Lesson: Work and Integration Mathematics

In this lesson, we will learn how to use integration to find the work done by a variable force.

Lesson Plan

Objectives

Students will be able to

use integration to find the work done by a variable force acting on a body over a given displacement.

Prerequisites

Students should already be familiar with

variable forces,
integration,
work as the product of force and displacement.

Exclusions

Students will not cover

integration by parts,
variable mass problems.

Lesson Explainer

Sample Question Videos

02:29
02:17

Lesson Worksheet

Q1:

The figure shows the magnitude of a force acting on a body as it moves a distance . Given that the force is measured in newtons and the distance is measured in meters, determine the work done in joules by the force to move the body from to .

Q2:

A body moves along the -axis under the action of a force, . Given that , where m is the displacement from the origin, determine the work done on the body by when the body moves from to .

Q3:

From Newton’s universal gravitational law, we know that a body at a distance from the center of Earth is affected by a gravitational force such that , where is a constant. Assuming the radius of Earth is 6,371 km, find the magnitude of the work required for a satellite of mass 793 kg to achieve vertical takeoff from the ground and reach orbit at an altitude of 831 km.