Concept explainers
(a).
To Calculate: The work done in pulling a rope hanging over the edge of a building to the top the building
(a).
Answer to Problem 11E
The work done is
Explanation of Solution
Given Information: Length of the rope is
Concept Used: The work done by a force
If the force is constant, then work done can be expressed as
The weight of an infinitesimally short elementof the rope with length
Work required to pull this infinitesimally small element to the top of the building is
The work required to pull the entire rope to the top of the building is the integral of
Therefore, the force required to pull the entire rope to the top of the building is
(b).
To Calculate: The work done in pulling up half of a rope hanging over the edge of a building.
(b).
Answer to Problem 11E
Explanation of Solution
Given Information: Length of the rope is
Concept Used: The work done by a force
If the force is constant, then work done can be expressed as
UPPER HALF:
Each part of the upper half of the rope travels a different distance. So, use integration to calculate the work done on the upper half as follows:
The weight of an infinitesimally short element of the rope with length
Work required to pull this infinitesimally small element to the top of the building is
The work required to pull the upper half of the rope to the top of the building is the integral of
Therefore, the force required to pull the upper half of the rope to the top of the building is
LOWER HALF:
The weight of an infinitesimally short element of the rope with length
Now, each part of the lower half of the rope moves up by exactly a distance of half the length of the rope.
So, the work done to pull this infinitesimally small length by a distance of half the length of the rope is given by
The total work done one the lower half of the rope is the integral of
Therefore, the total work
Chapter 6 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning