3 Nov 2021
Problem 11b
Page 473
Section 6.6: Applications to Physics and Engineering
Chapter 6: Application of Integration
Textbook ExpertVerified Tutor
3 Nov 2021
Given information
The length of the rope is 
. The weight of the rope is 
and the height of the building is 
.
Step-by-step explanation
Step 1.
Use integration to calculate the work done on the upper half part of the rope
The weight of an infinitesimally short element of the rope with length 
and at a distance at 
from the top of the building is given by the formula 
The work done in pulling this infinitesimally small element to the top of the building is given by the formula 
.
The work done in pulling the upper half of the rope to the top of the building is the integral of 
from 
for the top of the rope to 
for the mid-point of the rope. Therefore the work required for this is:
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805
Solutions
Chapter
Section
- Problem 1
- Problem 2
- Problem 3
- Problem 4
- Problem 5
- Problem 6
- Problem 7a
- Problem 7b
- Problem 8
- Problem 9
- Problem 10
- Problem 11b
- Problem 11b
- Problem 12
- Problem 14
- Problem 15
- Problem 16
- Problem 17
- Problem 18
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- Problem 25
- Problem 26
- Problem 28a
- Problem 28b
- Problem 29a
- Problem 29b
- Problem 29c
- Problem 30a
- Problem 30b
- Problem 30c
- Problem 31
- Problem 32
- Problem 33
- Problem 34
- Problem 35
- Problem 36
- Problem 37
- Problem 38
- Problem 39b
- Problem 39c
- Problem 39d
- Problem 40
- Problem 41
- Problem 42
- Problem 43
- Problem 44
- Problem 45
- Problem 46
- Problem 47
- Problem 48
- Problem 49
- Problem 50
- Problem 51a
- Problem 51b
- Problem 52a
- Problem 52b
- Problem 52c