### Work and Energy Problem: Lifting a Rope#### Problem Statement:A heavy rope, 90 ft long, weighs 1.4 lb/ft and hangs over the edge of a building 150 ft high. How much work in ft-lbs is done in pulling the rope up to the top of the building?#### Explanation:In this problem, you need to determine the amount of work required to lift a rope that is hanging off a building. The work is measured in foot-pounds (ft-lbs), a unit of energy or work in the foot-pound-second (FPS) system.To find the work done in pulling the rope up to the top, you can integrate the weight of the rope over the distance it needs to be lifted. Given the length and weight per unit of the rope and knowing how it changes position, you can set up the appropriate integral.Use appropriate mathematical and physics principles, such as the integration to solve the problem.### Solution Approach:1. **Determine the weight of the rope:** - Total length of the rope: 90 ft - Weight per foot: 1.4 lb/ft - Total weight = 1.4 lb/ft × 90 ft2. **Set up the integral to calculate work:** - Consider a small element of rope at a height \( x \) from the top of the building. - Work done for an infinitesimal piece of rope: \( dW = \text{weight} \times \text{height} \)3. **Integrate the expression:** - Integrate from 0 to 90 ft (the length of the rope).### Final Calculation:Evaluate the definite integral to find the total work done in pulling the rope to the top of the building.

Name: ### Work and Energy Problem: Lifting a Rope#### Problem Statement:A h
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: ### Work and Energy Problem: Lifting a Rope#### Problem Statement:A heavy rope, 90 ft long, weighs 1.4 lb/ft and hangs over the edge of a building 150 ft high. How much work in ft-lbs is done in pulling the rope up to the top of the building?#### Ex