### Educational Content on the Physics of Tension in Ropes#### Scenario Description:A cat burglar is planning a daring heist as depicted in the two diagrams above. The burglar weighs 150 lbs and intends to suspend himself using a long rope that can withstand a tension of 100 lbs, attached to a shorter, stronger rope made of Kevlar that can handle his full weight. The goal is to determine if his plan is feasible and to explore alternative configurations.#### Diagram Explanation:**Left Diagram:**- The burglar is suspended from a beam with ropes labeled \( T_1 \), \( T_2 \), and \( T_3 \).- Rope \( T_3 \) forms a 45° angle with the beam.- A downward force represents the burglar's weight (150 lbs).- The diagram is used to analyze if each rope segment can support the weight while maintaining the tension below 100 lbs.**Right Diagram:**- Presents a new setup with ropes labeled \( T_1 \) and \( T_2 \).- The angle \( \theta \) is formed between the ropes and the beam.- This configuration evaluates alternative methods to distribute weight and tension evenly.#### Physics Problem:##### Part (a)- **Objective:** Compute tensions \( T_1 \), \( T_2 \), and \( T_3 \) in the left diagram and assess the feasibility of the burglar's plan.- **Approach:** Analyze forces using the given angles and weights to determine if tensions exceed the rope's limit of 100 lbs.##### Part (b)- **Objective:** Design an alternate rope arrangement as shown in the right diagram to ensure tensions remain below 100 lbs.- **Challenge:** Calculate the maximum angle \( \theta \) for the configuration to support the burglar's weight without exceeding the tension limit.#### Note:Ignore the mass of the ropes in both parts of the problem to simplify calculations and focus purely on the tension mechanics involved with the burglar's weight and the rope angles.This exercise illustrates the practical application of physics concepts such as tension, force balancing, and vector resolution, pivotal in understanding static equilibrium in real-world scenarios.

The weight of the burglar is W = 150 lbs. Neglect the mass of the rope. The maximum tension that can…

A cat burglar is planning a daring heist. He will lower himself from a beam as shown in the figure on the left. The burglar weighs 150 lbs. He plans to use a long rope that can withstand a tension of 100 lbs to suspend himself from a shorter rope, reasoning that each segment of the longer rope will only need to support half his weight. (The short rope segment is Kevlar and can easily support the burglar's full weight.) (a) Despite your moral outrage, you decide to set the burglar straight. Compute the tensions T1, T2, and T3 and explain why the plan will not work. (b) As a strictly intellectual exercise, you design an alternative arrangement of ropes that will support the burglar's weight using the same long rope from part (a). In the configuration on the right, what is the maximum angle 0 that will result in a tension of less than 100 lbs in each segment of rope? You may ignore the mass of the rope in parts (a) and (b).

A cat burglar is planning a daring heist. He will lower himself from a beam as shown in the figure on the left. The burglar weighs 150 lbs. He plans to use a long rope that can withstand a tension of 100 lbs to suspend himself from a shorter rope, reasoning that each segment of the longer rope will only need to support half his weight. (The short rope segment is Kevlar and can easily support the burglar's full weight.) (a) Despite your moral outrage, you decide to set the burglar straight. Compute the tensions T1, T2, and T3 and explain why the plan will not work. (b) As a strictly intellectual exercise, you design an alternative arrangement of ropes that will support the burglar's weight using the same long rope from part (a). In the configuration on the right, what is the maximum angle 0 that will result in a tension of less than 100 lbs in each segment of rope? You may ignore the mass of the rope in parts (a) and (b).

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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Question

### Educational Content on the Physics of Tension in Ropes

#### Scenario Description:
A cat burglar is planning a daring heist as depicted in the two diagrams above. The burglar weighs 150 lbs and intends to suspend himself using a long rope that can withstand a tension of 100 lbs, attached to a shorter, stronger rope made of Kevlar that can handle his full weight. The goal is to determine if his plan is feasible and to explore alternative configurations.

#### Diagram Explanation:

**Left Diagram:**
- The burglar is suspended from a beam with ropes labeled \( T_1 \), \( T_2 \), and \( T_3 \).
- Rope \( T_3 \) forms a 45° angle with the beam.
- A downward force represents the burglar's weight (150 lbs).
- The diagram is used to analyze if each rope segment can support the weight while maintaining the tension below 100 lbs.

**Right Diagram:**
- Presents a new setup with ropes labeled \( T_1 \) and \( T_2 \).
- The angle \( \theta \) is formed between the ropes and the beam.
- This configuration evaluates alternative methods to distribute weight and tension evenly.

#### Physics Problem:

##### Part (a)
- **Objective:** Compute tensions \( T_1 \), \( T_2 \), and \( T_3 \) in the left diagram and assess the feasibility of the burglar's plan.
- **Approach:** Analyze forces using the given angles and weights to determine if tensions exceed the rope's limit of 100 lbs.

##### Part (b)
- **Objective:** Design an alternate rope arrangement as shown in the right diagram to ensure tensions remain below 100 lbs.
- **Challenge:** Calculate the maximum angle \( \theta \) for the configuration to support the burglar's weight without exceeding the tension limit.

#### Note:
Ignore the mass of the ropes in both parts of the problem to simplify calculations and focus purely on the tension mechanics involved with the burglar's weight and the rope angles.

This exercise illustrates the practical application of physics concepts such as tension, force balancing, and vector resolution, pivotal in understanding static equilibrium in real-world scenarios.

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