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Calculus III

Course: Calculus II
Topic: Physics
Subtopic: Work

Overview

Today's lesson is a topic from the calculus of physics, work. A force is applied to an object causing it to move a distance. Work is the product of the force and the distance. If the force is constant, this is an easy algebra problem. However variable force requires integration so calculus comes into play.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 7.1.1 Understand and be able to calculate common units of measure for force and work (newtons, joules, etc.)
• 7.1.2 Set-up and solve a problem involving work done by a constant force or variable force
• 7.1.3 Set-up and solve a problem involving work done stretching/compressing springs (Hooke's Law)
• 7.1.4 Set-up and solve a problem involving work done pumping liquids from containers

Terminology

Terms you should be able to define: Newton, Joule, force, constant force, variable force, work, Hooke's Law

Mini-Lectures and Examples

Supplemental Resources (recommended)

Explore these physics demonstrations at www.myphysicslab.com. Enjoy!

Supplemental Resources (optional)

PDF: First Applications of Definite Integrals, Dale Hoffman's Contemporary Calculus includes some work problems starting about half-way through this lesson.

Examples: Work by a Variable Force using Integration, IntMath has a variety of basic examples, an interactive diagram of a spring, and a leaky bucket problem

Examples: Force, Work, and Energy, Math24's Calculus has good sketches and a variety of physics examples

Application: Electric Charges by Integration, IntMath

rev. 2021-01-17