# Solving Tension in 2 Wires Attached to 360 g Sphere

• mofazfaz
In summary, two wires are tied to a 360 g sphere that is revolving at a constant speed of 6.5 m/s in a horizontal circle. To find the tension in each wire, you must consider the three forces acting on the sphere: gravity, and two tensions. By breaking the tensions into x and y components and setting the sum of their vertical components equal to the mass times the rotational acceleration of the sphere, you can solve for T2. Then, by setting the sum of the horizontal components equal to 0 and plugging in the expression for T2, you can solve for T1. Finally, plugging the value of T1 back into the expression for T2 will give you the tension in both wires.
mofazfaz

## Homework Statement

Two wires are tied to the 360 g sphere shown in Figure CP7.61. The sphere revolves in a hori*zontal circle at a constant speed of 6.5 m/s. What is the tension in each of the wires?

## Homework Equations

I can't figure how to find the tension. With so little given i dnt even knw where to start

## The Attempt at a Solution

At least you've got Figure CP7.61. We don't even have that.

There are three forces acting on the sphere. mg (gravity) pointing down and two different tensions pointing along the wires. Break the tensions into x and y components. The sum of their vertical components should cancel mg and the sum of the horizontal components should equal mass times the rotational acceleration of the sphere.

I just figured this out minutes ago. The trick is to sum your x forces and set them equal to mv^2/r. solve that for T2. Then sum up your y forces and set them equal to 0. plug in the expression you found when you solved for T2 into the T2 of the new expression. Everything will then be in terms of T1 and you can then solve for it. Then take that answer and plug it back in for the expression where you solved for T2. You now have the tension in both of your wires.

thanks man i think i got this one down

## 1. What is the formula for calculating tension in 2 wires attached to a 360 g sphere?

The formula for calculating tension in 2 wires attached to a 360 g sphere is T = (m*g)/2, where T is the tension, m is the mass of the sphere, and g is the acceleration due to gravity. This formula assumes that the wires are at equal angles and equally spaced from the center of the sphere.

## 2. How do you determine the angle at which the wires should be attached to the sphere?

The two wires should be attached at equal angles from the center of the sphere. This can be achieved by using a protractor to measure the angle between the wires or by using a ruler to measure the distance between the wires and ensuring they are equally spaced from the center of the sphere.

## 3. What is the role of gravity in determining the tension in the wires?

Gravity plays a crucial role in determining the tension in the wires. The weight of the sphere, due to gravity, creates a downward force that must be balanced by the tension in the wires pulling upwards. This results in an equilibrium where the tension in the wires is equal to the weight of the sphere.

## 4. Can the tension in the wires be greater than the weight of the sphere?

No, the tension in the wires cannot be greater than the weight of the sphere. This is because the weight of the sphere, due to gravity, is the maximum downward force that must be balanced by the tension in the wires. If the tension in the wires were to exceed the weight of the sphere, the sphere would no longer be in equilibrium and would accelerate downwards.

## 5. How can the tension in the wires be adjusted to accommodate a different mass of the sphere?

To accommodate a different mass of the sphere, the tension in the wires can be adjusted by changing the angle at which the wires are attached. As the mass of the sphere increases, the angle between the wires should decrease, and vice versa. This ensures that the tension in the wires remains equal to the weight of the sphere, maintaining equilibrium.

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