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
How do you express work as an integral when given a variable force function?
What units are typically used to measure work in physical applications?
How does the formula for work change if the force applied is constant?
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.