What is Work in Physics?
In everyday language, "work" means to use effort. In physics, the definition is much more specific: work is the energy transferred to or from an object when a force acts on it over a certain distance. If you push on a wall for an hour, you'll feel tired, but in physics, you've done zero work because the wall didn't move (distance = 0).
The Work Formula
The simplest form of the work formula applies when a constant force is applied to an object, causing it to move in the same direction as the force.
- Work (W): The energy transferred, measured in Joules (J).
- Force (F): The constant force applied, measured in Newtons (N).
- Distance (d): The distance the object moves, measured in meters (m).
This calculator uses this formula. It's important to note that if the force is applied at an angle, the full formula is `W = Fd cos(θ)`, where `θ` is the angle between the force and the direction of motion. Our calculator assumes the force is applied directly in the direction of motion, so `cos(0°) = 1`.
Units of Work: The Joule
The SI unit for work (and energy) is the Joule (J). A Joule is defined by the formula for work:
1 Joule = 1 Newton × 1 meter (1 J = 1 N·m)
This means one Joule is the amount of work done when a force of one Newton is applied over a distance of one meter. You can explore the definition of a Newton using our Force Calculator.
Solving for Force and Distance
By rearranging the work formula, we can also solve for force or distance if we know the other two values.
- To find Force (F):
- To find Distance (d):
Real-World Examples
- Lifting a Box: You lift a 5 kg box from the floor onto a shelf 2 meters high. First, you must apply a force equal to the box's weight. Using `F = mg` (where `g ≈ 9.8 m/s²`), the force is `5 kg × 9.8 m/s² = 49 N`. The work done is `W = 49 N × 2 m = 98 J`.
- Pushing a Mower: You push a lawnmower with a constant force of 50 N over a distance of 100 meters. The work you do on the mower is `W = 50 N × 100 m = 5,000 J` (or 5 kJ).
- No Work Done: You hold a 20 kg barbell over your head without moving it. You are applying a large upward force, but since the distance is zero, the work done on the barbell is `W = F × 0 m = 0 J`.
For a more detailed explanation of work in physics, the Wikipedia article on Work is an excellent resource.