# Centripetal Force String Tension

• scrambledeggs
In summary, the two masses M of equal amount are tied to strings of different lengths, L and 2L respectively. As both masses are swung in unison, the string with length 2L will break first due to the larger centripetal force/tension, which is affected by the longer radius. The formula used to determine centripetal force is Fc = mω^2r, where ω represents the angular speed in radians per second. Using this formula, we can compare the tangential speeds of the two masses and determine that the longer string will experience a greater force.
scrambledeggs

## Homework Statement

Two masses M of the same amount are tied to two stings of length L and 2L. If both masses are swung in unison faster and faster, which string will break first?

## Homework Equations

The formula I've been using is Tension = mv^2/r.

## The Attempt at a Solution

My understanding is that when the string breaks, tension will be 0. If I plug that into the formula the radius/length of the string will not matter. What am I doing wrong here?

Welcome to PF!

But you are looking for the tension in the string just before it breaks.

scrambledeggs said:

## Homework Statement

Two masses M of the same amount are tied to two stings of length L and 2L. If both masses are swung in unison faster and faster, which string will break first?

## Homework Equations

The formula I've been using is Tension = mv^2/r.

## The Attempt at a Solution

My understanding is that when the string breaks, tension will be 0. If I plug that into the formula the radius/length of the string will not matter. What am I doing wrong here?
Since the two masses have the same rotational speed, to compare the forces you may wish to use: Fc = mω^2r

AM

scrambledeggs said:

## Homework Statement

Two masses M of the same amount are tied to two stings of length L and 2L. If both masses are swung in unison faster and faster, which string will break first?

## Homework Equations

The formula I've been using is Tension = mv^2/r.

## The Attempt at a Solution

My understanding is that when the string breaks, tension will be 0. If I plug that into the formula the radius/length of the string will not matter. What am I doing wrong here?

So what variable in this equation changes due to the string length change and how does it affect your force?

Andrew Mason said:
Since the two masses have the same rotational speed, to compare the forces you may wish to use: Fc = mω^2r

AM

What is the value ω stand for? I don't think I'm familiar with that equation.

kinematics said:
So what variable in this equation changes due to the string length change and how does it affect your force?

Because the radius is the only thing that changes in the equation, this is what I'm thinking:

Fc = mv2/r

and

Fc = mv2/2r
2Fc = mv2/r

Therefore the longer the string the larger the centripetal force/tension. Am I correct or completely off?

scrambledeggs said:
What is the value ω stand for? I don't think I'm familiar with that equation.
ω is the angular speed in radians per second. There are 2π radians in a circle so if the number of rotations per second is f the angular speed is 2πf. Since T = 1/f you can express ω = 2π/T. Tangential speed v = ωr so mv2/r = mω2r = m4π2r/T2

Can you see how to use this to compare the centripetal force on each of these two rotating masses?
Because the radius is the only thing that changes in the equation, this is what I'm thinking:

Fc = mv2/r

and

Fc = mv2/2r
2Fc = mv2/r

Therefore the longer the string the larger the centripetal force/tension. Am I correct or completely off?

You have provided an excellent example of why getting the right answer is not very important when you are a student.

Are the tangential speeds the same for each rotating mass? Can you compare the tangential speeds? (hint: Can you see why using ω makes this a lot easier?)

AM

## 1. What is centripetal force?

Centripetal force is a force that acts towards the center of a circular motion. It keeps an object moving in a circular path by constantly changing the direction of its velocity.

## 2. What is the role of string tension in centripetal force?

String tension is one of the components of centripetal force. It is the force exerted by a string or rope that is attached to an object moving in a circular path. It is directed towards the center of the circle and helps to keep the object moving in its circular path.

## 3. How is string tension related to centripetal force?

String tension is directly proportional to centripetal force. This means that as the string tension increases, the centripetal force also increases. If the string tension is too low, the object will not be able to maintain its circular motion and will fly off in a straight line.

## 4. How can the string tension be calculated?

The string tension can be calculated using the formula T = mv²/r, where T is the string tension, m is the mass of the object, v is its velocity, and r is the radius of the circular path. This formula is derived from Newton's Second Law of Motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.

## 5. What factors can affect the string tension in centripetal force?

The string tension in centripetal force can be affected by the mass of the object, the velocity of the object, and the radius of the circular path. Other factors that can influence the string tension include the strength and elasticity of the string or rope, and any external forces acting on the object such as friction or air resistance.

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