work?
You provide either (a) mass, initial velocity, and final velocity so the calculator computes ΔKE = ½m(v_f² − v_i²) and equates it to net work, or (b) force, displacement, and angle so it computes W = F·d·cos(θ). Both modes show initial KE, final KE, and the net work or energy change.
Can this calculator be used for all types of physics problems?
This calculator covers the most common work-energy scenarios: work from kinematics (velocity change) and work from a constant force at an angle. It does not cover variable forces, rotational work, or thermodynamic work, which require more advanced integration or separate tools.
What is the difference between work and kinetic energy?
Kinetic energy (KE = ½mv²) is the energy an object possesses due to its motion — it is a state quantity. Work is the process of transferring energy via a force over a displacement. The work-energy theorem links them: the net work done on an object equals the change in its kinetic energy.