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4. How high can the worker safely climb the ladder? A ladder is leaning against a wall as shown in the image below. The wall is smooth, so friction can be ignored, and the top of the ladder can be considered to act as a roller support that transfers only a horizontal force, RT. (for "Reaction at Top") The base of the ladder is supported by a rough textured concrete slab. It can be considered to act as a pinned support that can cary both horizontal and vertical forces. Measurements indicate that due to friction between the concrete and the ladder, the base can withstand a 50-pound horizontal force before it slips while supporting a 200-pound contractor standing on the ladder. The 200-pound worker is ascending the ladder. How high can he safely climb if the 50-pound horizontal force is the limiting factor? Assume that the contractor's weight acts at a single point through the body center of gravity as indicated by the downward vector. a) Using linear and rotational equilibrium in an analytic calculation, ascertain the height. Hint: What yo'll find first is the horizontal distance, which then can be translated into the vertical distance. b) See if yoU can also solve this graphically. Remember to think in terms of lines of actions of the forces and draw the forces to a scale. The key to the graphic solution is understanding that all forces must intersect at one point in order that there not be any overall rotation. The distance is then found by measuring to scale, which should match the analytic calculation.

4. How high can the worker safely climb the ladder? A ladder is leaning against a wall as shown in the image below. The wall is smooth, so friction can be ignored, and the top of the ladder can be considered to act as a roller support that transfers only a horizontal force, RT. (for "Reaction at Top") The base of the ladder is supported by a rough textured concrete slab. It can be considered to act as a pinned support that can cary both horizontal and vertical forces. Measurements indicate that due to friction between the concrete and the ladder, the base can withstand a 50-pound horizontal force before it slips while supporting a 200-pound contractor standing on the ladder. The 200-pound worker is ascending the ladder. How high can he safely climb if the 50-pound horizontal force is the limiting factor? Assume that the contractor's weight acts at a single point through the body center of gravity as indicated by the downward vector. a) Using linear and rotational equilibrium in an analytic calculation, ascertain the height. Hint: What yo'll find first is the horizontal distance, which then can be translated into the vertical distance. b) See if yoU can also solve this graphically. Remember to think in terms of lines of actions of the forces and draw the forces to a scale. The key to the graphic solution is understanding that all forces must intersect at one point in order that there not be any overall rotation. The distance is then found by measuring to scale, which should match the analytic calculation.

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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4. How high can the worker safely climb the ladder? A ladder is leaning against a wall as shown in the image below. The wall is smooth, so friction can be ignored, and the top of the ladder can be considered to act as a roller support that transfers only a horizontal force, RT. (for "Reaction at Top") The base of the ladder is supported by a rough textured concrete slab. It can be considered to act as a pinned support that can cary both horizontal and vertical forces. Measurements indicate that due to friction between the concrete and the ladder, the base can withstand a 50-pound horizontal force before it slips while supporting a 200-pound contractor standing on the ladder. The 200-pound worker is ascending the ladder. How high can he safely climb if the 50-pound horizontal force is the limiting factor? Assume that the contractor's weight acts at a single point through the body center of gravity as indicated by the downward vector. a) Using linear and rotational equilibrium in an analytic calculation, ascertain the height. Hint: What yo'll find first is the horizontal distance, which then can be translated into the vertical distance. b) See if yoU can also solve this graphically. Remember to think in terms of lines of actions of the forces and draw the forces to a scale. The key to the graphic solution is understanding that all forces must intersect at one point in order that there not be any overall rotation. The distance is then found by measuring to scale, which should match the analytic calculation. 200 lbs 3 50 lbs R BV 4' R. 12'
Transcribed Image Text:4. How high can the worker safely climb the ladder? A ladder is leaning against a wall as shown in the image below. The wall is smooth, so friction can be ignored, and the top of the ladder can be considered to act as a roller support that transfers only a horizontal force, RT. (for "Reaction at Top") The base of the ladder is supported by a rough textured concrete slab. It can be considered to act as a pinned support that can cary both horizontal and vertical forces. Measurements indicate that due to friction between the concrete and the ladder, the base can withstand a 50-pound horizontal force before it slips while supporting a 200-pound contractor standing on the ladder. The 200-pound worker is ascending the ladder. How high can he safely climb if the 50-pound horizontal force is the limiting factor? Assume that the contractor's weight acts at a single point through the body center of gravity as indicated by the downward vector. a) Using linear and rotational equilibrium in an analytic calculation, ascertain the height. Hint: What yo'll find first is the horizontal distance, which then can be translated into the vertical distance. b) See if yoU can also solve this graphically. Remember to think in terms of lines of actions of the forces and draw the forces to a scale. The key to the graphic solution is understanding that all forces must intersect at one point in order that there not be any overall rotation. The distance is then found by measuring to scale, which should match the analytic calculation. 200 lbs 3 50 lbs R BV 4' R. 12'
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