A tugboat tows a ship at a constant velocity. The tow harness consists of a single tow cable attached to the tugboat at point A that splits at point B and attaches to the ship at points Cand D. The two rope segments BC and BD angle away from the D center of the ship at angles of ø = 28.0° and 0 = 21.0°, respectively. The tugboat pulls with a force of 1500 lb. What are the tensions TBc and Tpp in the rope segments BC and BD? Express your answers numerically in pounds to three significant figures separated by a comma. > View Available Hint(s)
A tugboat tows a ship at a constant velocity. The tow harness consists of a single tow cable attached to the tugboat at point A that splits at point B and attaches to the ship at points Cand D. The two rope segments BC and BD angle away from the D center of the ship at angles of ø = 28.0° and 0 = 21.0°, respectively. The tugboat pulls with a force of 1500 lb. What are the tensions TBc and Tpp in the rope segments BC and BD? Express your answers numerically in pounds to three significant figures separated by a comma. > View Available Hint(s)
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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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
![**Title: Finding Tensions in Tow Cables of a Tugboat**
**Problem Statement:**
A tugboat tows a ship at a constant velocity. The tow harness consists of a single tow cable attached to the tugboat at point \(A\) that splits at point \(B\) and attaches to the ship at points \(C\) and \(D\). The two rope segments \(BC\) and \(BD\) angle away from the center of the ship at angles of \(\phi = 28.0^\circ\) and \(\theta = 21.0^\circ\), respectively. The tugboat pulls with a force of 1500 lb.
**Question:** What are the tensions \(T_{BC}\) and \(T_{BD}\) in the rope segments \(BC\) and \(BD\)?
**Instructions for Students:**
Express your answers numerically in pounds to three significant figures separated by a comma.
**Diagram Explanation:**
- The diagram depicts a ship being towed by a tugboat.
- Point A is where the tow cable attaches to the tugboat.
- The tow cable splits at point B.
- The segments \(BC\) and \(BD\) attach the ship at points \(C\) and \(D\).
- The angle \(\phi = 28.0^\circ\) is between segment \(BC\) and the direction toward the tugboat.
- The angle \(\theta = 21.0^\circ\) is between segment \(BD\) and the direction toward the tugboat.
- There is a graphical interface provided for entering the calculated tensions \(T_{BC}\) and \(T_{BD}\) which must be entered in pounds.
**Interactive Component:**
Students can use the available hints and dedicated input box to calculate and input the tensions in the respective rope segments. The tensions should be entered in the format:
\[T_{BC}, T_{BD} = \_\_\_ \text{ lb}, \_\_\_ \text{ lb}\]
**Hints:**
1. Analyze the force components in both horizontal and vertical directions.
2. Use trigonometry to resolve the forces.
3. Apply equilibrium conditions for both vertical and horizontal forces to find \(T_{BC}\) and \(T_{BD}\).
This problem helps students practice their knowledge of statics and the resolution of forces, enhancing their understanding of force components in mechanical systems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb1a8ba3-371b-48d7-95b6-c118f740fa83%2F92ea8a7e-de7d-40e0-9cb6-224d65ffe915%2F9qnvugl_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Finding Tensions in Tow Cables of a Tugboat**
**Problem Statement:**
A tugboat tows a ship at a constant velocity. The tow harness consists of a single tow cable attached to the tugboat at point \(A\) that splits at point \(B\) and attaches to the ship at points \(C\) and \(D\). The two rope segments \(BC\) and \(BD\) angle away from the center of the ship at angles of \(\phi = 28.0^\circ\) and \(\theta = 21.0^\circ\), respectively. The tugboat pulls with a force of 1500 lb.
**Question:** What are the tensions \(T_{BC}\) and \(T_{BD}\) in the rope segments \(BC\) and \(BD\)?
**Instructions for Students:**
Express your answers numerically in pounds to three significant figures separated by a comma.
**Diagram Explanation:**
- The diagram depicts a ship being towed by a tugboat.
- Point A is where the tow cable attaches to the tugboat.
- The tow cable splits at point B.
- The segments \(BC\) and \(BD\) attach the ship at points \(C\) and \(D\).
- The angle \(\phi = 28.0^\circ\) is between segment \(BC\) and the direction toward the tugboat.
- The angle \(\theta = 21.0^\circ\) is between segment \(BD\) and the direction toward the tugboat.
- There is a graphical interface provided for entering the calculated tensions \(T_{BC}\) and \(T_{BD}\) which must be entered in pounds.
**Interactive Component:**
Students can use the available hints and dedicated input box to calculate and input the tensions in the respective rope segments. The tensions should be entered in the format:
\[T_{BC}, T_{BD} = \_\_\_ \text{ lb}, \_\_\_ \text{ lb}\]
**Hints:**
1. Analyze the force components in both horizontal and vertical directions.
2. Use trigonometry to resolve the forces.
3. Apply equilibrium conditions for both vertical and horizontal forces to find \(T_{BC}\) and \(T_{BD}\).
This problem helps students practice their knowledge of statics and the resolution of forces, enhancing their understanding of force components in mechanical systems.
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