Solve Crane Tension: 2 Cable Equations & Triangle Angles

In summary, the conversation discusses using a crane to lift a 5kN concrete pipe and solving algebraic equations for the force components. The equations for the x and y directions are provided and it is mentioned that the problem also involves finding the length of a hypotenuse and determining angles using trigonometric functions.
  • #1
juggalomike
51
0

Homework Statement


A crane is used to lift a concrete pipe weighing 5kN into place.


Homework Equations




The Attempt at a Solution


The picture is in my book, but i am certain my problem is in my algebra(i have the layout correct)

T_ac*cos(20)=T_ab*sin(3.58) X direction
5+T_ac*sin(20)=T_ab*cos(3.58) Y direction

I am for some reason drawing a blank when it comes to how i can work this out, i tried solving for T_ac in equation 1 then plugging that into equation 2 but then i am running into an algebraic nightmare. One other problem aswell(its part of the question)

I am given a triangle where Hypotenuse=4m and opposite=.25m, so using A^2+b^2=c^2 i got 3.99 for b. Then i used theta=arccos(adjacent/hypotenuse)=4.05, but for theta=arcsin(opposite/hypotenuse)=3.58. What am i doing wrong?
 
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  • #2
juggalomike said:

The Attempt at a Solution


The picture is in my book, but i am certain my problem is in my algebra(i have the layout correct)

T_ac*cos(20)=T_ab*sin(3.58) X direction
5+T_ac*sin(20)=T_ab*cos(3.58) Y direction

Since you didn't post a picture of the FBD, I will have to assume it is how I am expecting it to look.

The equation for the x-direction should be

Taccos(20)=Tabcos(3.58)

and for y-direction

5=Tacsin(20)+Tabcos(3.58)

in which you'd just solve simultaneously.
 

What is the purpose of solving crane tension using 2 cable equations and triangle angles?

The purpose of solving crane tension using 2 cable equations and triangle angles is to determine the amount of force or tension required to keep the crane stable and balanced. This is important for ensuring the safety and efficiency of the crane's operation.

How do 2 cable equations and triangle angles relate to solving crane tension?

2 cable equations and triangle angles are mathematical tools used to analyze the forces acting on the crane. The equations take into account the tension in the cables and the angles formed by the cables, which are crucial factors in determining the overall tension on the crane.

What information is needed to solve crane tension using 2 cable equations and triangle angles?

To solve crane tension using 2 cable equations and triangle angles, you will need the length and angle of each cable, as well as the weight of the load being lifted. This information can be obtained from the crane's specifications or through measurements and calculations.

What are the potential sources of error when solving crane tension using 2 cable equations and triangle angles?

Some potential sources of error when solving crane tension using 2 cable equations and triangle angles include inaccurate measurements of cable lengths and angles, incorrect load weight, and neglecting external factors such as wind or movement of the crane itself. It is important to carefully gather and verify all necessary information to minimize error.

Are there any limitations to using 2 cable equations and triangle angles to solve crane tension?

Yes, there are limitations to using 2 cable equations and triangle angles to solve crane tension. These equations assume ideal conditions, such as perfectly straight and rigid cables, which may not always be the case in real-world scenarios. Other factors, such as the elasticity of the cables, may also need to be considered for more accurate results.

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