### Problem DescriptionAn adventurous archaeologist crosses between two rock cliffs by slowly going hand over hand along a rope stretched between the cliffs. He stops to rest at the middle of the rope (Figure 5.43). The rope will break if the tension in it exceeds \(2.50 \times 10^4 \, \text{N}\). Our hero's mass is \(90.0 \, \text{kg}\).#### Tasks:- **(a)** If the angle \(\theta\) is \(10.0^\circ\), find the tension in the rope. Start with a free-body diagram of the archaeologist.- **(b)** What is the smallest value the angle \(\theta\) can have if the rope is not to break?### Diagram ExplanationAlthough the diagram (Figure 5.43) isn't visible, the description implies a free-body diagram where:- The archaeologist is at the center of the rope.- The force of gravity acts downward on the archaeologist.- Tension forces act along the rope on either side, directed toward the cliffs.To solve the problem, apply principles of equilibrium and trigonometry, considering the balance of forces vertically and horizontally.

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An adventurous archaeologist cros- ses between two rock cliffs by slowly going hand over hand along a rope stretched between the cliffs. He stops to rest at the middle of the rope (Figure 5.43). The rope will break if the tension in it exceeds 2.50 × 104 N. Our hero's mass is 90.0 kg. (a) If the angle 0 is 10.0º, find the tension in the rope. Start with a free-body diagram of the archaeologist. (b) What is the smallest value the angle 8 can have if 0 the rope is not to break?

An adventurous archaeologist cros- ses between two rock cliffs by slowly going hand over hand along a rope stretched between the cliffs. He stops to rest at the middle of the rope (Figure 5.43). The rope will break if the tension in it exceeds 2.50 × 104 N. Our hero's mass is 90.0 kg. (a) If the angle 0 is 10.0º, find the tension in the rope. Start with a free-body diagram of the archaeologist. (b) What is the smallest value the angle 8 can have if 0 the rope is not to break?

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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