In this full lesson, we introduce the concept of work in physics and calculus, starting with constant force and moving into variable force and spring problems using Hook’s Law. You will learn how work is connected to force and displacement, how to interpret work as area under a force curve, and how definite integrals are used to calculate work when the force is not constant.
We begin with the basic definition of work as force times distance, then transition into the calculus definition of work as an integral of a force function. From there, we apply these ideas to spring motion and Hook’s Law problems, including how to find the spring constant and how to set up and evaluate definite integrals to compute work.
This lesson includes:
Definition of work in physics
Units of force and work in metric and imperial systems
Work with constant force
Graphical interpretation of work as area under a curve
Work with variable force using definite integrals
Hook’s Law for springs
How to find the spring constant
Work done stretching a spring
Work over different intervals
Unit conversions from kilometers to meters
Work measured in newton meters and foot pounds
If you are studying Calculus 2, applications of integrals, or physics-based work problems, this video will help you understand both the conceptual meaning and the step-by-step setup. These are common topics in AP Calculus AB, AP Calculus BC, and college-level Calculus 1 and Calculus 2 courses.
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