Statics Question: Projection

In summary, the homework statement is:What's the projection of the resultant force onto an said axis?
  • #1
flgdx
8
0

Homework Statement


What's the projection of the resultant force onto an said axis?

Homework Equations


Sine Law, Cosine Law

The Attempt at a Solution


For problem 2/20, the projection onto the b axis was found by multiplying the resultant force by the cosine of 30 degrees. Why does this method not work for problem 2/4? Why do we need to add in the b-component of the resultant force? The questions are uploaded as pictures along with the solutions. Thank you!
Problem 2.023.PNG
problem 2.4.png
 
Physics news on Phys.org
  • #2
Hello fl, :welcome:

Nice pictures. I can imagine you don't want to copy all the typesetting and the pictures. But I can't really imagine what it is that you could want from a possible helper ! :smile:

[edit] Ahhh, the problem was in the solution... Goes to show how well posts are being read by helpful helpers who just got out of bed :sleep:. Fortunately haru has had his lunch already !
 
Last edited:
  • #3
flgdx said:
For problem 2/20, the projection onto the b axis was found
No, it is the projection onto the a axis. The references to Pb in the equations are wrong.
Also, in 2/20, R is not shown as being a resultant of other forces; it is the only force.
flgdx said:
Why do we need to add in the b-component of the resultant force?
It is not adding a b component of R. The calculation of the projection onto the b axis here does not use R at all. It goes back to the two constituent forces and adds their b components.
This should equal the b component of R. To check that, you would need to find the angle R makes to the b axis. It seems to be a bit less than 30 degrees.
 
  • #4
haruspex said:
No, it is the projection onto the a axis. The references to Pb in the equations are wrong.
Also, in 2/20, R is not shown as being a resultant of other forces; it is the only force.

It is not adding a b component of R. The calculation of the projection onto the b axis here does not use R at all. It goes back to the two constituent forces and adds their b components.
This should equal the b component of R. To check that, you would need to find the angle R makes to the b axis. It seems to be a bit less than 30 degrees.

Yes sorry! I meant to say the a axis on problem 2/20. Also for 2/4, I was talking about the b-component of the 100N Force. Sorry I made this post before going to bed hence the number of mistakes. Let me clear up my question since it sounds a bit confusing. So for problem 2/20, the projection was found using simple trigonometry, without the additional component while the case wasn't the same for 2/4. For 2/4, we needed to solve for the b-component of the 100N Force, 100*cos(50), and add that to F2 which is in line with the b axis. So what I don't get is why is the approach to each question different? Aren't they basically the same question with just different angles and values? Why can't we find the projection for 2/4 using the same method? Why doesn't 80*cos(20) give us the projection onto the b axis?
 
  • #5
flgdx said:
Why doesn't 80*cos(20) give us the projection onto the b axis?
The 80N is F2. That acts along the b axis, so its projection onto the b axis is still 80N.
80cos20 would give its projection onto the horizontal axis.
 
  • #6
flgdx said:
Aren't they basically the same question with just different angles and values?
It is the same approach.
In 2/20 you have one known force at a known angle to the desired axis. In 2/4 you have two forces at known angles to the desired axis. In each case you can describe the approach as ΣFicos(θi), where θi is the angle Fi makes to the projection axis.
 
  • #7
haruspex said:
The 80N is F2. That acts along the b axis, so its projection onto the b axis is still 80N.
80cos20 would give its projection onto the horizontal axis.
Oh sorry, I meant why does Rcos(20) not give us the projection for 2/4?
 
  • #8
flgdx said:
Oh sorry, I meant why does Rcos(20) not give us the projection for 2/4?
Because the angle between R and the b axis is not 20°. As I posted, it is a little under 30°.
 
  • #9
Oh okay. I see where my fault lies now. It's because I assumed that R is completely horizontal with an angle of 0 degrees in reference to the dotted lines in reference to the first picture in problem 2/4. Thank you so much!
 
  • #10
oh and one last question pls. Why does cosine law work for 2/4 when solving for R but when I try to use sine law I get a different value?
 

1. What is a projection in statics?

A projection in statics refers to the process of determining the components of a vector in a specific direction. It involves breaking down a vector into its horizontal and vertical components, which are referred to as projections.

2. Why is projection important in statics?

Projection is important in statics because it allows us to analyze the forces acting on an object or structure in a specific direction. By breaking down vectors into their components, we can better understand the forces at play and make accurate calculations for stability and equilibrium.

3. How do you calculate the projection of a vector?

The projection of a vector can be calculated using trigonometric functions. For example, the horizontal component (or projection) of a vector can be found by multiplying the magnitude of the vector by the cosine of the angle it makes with the horizontal axis. Similarly, the vertical component can be found by multiplying the magnitude by the sine of the angle.

4. Can projection affect the stability of a structure?

Yes, projection can affect the stability of a structure. If the projections of the forces acting on a structure are not balanced, it can lead to an unbalanced moment, which can cause the structure to topple or collapse. Therefore, it is important to consider the projections of forces when analyzing the stability of a structure.

5. Are there any real-world applications of projection in statics?

Yes, there are many real-world applications of projection in statics. For example, engineers use projection to analyze the forces acting on a bridge or building to ensure its stability. Projections are also used in physics and mechanics to understand the motion of objects in a specific direction. Additionally, projection is used in navigation to determine the position of a ship or plane in relation to a specific direction.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
6
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
5
Views
772
  • Engineering and Comp Sci Homework Help
Replies
4
Views
670
  • Engineering and Comp Sci Homework Help
Replies
1
Views
934
  • Engineering and Comp Sci Homework Help
Replies
4
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
8
Views
5K
Replies
1
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
809
  • Engineering and Comp Sci Homework Help
Replies
8
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
14
Views
2K
Back
Top