Tension Vector Explanation: Solving Homework Questions with Pictures

[Gamegoofs2]

Homework Statement

My books doesn't seem to give a good explanation of tension vectors. I was hoping someone on here could explain them better.

I put the picture from the book up.

The two questions with pictures are the one's I'm having trouble with.
In case you can't read them:
The one with the red box says,
A 112.1-kg sign is hung from two strings as shown below. What is the tension in each string?
[tex]\theta[/tex] = 35.0 degrees on the string going to the right and [tex]\theta[/tex] = 50.0 degrees

The second question with the fish says,
A fisherman is deisplaying his prize catch by hanging it as illustrated below. The horizontal string in the hanging apparatus is weak and will only be able to stand a tension of 13.0 pounds before it breaks. What is the maximum weight for a fish to hang on this system?

T= 13.0 lbs max [tex]\theta[/tex] = 40.0 degrees

I get think I get the concept it's the math and finding what information I already know that's giving me the trouble.

Thanks for any help.

 

[tiny-tim]

Hi Gamegoofs2!

(have a theta: θ )

I get think I get the concept it's the math and finding what information I already know that's giving me the trouble.

The great thing about tension is that you always know the direction, it has to be along the string.

The general trick is to call the tensions T₁ and T₂, find two equations, and solve.

The two equations are usually by taking components of force in the x and y directions (or any two other convenient directions). Sometimes you take moments about a convenient point, instead of one of the directions.

If you're still worried, show us how you'd deal with one or both of those problems.

 

[kerimek]

I can understand your frustration with understanding tension vectors. Tension vectors are a crucial concept in understanding forces and their effects on objects. In simple terms, a tension vector is a force that is transmitted through a string, rope, or cable when it is pulled from both ends. It is a reaction force that is exerted by an object on another object that is pulling on it.

In the first question, the tension vector is the force exerted by the strings on the sign. To solve this problem, you need to break down the forces acting on the sign into components along the strings. This is where the angles (\theta) come into play. Using trigonometry, you can calculate the components of the force along each string and then add them together to get the total tension in each string. This will give you the answer to the question.

In the second question, the tension vector is the force exerted by the horizontal string on the fish. In this case, you need to find the maximum weight that the string can support before it breaks. This can be done by setting up an equation where the weight of the fish is equal to the tension in the string, and solving for the maximum weight.

I understand that the math involved in solving these problems can be challenging, but it is important to remember the concept of tension vectors and how they relate to forces and objects. With practice and a solid understanding of trigonometry, you will be able to solve these types of problems with ease. I hope this explanation has helped you in understanding tension vectors better. Keep up the good work!