# Statics of hangman beam / guitar neck under load

• shabbily
In summary, the relationship between the length or height h of a guitar neck and its displacement (δ) is analogous to a hangman diagram and an end load cantilever beam. The tension in the strings and the width of the neck are important factors that affect the amount of displacement (δ).
shabbily
Hello all, I am trying to understand what the relationship is between the length or height h of a guitar neck and how far in the x direction it is displaced (δ) given the same tension in the strings and width of the neck, and assuming the neck is anchored and rigid at the guitar's body. Is it analogous to the attached hangman diagram? My gut says the two seem analogous to an end load cantilever beam but I don't know if it is that simple. Hopefully this makes sense... I am not a physics person and may be using some of these terms incorrectly.

#### Attachments

• physics_hangman.jpg
28.1 KB · Views: 373
• physics_guitarneck.jpg
16.4 KB · Views: 406
Yes, the relationship between the length or height h of a guitar neck and its displacement (δ) is analogous to the hangman diagram. It is also analogous to an end load cantilever beam. The tension in the strings and the width of the neck are factors that will affect the amount of displacement (δ). In the case of an end load cantilever beam, the displacement (δ) is proportional to the load (F) divided by the stiffness (k) of the beam, where F is the force applied at the end of the beam and k is the stiffness of the beam itself. So, if you increase the tension in the strings, the displacement (δ) of the guitar neck will increase. Similarly, if you increase the width of the neck, the stiffness (k) of the beam will increase, resulting in less displacement (δ).

## 1. What is the purpose of studying the statics of hangman beam/guitar neck under load?

The purpose of studying the statics of hangman beam/guitar neck under load is to understand how the beam/neck will behave when subjected to external forces. This knowledge is essential for designing safe and stable structures, such as guitars, and ensuring their longevity.

## 2. How does the load affect the statics of a hangman beam/guitar neck?

The load applied to a hangman beam/guitar neck will cause it to bend or deform, resulting in a change in its shape and stress distribution. This change in shape and stress can be analyzed using principles of statics to determine the strength and stability of the beam/neck.

## 3. What factors influence the statics of a hangman beam/guitar neck under load?

The statics of a hangman beam/guitar neck under load is influenced by various factors such as the material properties of the beam/neck, the magnitude and direction of the load, and the geometry of the beam/neck. Other factors like temperature, moisture, and external vibrations can also affect the statics of the beam/neck.

## 4. What are the key principles of statics used to analyze the hangman beam/guitar neck under load?

The key principles of statics used to analyze the hangman beam/guitar neck under load include equilibrium, which states that the sum of all forces acting on a body must be zero, and the principle of superposition, which allows us to break down complex forces into simpler components for analysis. Other principles include moment equilibrium and free body diagrams.

## 5. How is the statics analysis of a hangman beam/guitar neck used in real-world applications?

The statics analysis of a hangman beam/guitar neck is used in various real-world applications, including the design and construction of bridges, buildings, and other structures. It is also applied in the design and manufacturing of musical instruments, such as guitars, to ensure their stability and performance under load.

Replies
4
Views
2K
Replies
8
Views
3K
Replies
1
Views
2K
Replies
1
Views
1K
Replies
5
Views
2K
Replies
4
Views
2K
Replies
1
Views
2K
Replies
5
Views
4K
Replies
3
Views
4K
Replies
4
Views
1K