# Finding Tension with angles

• Maty
In summary, a ball of weight 5 Newtons is suspended by two strings. The tension in each direction is determined by the formulas T1 - T2 = 0 and T1 + T2 = mg.

## Homework Statement

A ball of weight 5 Newtons is suspended by two strings as shown above. Determine the magnitude of each of the forces, T1 and T2. (Note: sin 37° = 0.6; cos37° = 0.8)

T = mg

## The Attempt at a Solution

I couldn't go anywhere because I need a formula that uses sin or cos, and I can't remember any right now. Can anyone supply me with the equations and a start? And I'll attempt at the solution with that. Please.

Last edited:
Would this work? T x cos θ1 + T x cos θ2 = mg, where θ1 and θ2 are the angles the two sides.

Maty said:

## Homework Statement

A ball of weight 5 Newtons is suspended by two strings as shown above. Determine the magnitude of each of the forces, T1 and T2. (Note: sin 37° = 0.6; cos37° = 0.8)

http://bb.mivu.org/courses/1/M-APhB1-S112-01/assessment/685f98ac2d604bddbf30b5bb28f9f01b/Q5.jpg

T = mg

## The Attempt at a Solution

I couldn't go anywhere because I need a formula that uses sin or cos, and I can't remember any right now. Can anyone supply me with the equations and a start? And I'll attempt at the solution with that. Please.

Maty said:
Would this work? T x cos θ1 + T x cos θ2 = mg, where θ1 and θ2 are the angles the two sides.

Oops, there I edited the first post and it should be there now.

Also, after I posted that second post, I realized that nowhere in there it had any variables for the length of the string, which likely play a part in here. So I think I'm not supposed to use that equation.

Maty said:
Oops, there I edited the first post and it should be there now.

Also, after I posted that second post, I realized that nowhere in there it had any variables for the length of the string, which likely play a part in here. So I think I'm not supposed to use that equation.

On these problems, always start by drawing a Free Body Diagram (FBD) of the object (the mass in this case). Show the forces on the object, including the force down due to gravity. Then write the two equations to sum all of the forces in the x and y directions to zero (since the object is not moving). then solve away!

I have one drawn right in front of me right now, but I just don't know what formula to use, or how to find ALL of the forces in both axis.

Maty said:
I have one drawn right in front of me right now, but I just don't know what formula to use, or how to find ALL of the forces in both axis.

How many forces act in the horizontal direction? What are they? Label forces in the +x direction positive, and forces in the -x direction negative.

How many forces act in the vertical direction? What are they? Forces up are positive, and forces down are negative.

Since the object is not accelerating, you know that the sum of the forces in the x direction needs to equal zero. Same thing for the y direction. Those are the two equations you write and solve for the tension forces.

In the x direction T1 - T2 = 0?

And in the y direction. T1 + T2 = mg?

So i'll have to use Trig to find the numbers for each axis, but the only number I have is length, how would that help me?

Maty said:
In the x direction T1 - T2 = 0?

And in the y direction. T1 + T2 = mg?

So i'll have to use Trig to find the numbers for each axis, but the only number I have is length, how would that help me?

That is much closer. Good.

But you need to use the "components" of the tensions in the x and y directions, and that is where the sin and cos functions come in. Those are used to resolve vectors (like the tension forces applied at angles) into their x and y components.

See the "Intro to Vector Mathematics" link at the bottom of this FBD tutorial, for example:

.

I am still back to the beginning. I know 'what' to do, I just don't know 'how' to do it. What numbers do I use, what equation?

Your first step is to break up the tensions into vertical and horizontal parts, then since the ball isn't moving the vertical parts add to balance the force of gravity and the two horizontal parts must cancel with each other :)

## 1. What is tension?

Tension is a force that occurs when an object is being stretched or pulled by another object. It is a type of force that is present in various situations, such as when a rope is pulled or when an object is suspended.

## 2. How do you calculate tension with angles?

To calculate tension with angles, you need to use trigonometric functions such as sine, cosine, and tangent. First, draw a free-body diagram of the object and identify all the forces acting on it. Then, use the angle and the trigonometric function to calculate the component of the force in the direction of the angle. Finally, use the component of the force and the trigonometric function to calculate the tension.

## 3. What are the key factors that affect tension with angles?

The key factors that affect tension with angles include the magnitude of the force applied, the angle at which the force is applied, and the weight of the object. Other factors such as friction and air resistance may also affect the tension.

## 4. How can finding tension with angles be useful in real-life situations?

Finding tension with angles can be useful in various real-life situations, such as engineering and construction. It can be used to determine the strength of materials and structures, as well as to ensure the safety and stability of buildings and bridges. It can also be used in sports, such as rock climbing, to determine the amount of tension needed in ropes.

## 5. What are some common mistakes when calculating tension with angles?

Some common mistakes when calculating tension with angles include not considering all the forces acting on the object, not using the correct trigonometric function, and not converting units appropriately. It is important to carefully draw the free-body diagram and double-check all calculations to avoid these mistakes.