Work
Winding Cable
Copyright Maplesoft, a division of Waterloo Maple Inc., 2007
Introduction
This application is one of a collection of examples teaching Calculus with Maple. These applications use Clickable Calculus� methods to solve problems interactively. Steps are given at every stage of the solution, and many are illustrated using short video clips. Click on the buttons to watch the videos.
This application is reusable. Modify the problem, then click the !!! button on the toolbar to reexecute the document to solve the new problem.
Problem Statement
With a rope weighing , roofing material weighing is hoisted to the top of a building. Find the total amount of mechanical work done.
Solution
Step

Result

Calculate the work done in raising the roofing material. Since the force is constant, the work done (W) is equal to the product of the force (F) and the distance (d) through which the force acts so .
Type in the numerical value of the weight, then select from the Units (FPS) palette. Repeat for the distance value, this time selecting as the unit.
Construct and evaluate the integral required to calculate the amount of work done to hoist the rope to the top of the building. Let be the work done lifting a segment of rope of length . The weight of this segment is and it travels through a distance of , where is measured upwards from the base of the building. Thus, and
.
From the Expression palette select the definite integral symbol, Fill in the required fields by navigating through each field using the [Tab] key. Press [Enter].
Calculate the total work done by adding the work done in lifting the roofing materials and the work done in hoisting the rope to the top of the building.
Add the work done by each component using equation labels. To insert an equation label press [CTRL][L] and type in the reference number. Once the expression is formed press [Enter].


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Legal Notice: The copyright for this application is owned by Maplesoft. The application is intended to demonstrate the use of Maple to solve a particular problem. It has been made available for product evaluation purposes only and may not be used in any other context without the express permission of Maplesoft.