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A crane lifts a 650-kg beam vertically upward 23.0 m and then swings it horizontally a distance of 18.0 m. How much work does the crane do? Neglect friction, and assume the beam moves with constant speed.

A crane lifts a 650-kg beam vertically upward 23.0 m and then swings it horizontally a distance of 18.0 m. How much work does the crane do? Neglect friction, and assume the beam moves with constant speed.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Problem Statement:** A crane lifts a 650-kg beam vertically upward 23.0 m and then swings it horizontally a distance of 18.0 m. How much work does the crane do? Neglect friction, and assume the beam moves with constant speed. **Explanation:** In order to calculate the work done by the crane, consider the two motions separately. 1. **Vertical Lift:** - The crane lifts the beam vertically, which involves doing work against gravity. - The formula for work done against gravity is \( W = m \cdot g \cdot h \), where: - \( m = 650 \, \text{kg} \) is the mass of the beam. - \( g = 9.81 \, \text{m/s}^2 \) is the acceleration due to gravity. - \( h = 23.0 \, \text{m} \) is the vertical distance lifted. 2. **Horizontal Movement:** - For horizontal movement at constant speed, with no friction, no additional work is done, as the force is perpendicular to the displacement. **Note:** Since friction is neglected and the horizontal speed is constant, the crane only does work in lifting the beam vertically.
Transcribed Image Text:**Problem Statement:** A crane lifts a 650-kg beam vertically upward 23.0 m and then swings it horizontally a distance of 18.0 m. How much work does the crane do? Neglect friction, and assume the beam moves with constant speed. **Explanation:** In order to calculate the work done by the crane, consider the two motions separately. 1. **Vertical Lift:** - The crane lifts the beam vertically, which involves doing work against gravity. - The formula for work done against gravity is \( W = m \cdot g \cdot h \), where: - \( m = 650 \, \text{kg} \) is the mass of the beam. - \( g = 9.81 \, \text{m/s}^2 \) is the acceleration due to gravity. - \( h = 23.0 \, \text{m} \) is the vertical distance lifted. 2. **Horizontal Movement:** - For horizontal movement at constant speed, with no friction, no additional work is done, as the force is perpendicular to the displacement. **Note:** Since friction is neglected and the horizontal speed is constant, the crane only does work in lifting the beam vertically.
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