Answer:
560 ft lb
Explanation:
We are given that a heavy rope 40 ft long ,weighs 0.7 lb/ft and hang over the edge of a building 90 ft high.
We have to find the amount of work is done in pulling the rope to the top of the building
Suppose start subdividing the length which is the longest distance any point on the rope can travel into n equal sub-intervals
[tex]0=x_0<x_1<x_2<.........<x_n=40[/tex]
Length of sub-intervals=[tex]\frac{40}{n}[/tex]
[tex]x_i=i\frac{40}{n}[/tex] .For each i we choose x_i*[tex]\in[x_{i-1},x_i][/tex]
Weight density =0. lb/ft
Using rieman sum we are finding approximation work done
[tex]W_i\simeq 0.7 [/tex]delta x[tex] \cdot x*_i[/tex]
Total approximation work done
[tex]W\simeq \sum_{i=1}^{n} 0.7 [/tex]delta x[tex]\cdot x_i*[/tex]
When n tends to infinity then we get
Total work done
[tex]\int_{0}^{40}0.7 x dx=0.7 \frac{(40)^2-0}{2}=0.7\times 800[/tex]=560 ft lb.
The amount of work is done in pulling the rope to the top of the building=560 ft lb
