Vector problem: flagpole with wires at different angle

In summary, the two supporting wires for a flagpole must have equal and opposite horizontal tension components to keep the pole in a vertical position. The vertical components may be different. Using basic trigonometry, the ratio of tensions in the shorter wire to the longer wire can be calculated. By resolving the vector components, the ratio is found to be approximately 1:1.2.
  • #1
prime-factor
77
0

Homework Statement



Two supporting wires keep a flagpole in its
vertical position. The horizontal components of the tensions in
the supporting wires must be equal and opposite,
otherwise the pole will move laterally. The
vertical components may be different.
The longer wire forms a 30 degree angle with the ground, and
the shorter wire forms a 45 degree angle with the ground.
a Calculate the ratio of the tension in the
shorter wire to the tension in the longer wire.
b If the tension in the shorter wire is 600 N, calculate the magnitude of the tension
in the longer wire.

(Refer to picture) in the word document.

Homework Equations



basic trigonometry:

sine, cosine, tan,

possibly cosine/sine rules

The Attempt at a Solution



I am not sure, what to do with this problem.
I have attempted it, but haven't a clue
how to do it correctly. Please help.
I've just started this topic, and haven't been
taught this yet.
 

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  • #2


Do you know how to resolve a vector into two component vectors? For example, if you are driving North East at speed V you have a North vector and an equal East vector. These two vectors would each be of size V*cos(45°). If you now turn a bit to the left so you are driving at 30° East of North then the North vector will now be V*cos(30°) and the East vector will be V*cos(60°). Does this help?
 
  • #3


I am having trouble understanding.

So with my question, V would be the magnitude of the vector, and I would have:

r.cos(30) , and r.cos(45) ?

I don't really get it. Because I don't have a magnitude.
 
  • #4


You need tensions; just call them T1 and T2. They won't be equal. The horizontal components are equal and the vertical ones are different.
 
  • #5


Ahhh :)

Okay.

So let horizontal components equal x, and vertical components equal T1, T2

=>cos (theta1) = x/T1
T1 = x / cos (theta1)

=>cos(theta2) = x/T2
T2 = x / cos (theta1)

Then let's say I choose an arbitrary value...2

2/ cos(30) = 2.30

2/ cos(45) = 2.82

=> 2.82 : 2.3 = 1: 1.2(approx) , so that's my ratio?

Or I could have just done cos(30) : cos(45)
 
  • #6


You answer is incorrect I fear.
That wasn't quite what I had in mind.

Longer cable has tension T1.
The horizontal component will then be T1*cos(60°)
The vertical component will then be T1*cos(30°)
Repeat this exercise for the shorter rope with tension T2 and equate the horizontal components.
From here you can get the ratio of tensions.
 
  • #7


I did that and got:

cos(30)(T1) = cos(45)(T2)

and get the same: 1.224:1

which is the same as what I get doing it the way you feared was incorrect.

It ends up being the same, because I was equating the horizontal components
 
  • #8


My horizontal component is T1*cos(60°); yours is cos(30)(T1). Not the same!
 
  • #9


prime-factor

I broke the golden rule and didn't draw a diagram.
Your solution was correct.
 
  • #10


Hey. No problems :). I appreciate your help nonetheless. I needed to resolve to resolve the components and you reminded me too, so Thankyou.
 

Related to Vector problem: flagpole with wires at different angle

1. What is a vector problem?

A vector problem is a mathematical problem that involves the use of vectors, which are quantities that have both magnitude (size) and direction.

2. How do you solve a vector problem?

To solve a vector problem, you must first determine the magnitude and direction of each vector involved. Then, use trigonometry or vector addition/subtraction to find the resulting vector. Finally, use the resulting vector to solve the problem.

3. What is the flagpole with wires at different angle problem?

The flagpole with wires at different angle problem involves a flagpole supported by two wires at different angles, and finding the tensions in each wire and the angle each wire makes with the flagpole.

4. How do you approach the flagpole with wires at different angle problem?

To approach the flagpole with wires at different angle problem, begin by drawing a diagram and labeling the relevant information, such as the lengths of the wires and the angle they make with the flagpole. Then, use trigonometry or vector addition/subtraction to find the tensions in the wires and the angle each wire makes with the flagpole.

5. What are some real-life applications of the flagpole with wires at different angle problem?

The flagpole with wires at different angle problem has real-life applications in engineering, such as determining the forces on a bridge or other structure supported by cables at different angles. It can also be used in physics to analyze the forces acting on an object suspended by multiple ropes or cables at different angles.

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