Vectors Design Angle Problem

In summary, the problem asks to find the design angle θ for strut AB so that a 400-lb horizontal force has a component of 500lb directed from A towards C. The x-component and y-component equations are provided. The solution is θ = 53.5° and the force acting along member AB is 621lb. The position of the struts in the first diagram is confusing, but can be solved by manipulating the diagram. The given angle ϕ = 40° is also important for solving the problem accurately.
  • #1
Rybka
5
0

Homework Statement



"Determine the design angle θ (0° ≤ θ ≤ 90°) for strut AB so that the 400-lb horizontal force has a component of 500lb directed from A towards C. What is the component of force acting along member AB? Take ϕ = 40°"


Homework Equations



x-component: magnitude*cos(θ)
y-component: magnitude*sin(θ)

The Attempt at a Solution



I understand what is being asked, I'm just unsure as to how I would get that AC component with what is given.

-Rybka
 

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  • #2
Hi Rybka. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

Take ϕ = 40°
Please correct this.

You have 3 forces, they must form a closed triangle. Struts exert their force in line with their length, so this tells you the directions of their contributions.

Are you given the correct answer?
 
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  • #3
Good evening!

The solution is: θ = 53.5°, ForceAB = 621lb
 
  • #4
I figured it out.

The position of the struts in the first diagram is confusing, but the fact that we're solving for θ means their shape is variable.

Once I moved things around a little bit, it all became clear. :smile:
 

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  • #5
Rybka said:
The solution is: θ = 53.5°, ForceAB = 621lb
It's always useful to know the answer. I was hoping you'd edit your post so it tells us exactly what is 40°. That would be useful for someone following along.

Good to know you worked it out.
 
  • #6
The problem in the drawing does not give accurate dimensions
 

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1. What is a vector in design?

A vector in design refers to a type of graphic element that is created using mathematical equations, rather than pixels. This allows for the image to be scaled to any size without losing quality.

2. How do you determine the angle of a vector in design?

The angle of a vector in design can be determined by using trigonometric functions such as sine, cosine, and tangent. The angle is typically measured in degrees or radians and represents the direction in which the vector is pointing.

3. What is the significance of vectors in design?

Vectors in design are significant because they allow for the creation of high-quality graphics that can be scaled to any size without losing clarity. They are also commonly used in logo design, illustrations, and animations.

4. How do you solve vector design angle problems?

To solve vector design angle problems, you can use geometric principles and trigonometric functions to determine the magnitude and direction of the vector. It is important to carefully analyze the given information and use the appropriate formulas to find the solution.

5. Can vectors be used in any design software?

Yes, vectors can be used in many design software programs such as Adobe Illustrator, CorelDRAW, and Inkscape. These programs have tools and features specifically designed for creating and manipulating vector graphics.

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