# Calculating Tension of a bob moving in horizontal circles

• junkie_ball
In summary, the conversation is about a problem involving circular motion and finding the tension in a string attached to a bob. The individual is struggling with the concept and has provided their attempted solution, which includes using the incorrect equation of Tanθ instead of Sinθ. They are reassured that they are on the right track and express their frustration with understanding the subject.
junkie_ball
Could someone please look at the problem below and see if i am on the right lines of solving it? I am finding the whole subject of circular motion hard to get my head around and therefore not 100% confident in my workings. I have also attached my free body diagram.

## Homework Statement

Calculate the tension in a 3m string attached to a 3kg bob that is moving in horizontal circles of 0.6m radius

## Homework Equations

Tanθ = Opposite/Hypotenuse

TCosθ = mg

## The Attempt at a Solution

θ = Tan-1 0.6/3
θ = 10.32°

TCosθ = mg
T = mg/Cosθ
T = (3Kg x 9.81) / Cos 10.32
T = 29.91 N

#### Attachments

• Free Body Diagram.doc
27 KB · Views: 294
junkie_ball said:
θ = Tan-1 0.6/3
The radius over the hypotenuse would equal sinθ, not tanθ.

Other than that, you're doing fine.

Doc Al said:
The radius over the hypotenuse would equal sinθ, not tanθ.

Other than that, you're doing fine.

Thanks for that i have just noticed i used TAN not SIN for my workings myself which obviously changes my final answer slightly. Thanks for the reassurance I'm on the right track. I have spent many long hours trying to get my head around this whole subject.

## 1. How do I calculate the tension in a bob moving in horizontal circles?

To calculate the tension in a bob moving in horizontal circles, you will need to know the mass of the bob, the radius of the circle, and the speed of the bob. The formula for tension in this scenario is T = mv^2/r, where T is the tension, m is the mass, v is the speed, and r is the radius.

## 2. What is the significance of tension in a bob moving in horizontal circles?

Tension is the force that is pulling on the bob in order to keep it moving in a circular path. Without tension, the bob would not be able to maintain its circular motion and would fly off in a straight line.

## 3. How does the mass of the bob affect the tension in a horizontal circle?

The mass of the bob has a direct effect on the tension in a horizontal circle. The heavier the bob, the greater the tension needed to keep it moving in a circular path. This is because the greater the mass, the greater the force needed to accelerate it.

## 4. Can the tension in a bob moving in horizontal circles ever be zero?

No, the tension in a bob moving in horizontal circles can never be zero. This is because there will always be some force acting on the bob, whether it is from gravity, friction, or another source. Tension is necessary to counteract these forces and maintain the circular motion.

## 5. How does the radius of the circle affect the tension in a bob moving in horizontal circles?

The radius of the circle has an inverse relationship with the tension in a bob moving in horizontal circles. This means that as the radius increases, the tension decreases, and vice versa. This is because a larger radius means the bob has to travel a greater distance in the same amount of time, requiring less tension to maintain its speed.

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