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Group Problem: You are planning to build a log cabin in Northern Minnesota on a remote hill with a beautiful view of the setting sun. You will drag the logs up a long sometimes rocky hill to the building site by means of a rope attached to a winch. You will need a rope for this job so you aim to know how much weight the rope would safely support. You are operating on a tight budget so matching the rope strength would be a cost saver. You know that the logs are heavy, and estimate the heaviest as 1,000 lbs. From maps you verify the hill is steeped at an angle of 0 = 70° with respect to the vertical, and you estimate a coefficient of kinetic friction between a log and the earthen hill as 0.5. When pulling a log you will ensure that the uphill acceleration is never more than 3.0 ft/s². The maximum recommended load is th of the nominal strength for the ropes considered as stated on the product labels, you have three ropes in mind: 12 kN, 18 kN, & 24 kN. Which one of these three rope strengths is best? SOLUTION: Using the step-wise strategy that we have practiced throughout this course, for forces that includes the drawing of Freebody and Force Diagrams, and an inventory of known quantities: max. log weight: W = 1,000 lbs, hill incline: 0= 20° (w.r.t. horizontal), coefficient of kinetic friction: μ = 0.5, and maximum acceleration for the log: amaz = 3 ft/s². Express the maximum log weight as a mass: mlog = kg. STEP A: Identify the forces on the Scenario, Freebody, and Force Diagrams below: LOG ROPE 10 = 20° HILL SCENARIO WINCH *** Fnet = mă →→→ FREEBODY STEP B: Apply Newton's 2nd Law independently in the horizontal and vertical directions to develop relation- ships for the forces en-route to the solution to the problem: Find the tension in the log-pulling rope. FORCE I: Fnet = maz y: Fnet = may

Group Problem: You are planning to build a log cabin in Northern Minnesota on a remote hill with a beautiful view of the setting sun. You will drag the logs up a long sometimes rocky hill to the building site by means of a rope attached to a winch. You will need a rope for this job so you aim to know how much weight the rope would safely support. You are operating on a tight budget so matching the rope strength would be a cost saver. You know that the logs are heavy, and estimate the heaviest as 1,000 lbs. From maps you verify the hill is steeped at an angle of 0 = 70° with respect to the vertical, and you estimate a coefficient of kinetic friction between a log and the earthen hill as 0.5. When pulling a log you will ensure that the uphill acceleration is never more than 3.0 ft/s². The maximum recommended load is th of the nominal strength for the ropes considered as stated on the product labels, you have three ropes in mind: 12 kN, 18 kN, & 24 kN. Which one of these three rope strengths is best? SOLUTION: Using the step-wise strategy that we have practiced throughout this course, for forces that includes the drawing of Freebody and Force Diagrams, and an inventory of known quantities: max. log weight: W = 1,000 lbs, hill incline: 0= 20° (w.r.t. horizontal), coefficient of kinetic friction: μ = 0.5, and maximum acceleration for the log: amaz = 3 ft/s². Express the maximum log weight as a mass: mlog = kg. STEP A: Identify the forces on the Scenario, Freebody, and Force Diagrams below: LOG ROPE 10 = 20° HILL SCENARIO WINCH *** Fnet = mă →→→ FREEBODY STEP B: Apply Newton's 2nd Law independently in the horizontal and vertical directions to develop relation- ships for the forces en-route to the solution to the problem: Find the tension in the log-pulling rope. FORCE I: Fnet = maz y: Fnet = may

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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**Educational Content: Log Pulling Problem Using Physics** **Group Problem:** You are planning to build a log cabin in Northern Minnesota on a remote hill with a beautiful view of the setting sun. You will drag logs up a long, sometimes rocky hill to the building site using a rope attached to a winch. You need a rope for this job, so you aim to know how much weight the rope can safely support. You are operating on a tight budget, so matching the rope strength would be a cost saver. You know that the logs are heavy, and estimate the heaviest as 1,000 lbs. From maps, you verify the hill is steeped at an angle of θ = 20º with respect to the vertical, and you estimate a coefficient of kinetic friction between a log and the earthen hill as 0.5. When pulling a log, you will ensure that the uphill acceleration is never more than 3.0 ft/s². The maximum recommended load is 1/10th of the nominal strength for the ropes considered as stated on the product labels. You have three ropes in mind: 12 kN, 18 kN, & 24 kN. Which one of these three rope strengths is best? **SOLUTION:** Using the step-wise strategy that we have practiced throughout this course, for forces that include the drawing of Freebody and Force Diagrams, and an inventory of known quantities: - max. log weight: W = 1,000 lbs - hill incline: θ = 20º (w.r.t. horizontal) - coefficient of kinetic friction: μ = 0.5 - maximum acceleration for the log: aₘₐₓ = 3 ft/s² Express the maximum log weight as a mass: mₗₒg = ____ kg. --- **STEP A:** Identify the forces on the Scenario, Freebody, and Force Diagrams below: - **Scenario Diagram:** Shows the log on a hill inclined at 20° with a rope connecting the log to a winch. - **Freebody Diagram:** Illustrates forces acting on the log, including tension, gravitational force, normal force, and friction. - **Force Diagram:** Breaks down forces into x and y components for analysis. --- **STEP B:** Apply Newton’s 2nd Law independently in the horizontal and vertical directions to develop relationships for the forces en-route to
Transcribed Image Text:**Educational Content: Log Pulling Problem Using Physics** **Group Problem:** You are planning to build a log cabin in Northern Minnesota on a remote hill with a beautiful view of the setting sun. You will drag logs up a long, sometimes rocky hill to the building site using a rope attached to a winch. You need a rope for this job, so you aim to know how much weight the rope can safely support. You are operating on a tight budget, so matching the rope strength would be a cost saver. You know that the logs are heavy, and estimate the heaviest as 1,000 lbs. From maps, you verify the hill is steeped at an angle of θ = 20º with respect to the vertical, and you estimate a coefficient of kinetic friction between a log and the earthen hill as 0.5. When pulling a log, you will ensure that the uphill acceleration is never more than 3.0 ft/s². The maximum recommended load is 1/10th of the nominal strength for the ropes considered as stated on the product labels. You have three ropes in mind: 12 kN, 18 kN, & 24 kN. Which one of these three rope strengths is best? **SOLUTION:** Using the step-wise strategy that we have practiced throughout this course, for forces that include the drawing of Freebody and Force Diagrams, and an inventory of known quantities: - max. log weight: W = 1,000 lbs - hill incline: θ = 20º (w.r.t. horizontal) - coefficient of kinetic friction: μ = 0.5 - maximum acceleration for the log: aₘₐₓ = 3 ft/s² Express the maximum log weight as a mass: mₗₒg = ____ kg. --- **STEP A:** Identify the forces on the Scenario, Freebody, and Force Diagrams below: - **Scenario Diagram:** Shows the log on a hill inclined at 20° with a rope connecting the log to a winch. - **Freebody Diagram:** Illustrates forces acting on the log, including tension, gravitational force, normal force, and friction. - **Force Diagram:** Breaks down forces into x and y components for analysis. --- **STEP B:** Apply Newton’s 2nd Law independently in the horizontal and vertical directions to develop relationships for the forces en-route to
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mlog=1000 lbsamax=3 ft/s2μ=0.5θ=20°

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