Understanding x(θ) and h(θ) in a Triangle Support Beam Problem

In summary, the length of one rod is used to define the reference points for h(θ) and x(θ) in relation to the triangular support beam. These values are calculated using basic trigonometry and the length of the rod.
  • #1
pyroknife
613
3

Homework Statement


I have attached the problem. I am confused about how they got x(θ) and h(θ). From the diagram it looks like they made it with reference to the triangular support beam. Why?


Homework Equations





The Attempt at a Solution

 

Attachments

  • Untitled.png
    Untitled.png
    29.2 KB · Views: 437
Physics news on Phys.org
  • #2
This is late and my be of no use. You wrote,

From the diagram it looks like they made it with reference to the triangular support beam. Why?

It is a reference point that doesn't move? h(θ) is pretty straight forward, and if you set θ = 0 , x(0) = 3b/2 makes sense.
 
  • #3
pyroknife said:

Homework Statement


I have attached the problem. I am confused about how they got x(θ) and h(θ). From the diagram it looks like they made it with reference to the triangular support beam. Why?

The length of one rod is b. b/2 at angle θ coincides with the vertical position that you want to use to define h(θ). From basic trig, h/(b/2) = sin(θ). Thus h(θ) = b/2*sin(θ).


Similarly x coincides with the horizontal position that the 1 + 1/2 rods make at angle θ. So then x = b*cos(θ) + 1/2*b*cos(θ) = 3b/2*cos(θ).
 

1. What is x(θ) and h(θ) in a Triangle Support Beam Problem?

X(θ) and h(θ) are the variables used to represent the length and height of the triangle support beam in a problem. They are important in calculating the forces and stresses acting on the beam.

2. How do I calculate x(θ) and h(θ) in a Triangle Support Beam Problem?

X(θ) and h(θ) can be calculated using trigonometric functions such as sine, cosine, and tangent. These functions can be applied to the known angles and lengths of the triangle to determine the values of x(θ) and h(θ).

3. Why is understanding x(θ) and h(θ) important in a Triangle Support Beam Problem?

Understanding x(θ) and h(θ) is important because they are essential in determining the stability and strength of the support beam. They help in analyzing the forces and stresses acting on the beam and ensuring that it can withstand the weight and load placed on it.

4. What are some common mistakes when dealing with x(θ) and h(θ) in a Triangle Support Beam Problem?

Some common mistakes include using the wrong trigonometric function, miscalculating the angles or lengths of the triangle, and not considering all the forces acting on the beam. It is important to double-check all calculations and consider all variables in order to avoid these mistakes.

5. Are there any tips for solving problems involving x(θ) and h(θ) in a Triangle Support Beam Problem?

One tip is to draw a clear and accurate diagram of the triangle to visualize the problem. It is also helpful to label all given information and use the appropriate trigonometric function for each calculation. Additionally, it is important to understand the concepts and formulas related to triangles and forces in order to solve these types of problems effectively.

Similar threads

  • Introductory Physics Homework Help
Replies
10
Views
4K
  • Introductory Physics Homework Help
Replies
15
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
117
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
3K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
11
Views
2K
  • Introductory Physics Homework Help
Replies
10
Views
4K
Back
Top