# Analysis of a Figure to Calculate Force and Moment

• Guillem_dlc
In summary, we are given a bent bar supported by bearings and a cable, with a load applied at a specific point. Using static equations and trigonometry, we calculate the tension in the cable to be 853.13 N.
Guillem_dlc
Homework Statement
The bent bar ##ABDE## is supported by spherical plain bearings at ##A## and ##E## and by the cable ##BF##. If a load of ##600\, \textrm{N}## is applied at ##C##, as shown in the figure, determine the tension in the cable.

Solution: ##853\, \textrm{N}##
Relevant Equations
Static equations, trigonometry
Figure:

My attempt at a Solution:

$$\overrightarrow{TFD}=TFD\dfrac{(-0,16\widehat{i}+0,11\widehat{j}-0,08\widehat{k})}{0,21}$$
View from above:

We calculate ##D##:
$$\sigma =90-\arctan \left( \dfrac{0,07}{0,240}\right)=73,74\, \textrm{º}$$
$$d=0,16\cdot \sin (\sigma)=0,1536\, \textrm{m}$$
##TF_x## does not make moment and ##TF_z## does not make time ##\rightarrow \alpha =16,26\, \textrm{º}##
$$\sum M_{EA}=TF_x\cdot \sin \alpha \cdot d+TF_z\cdot \cos \alpha \cdot d+TF_yd -600\cdot d'$$
$$\rightarrow TFD\dfrac{0,16}{0,21}\sin \alpha d+TFD\dfrac{0,08}{0,21}\cos \alpha d+TFD\dfrac{0,11}{0,21}d=600d'\rightarrow$$
$$\rightarrow TFD=\dfrac{0,21\cdot 600d'}{d}\cdot \left( \dfrac{1}{0,16\sin \alpha +0,08\cos \alpha +0,11}\right)=405,2\, \textrm{N}$$
Could you have a look at this one?

What do you get for the system if you just apply ## \sum_{x,y,z} F = 0## ##\sum_{A,E} M = 0 ## using the coordinate system already in place?

I find ##T \approx 853 \rm{N} ##. You will only actually need 3 equations in the end to answer this question by using a coordinate system offset through the point ##E## to generate the remaining two equations (you already have the third for the tension ##T## in terms of its components).

Guillem_dlc said:
##TF_x## does not make moment and ##TF_z## does not make time ##\rightarrow \alpha =16,26\, \textrm{º}##
$$\sum M_{EA}=TF_x\cdot \sin \alpha \cdot d+TF_z\cdot \cos \alpha \cdot d+TF_yd -600\cdot d'$$
You state correctly that the x component of tension has no moment about AE, but you include such a term in the equation. Similarly the z component (but "does not make time"?).

Guillem_dlc said:
Homework Statement:: The bent bar ##ABDE## is supported by spherical plain bearings at ##A## and ##E## and by the cable ##BF##. If a load of ##600\, \textrm{N}## is applied at ##C##, as shown in the figure, determine the tension in the cable.

Solution: ##853\, \textrm{N}##
Relevant Equations:: Static equations, trigonometry

Figure:
View attachment 316451

My attempt at a Solution:
View attachment 316452
$$\overrightarrow{TFD}=TFD\dfrac{(-0,16\widehat{i}+0,11\widehat{j}-0,08\widehat{k})}{0,21}$$
View from above:
View attachment 316453
We calculate ##D##:
$$\sigma =90-\arctan \left( \dfrac{0,07}{0,240}\right)=73,74\, \textrm{º}$$
$$d=0,16\cdot \sin (\sigma)=0,1536\, \textrm{m}$$
##TF_x## does not make moment and ##TF_z## does not make time ##\rightarrow \alpha =16,26\, \textrm{º}##
I've ended up doing it this way now and I got it:
$$\sum M_{EA}=TF_yd-600\cdot d'=0\rightarrow TFD\dfrac{0,11}{0,21}d=600d'\rightarrow$$
$$\rightarrow \boxed{TFD=853,13\, \textrm{N}}$$

## 1. What is the purpose of analyzing a figure to calculate force and moment?

The purpose of analyzing a figure to calculate force and moment is to determine the forces and moments acting on a body or structure. This information is crucial for understanding the stability, strength, and behavior of the object in question.

## 2. What is the difference between force and moment?

Force is a physical quantity that causes an object to accelerate, while moment is a measure of the tendency of a force to rotate an object around a specific point. In other words, force acts in a linear direction, while moment acts in a rotational direction.

## 3. How do you calculate the force and moment on a figure?

To calculate the force and moment on a figure, you will need to use the principles of statics, which include equilibrium equations and free-body diagrams. These tools allow you to analyze the forces and moments acting on a body and determine their magnitudes and directions.

## 4. What factors can affect the force and moment on a figure?

The force and moment on a figure can be affected by a variety of factors, including the shape and size of the object, the materials it is made of, and the external forces acting on it. Additionally, the position and orientation of the object can also impact the forces and moments acting on it.

## 5. How can the analysis of force and moment help in real-world applications?

The analysis of force and moment is essential in many real-world applications, such as engineering and construction, where it is used to design and test structures for safety and stability. It is also used in fields like biomechanics and physics to understand the forces and moments involved in human movement and natural phenomena.

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