Equilibrium Problem: Help Solving

• Matt1234
In summary, the problem involves using the Lami's theorem to solve for the unknown angle θ in a system of forces. The equations to be used are (1) for the FBD-C and (2) for the FBD-F, which are then substituted into each other to eliminate T(BC) and solve for θ. The quadratic equation formed using the identity cos^2(θ) = 1 - sin^2(θ) can be solved to find the value of sinθ and ultimately θ.
Matt1234

Homework Statement

[PLAIN]http://img148.imageshack.us/img148/7880/95204069.jpg

The Attempt at a Solution

Im not sure how to solve, i tried substitution but it gets really messy and trig identities are needed, some of which i don't know.

[PLAIN]http://img7.imageshack.us/img7/716/lastscantq.jpg

Last edited by a moderator:

You can apply the Lami's theorem.

For FBD-C

E/sin(150 + θ) = T(CB)/sin(90 + 30) ...(1)

For FBD - F

F/sin(135 - θ) = T(BC)/sin(90 + 45)...(2)

T(CB) = - T(BC)

E*sin(90 + 30)/sin(150 + θ) = T(CB)

F*sin(90 + 45)/sin(135 - θ) = T(BC)

E*sin(90 + 30)/sin(150 + θ) = - F*sin(90 + 45)/sin(135 - θ)

Substitute the known values.

Using sin(A+B) =sinAcosB + cosAsinB

and sin(A-B) = sinAcosB - cosAsinB

Find cosθ in terms of sinθ.

Using the identity cos^2(θ) = 1 - sin^2(θ), form a quadratic equation and then solve for sinθ and hence θ.

1. What is an equilibrium problem?

An equilibrium problem is a mathematical problem that involves finding the values of unknown variables that satisfy a set of conditions or constraints. It is commonly used in economics and physics to model systems that are in a state of balance or stability.

2. How do you solve an equilibrium problem?

To solve an equilibrium problem, you need to first identify the variables, constraints, and equations involved in the problem. Then, you can use mathematical techniques such as substitution, elimination, or graphing to find the values of the unknown variables that satisfy the given conditions.

3. What are the different types of equilibrium problems?

There are two main types of equilibrium problems: static and dynamic. Static equilibrium problems involve finding the values of variables at a specific point in time, while dynamic equilibrium problems involve finding the values of variables over a period of time.

4. What is the significance of equilibrium problems in science?

Equilibrium problems are essential in science as they allow us to model and understand complex systems and their behavior. They are commonly used in fields such as economics, physics, chemistry, and biology to predict and analyze the behavior of systems in balance or stability.

5. What are some common strategies for solving equilibrium problems?

Some common strategies for solving equilibrium problems include identifying and simplifying the problem, using mathematical techniques such as substitution or elimination, and checking the solution to ensure it satisfies all the constraints and equations. It is also helpful to break the problem into smaller parts and to practice with similar problems to improve problem-solving skills.

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