Equilibrium problem help

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In summary, the problem is asking to calculate the tension in a rope when a person with a mass of 52.0kg is standing at the midpoint of the rope, which is 10.0 degrees below the horizontal. The formula used to solve this problem is Ft=(m*g)/(2*sinθ), where Ft is the tension in the rope, m is the mass of the person, g is the acceleration due to gravity, and θ is the angle of sag in the rope. This formula comes from setting the y-component of the net force equal to zero, as the person is in equilibrium.
  • #1

Homework Statement


Arlene is to walk across a "high wire" strung horizontally between two buildings 14.0m apart. The sag in the rope when she is at the midpoint is 10.0 degrees. If her mass is 52.0kg , what is the tension in the rope at this point?

Homework Equations


Fnet=ma
a=0 so fnet=0

The Attempt at a Solution


So I know that Fg=9.8*52=509.6 N, and I broke down Ft into Ftx and Fty. sin10=Fty/Ft but I have no idea how to use Fg in that formula to find Ft.
In my notes I have "Ft=(m*g)/(2sinθ) which gives the correct answer, but I don't understand how I got that formula. Can someone explain where it came from/give me some guidance. Why 2sin?
 
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  • #2
Since she is in equilibrium, ƩF = 0. In particular, the y-component of the net force must equal zero.

What forces act on her? What are their y-components?
 

1. What is an equilibrium problem?

An equilibrium problem is a mathematical problem that involves finding the state of balance or stability in a system. This can include finding the optimal solution to a set of equations or determining the point at which a system reaches its steady state.

2. What types of systems can be solved using equilibrium problems?

Equilibrium problems can be applied to a variety of systems, including physical, chemical, biological, and economic systems. Any system that is influenced by different forces or factors that need to be balanced can be solved using equilibrium problems.

3. How do you solve an equilibrium problem?

To solve an equilibrium problem, you typically need to set up a set of equations based on the given information and conditions of the system. These equations can then be solved using various mathematical techniques, such as substitution, elimination, or graphical methods.

4. What are some real-life applications of equilibrium problems?

Equilibrium problems have many practical applications, such as predicting chemical reactions, determining optimal production levels in economics, and analyzing population dynamics in biology. They are also used in engineering for designing stable structures and systems.

5. What are some common challenges when solving equilibrium problems?

One of the main challenges in solving equilibrium problems is accurately identifying and setting up the relevant equations for the given system. Additionally, some problems may have multiple solutions or no solutions at all, making it important to carefully analyze the results to ensure they make sense in the context of the problem.

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