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 o = 27.0 ° and 0 = 23.0 ° , respectively. The tugboat pulls with a force o B A 4800 lb. What are the tensions TBc and TBD in the rope segments BC and BD? Express your answers numerically in pounds to three significant figures separated by a comma.
Plane Trusses
It is defined as, two or more elements like beams or any two or more force members, which when assembled together, behaves like a complete structure or as a single structure. They generally consist of two force member which means any component structure where the force is applied only at two points. The point of contact of joints of truss are known as nodes. They are generally made up of triangular patterns. Nodes are the points where all the external forces and the reactionary forces due to them act and shows whether the force is tensile or compressive. There are various characteristics of trusses and are characterized as Simple truss, planar truss or the Space Frame truss.
Equilibrium Equations
If a body is said to be at rest or moving with a uniform velocity, the body is in equilibrium condition. This means that all the forces are balanced in the body. It can be understood with the help of Newton's first law of motion which states that the resultant force on a system is null, where the system remains to be at rest or moves at uniform motion. It is when the rate of the forward reaction is equal to the rate of the backward reaction.
Force Systems
When a body comes in interaction with other bodies, they exert various forces on each other. Any system is under the influence of some kind of force. For example, laptop kept on table exerts force on the table and table exerts equal force on it, hence the system is in balance or equilibrium. When two or more materials interact then more than one force act at a time, hence it is called as force systems.
![**Problem Solving Application: Tension in Tow Cables**
**Scenario:**
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 \(\phi = 27.0^\circ \) and \(\theta = 23.0^\circ \), respectively. The tugboat pulls with a force of 4800 lb.
**Question:**
What are the tensions \( T_{BC} \) and \( T_{BD} \) in the rope segments \( BC \) and \( BD \)?
**Task:**
Express your answers numerically in pounds to three significant figures separated by a comma.
**Hints:**
You may click on "View Available Hint(s)" for additional guidance on solving the problem.
**Solution Input:**
Enter the tensions below:
\[ T_{BC}, T_{BD} = \]
**Diagram Description:**
- The diagram illustrates the tow cable setup.
- Point \( A \) represents the point where the tow cable is attached to the tugboat.
- Point \( B \) is where the cable splits into two segments.
- Points \( C \) and \( D \) are the attachment points on the ship.
- Angles \(\phi \) (27.0°) and \(\theta \) (23.0°) show the direction of the two rope segments \( BC \) and \( BD \) respectively.
- \( \vec{F} \) represents the force exerted by the tugboat, which is 4800 lb.
Ensure calculations are accurate and formatted correctly for a clear and concise educational resource.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb1a8ba3-371b-48d7-95b6-c118f740fa83%2Fb140c954-c1cc-4321-94ec-b6d769b7730e%2Fu5d0cug_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
