Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025
Definition
Work is the integral of force over a distance. In calculus, it is often represented as $W = \int_a^b F(x) \, dx$.
5 Must Know Facts For Your Next Test
Work can be calculated using the integral of a force function $F(x)$ over an interval $[a, b]$.
When the force is constant, work simplifies to $W = F \cdot d$, where $d$ is the distance.
In physics applications, work is often measured in joules (J).
The concept of work can apply to varying force fields, such as gravitational or elastic forces.
When dealing with variable forces, it's important to correctly set up the integral limits and ensure the force function is properly defined.
Review Questions
Related terms
Force: A vector quantity that tends to produce an acceleration of a body in the direction of its application; commonly denoted by $F$.
Distance: A scalar quantity representing how much ground an object has covered during its motion.
Integral: A fundamental concept in calculus that represents accumulation of quantities and can be used to calculate areas under curves, among other things.