Engineering statics questions

In summary, the conversation discusses a problem involving finding the angle γ and solving for the projected portion of a triangle. One person made a mistake in their calculations and another person provides guidance on how to correctly approach the problem. The conversation also discusses the relationship between angles and their measurements on different planes.
  • #1
Mdhiggenz
327
1

Homework Statement


Hello everyone,

I have a few questions regarding the problem below.

1. I did the process for solving γ correct however I took the 60° angle instead of the 120° angle. The below solution states that γ>90°. Why must is be greater, than 90°, and when would it have been smaller?

2. I got a big confused when solving for the projected portion of the triangle. What I did initially was solve for the hypotenuse of the projection which I thought would be

F'=450sin(45°), and just use that F' to find the x, and y components, however that was completely wrong it seems.


2cgboy0.png




Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
  • #2
Mdhiggenz said:

Homework Statement


Hello everyone,

I have a few questions regarding the problem below.

1. I did the process for solving γ correct however I took the 60° angle instead of the 120° angle. The below solution states that γ>90°. Why must is be greater, than 90°, and when would it have been smaller?
Where is γ measured from?
If F2 pointing above pr below the x-y plane?

2. I got a big confused when solving for the projected portion of the triangle. What I did initially was solve for the hypotenuse of the projection which I thought would be

F'=450sin(45°), and just use that F' to find the x, and y components, however that was completely wrong it seems.
F1 forms the hypotenuse of a 45deg triangle, Is this the one you mean?

The x-y projection would start with what you did[*]: F'=F1/√2
How did you get the x and y components from there?

Note: the angles are very friendly.
i.e. sin(45)=cos(45)=1/√2, sin(30)=cos(30)=1/2, etc.

-------------------------

[*] except it's the cosine - doesn't matter to the result though.
Does matter for the next results.
 
Last edited:
  • #3
γ is measured from the z axis to F2. It seems that F2 is below the xy plane. For the projection what I mean was for the 30degree the way my mind analyzes it is that we get the x components of both triangles e.g 30 and 45 degree.

Which would mean that 450*cos(45) would be the x component for the 45 degree right triangle, and cos(30) would be for the 30 degree triangle.

Which would make the i comonent. 450*cos(45)cos(30), however the solution above has it as 450*cos(45) sin(30)
 
  • #4
Mdhiggenz said:
γ is measured from the z axis to F2. It seems that F2 is below the xy plane.
... and? Relate this answer back to your question:
The below solution states that γ>90°. Why must is be greater, than 90°, and when would it have been smaller?

What does your answer mean for the size of γ?
If F2 were exactly in the x-y plane, what would γ equal?
Since it is below the x-y plane, would γ be bigger or smaller than this value?



For the projection what I mean was for the 30degree the way my mind analyzes it is that we get the x components of both triangles e.g 30 and 45 degree.

Which would mean that 450*cos(45) would be the x component for the 45 degree right triangle, and cos(30) would be for the 30 degree triangle.

Which would make the i comonent. 450*cos(45)cos(30), however the solution above has it as 450*cos(45) sin(30)

Looks like you got the sines and cosines mixed up.
You got it right for if the 30deg angle was measured from the +x axis like normal - but it isn't.
It can help if you sketch the triangle out separately and label the sides before working out which is the adjacent and which the opposite sides.
 
  • #5
Oh because since it is below the xy plane that would mean it would be in either quadrants 3 or 4, but would that mean it should be γ>180 not 90?. I do understand though that the max a triangle can be is 180 I just don't understand that relation.

For the projection of the 30 degree triangle I now see that it is on the yz plane. But still don't see how that would help me. Even if I labeled the sides, for example I know that cos(30) would be on the y-axis now. But I can't see how that is in any way related to the X axis.
 
  • #6
Mdhiggenz said:
Oh because since it is below the xy plane that would mean it would be in either quadrants 3 or 4, but would that mean it should be γ>180 not 90?. I do understand though that the max a triangle can be is 180 I just don't understand that relation.
Careful: ##\gamma## cannot be bigger than 180deg.

What is the angle between the z-axis and anywhere on the x-y plane?

For the projection of the 30 degree triangle I now see that it is on the yz plane.
It isn't. But the angle is to the y-axis in the x-y plane. The formula ##x=r\cos\theta## only works for when ##\theta## is measured from the x axis.

But still don't see how that would help me. Even if I labeled the sides, for example I know that cos(30) would be on the y-axis now. But I can't see how that is in any way related to the X axis.
If ##\cos(30)## is on the y axis, then what is the trig function that would be on the x axis?
 

1. What is engineering statics and why is it important?

Engineering statics is a branch of mechanics that deals with the study of objects at rest or in uniform motion. It is important because it helps engineers understand the forces acting on a structure or object, and how those forces can be balanced to ensure stability and safety.

2. What are some common applications of engineering statics?

Engineering statics is used in a wide range of applications, including structural engineering, civil engineering, mechanical engineering, and aerospace engineering. It is used to analyze and design structures such as bridges, buildings, and machines, as well as to understand the behavior of materials and fluids.

3. What are some key principles of engineering statics?

Some key principles of engineering statics include the concept of equilibrium, which states that the sum of all forces acting on an object must equal zero for it to be at rest or in uniform motion. Other principles include the use of free body diagrams and the understanding of different types of forces, such as tension, compression, and shear.

4. How is engineering statics related to other branches of engineering?

Engineering statics is closely related to other branches of engineering, such as dynamics and mechanics of materials. It provides a foundation for understanding the behavior of structures and materials, which is essential for the design and analysis of various engineering systems.

5. What are some common challenges faced when solving engineering statics problems?

Some common challenges when solving engineering statics problems include identifying all the forces acting on a system, determining the correct coordinate system to use, and applying the correct equations and principles. It also requires a strong understanding of mathematical and physical concepts, as well as critical thinking skills.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
4
Views
670
  • Engineering and Comp Sci Homework Help
Replies
2
Views
636
  • Engineering and Comp Sci Homework Help
Replies
5
Views
772
  • Engineering and Comp Sci Homework Help
Replies
1
Views
809
  • Engineering and Comp Sci Homework Help
Replies
6
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
27
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
934
Replies
5
Views
792
  • Engineering and Comp Sci Homework Help
Replies
2
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
3
Views
2K
Back
Top