# Solving Tension in Two Wires Attached to 200 g Sphere

• juggalomike
In summary, the problem involves a 200 g sphere revolving in a horizontal circle at a constant speed of 6.80 m/s. The goal is to find the tensions in the two strings attached to the sphere. Using trigonometry and Newton's laws, it can be determined that the tensions in the strings will not be equal due to the weight of the sphere and the vertical component of the tension. Two equations can be used to solve for the tensions.

## Homework Statement

Two wires are tied to the 200 g sphere shown in figure. The sphere revolves in a horiIzontal circle at a constant speed of 6.80 m/s.

http://img684.imageshack.us/img684/6537/knightfigure0761.jpg [Broken]

Ca=m*v^2/r
f=ma

## The Attempt at a Solution

I was able to find the radius using triangles, and with that
I know the centrifical acceleration is .200*6.8^2/.866=10.679
But i have no idea where to go from here

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Use trig to find what tension provides a horizontal component of half the centripetal force m*v^2/r

Does that meen the tension of the 2 strings will be equal? that is what's throwing me off

Yes. The tensions must be equal because it is perfectly symmetrical.

Delphi51 said:
Yes. The tensions must be equal because it is perfectly symmetrical.
What about the weight of the sphere? Will it not contribute to the tension.

I may be wrong, but I don't see how it's possible for the tensions to be equal. In addition to the radial acceleration, there is also the vertical weight of the sphere. So, the upper string will be supporting the weight of the sphere, but the bottom string won't.

Imagine the system is just starting to spin. The sphere will hang, making the upper string tight, but the lower string will be slack. As the system spins, the ball will be forced outward. If the lower string weren't there, the top string might almost reach a horizontal angle if the rotation is fast enough. But the bottom string will kick in and keep the sphere from rising above a certain point. No matter how fast it spins, the top string will never be slack, and the way I figure it, the top string will always have greater tension than the bottom string.

Is that incorrect?

chudd88 said:
I may be wrong, but I don't see how it's possible for the tensions to be equal. Is that incorrect?
I think you may be correct, however, in order to find out, the OP will have to assume that they are not equal and sum forces in the x direction and y directions and use Newton's laws, and then be sure that ther lower rope does not stay slack. Juggalomike, what's the acceleration in the x direction, and in the y direction?

i believe acceleration in the x direction is 10.679 and the y direction is M*G

juggalomike said:
i believe acceleration in the x direction is 10.679
that's the net centripetal force, in Newtons
and the y direction is M*G
Is there any acceleration in the y direction? And you are confusing acceleration with force, which are related by Newton's 2nd law: F_net = ma.

Let T1 and T2 are the tensions in upper and lower strings. Let 2θ be the angle between two strings. Then
T1*cosθ + T2*cosθ = m*v^2/R...(1)
T1*sinθ = T2*sinθ + mg...(2)
Solve these two equations to find T1 and T2.

## What is the best method for solving tension in two wires attached to a 200 g sphere?

The best method for solving tension in two wires attached to a 200 g sphere is to use the equations of static equilibrium. This involves setting up a free body diagram of the system and applying Newton's laws of motion to find the tension in each wire.

## How does the weight of the sphere affect the tension in the wires?

The weight of the sphere will cause a downward force, which will increase the tension in the wires. This is because the wires must support the weight of the sphere, and the tension must be strong enough to balance out this force.

## What other factors can affect the tension in the wires?

Other factors that can affect the tension in the wires include the angle at which the wires are attached to the sphere, the material and thickness of the wires, and any external forces acting on the system.

## Is it possible for the tension in one wire to be zero?

Yes, it is possible for the tension in one wire to be zero if the wires are attached at a specific angle and the weight of the sphere is evenly distributed between the two wires. In this case, the tension in one wire would be completely balanced out by the tension in the other wire.

## Can the tension in the wires ever exceed the weight of the sphere?

No, the tension in the wires cannot exceed the weight of the sphere. This would violate the laws of static equilibrium, as the wires would be unable to support the weight of the sphere and the system would collapse.