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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?

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### Problem Description An 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 Explanation Although 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.
Transcribed Image Text:### Problem Description An 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 Explanation Although 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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