# Vertical Circle (Circular Motion)

• Mohammed S
In summary, the speed of the ball does not change, but the tension in the string is always taut. The mass of the ball is 1.02 kg.
Mohammed S

## Homework Statement

You swing a 1.60m long string with a metal ball attached to its end in a vertical circle, such that the speed of the ball does not change but the rope is always taut. The tension in the string when the ball is at the bottom of the circle is 60.0N more than the tension when the ball is at the top. Find the mass of the ball.

## Homework Equations

Fc=mv^2/r
ac=v^2/r
Equations that have to do with vertical circle

## The Attempt at a Solution

I do not understand vertical circles but I tried doing the Tbottom=Ttop+6mg
I am unsure of the answer but I did 60+Ttop=Ttop+6mg
60=6mg
10=mg
m=1.02 kg
but I think its wrong

Mohammed S said:
Tbottom=Ttop+6mg
Can you explain how you arrived at this equation. In particular, what does the 6mg denote?

Draw a diagram showing the forces on the ball at the top and at the bottom of the circle.

CWatters
Mohammed S said:
You swing a 1.60m long string with a metal ball attached to its end in a vertical circle, such that the speed of the ball does not change but the rope is always taut.
Question: How can the speed not change? What happened to conservation of energy? Is this the exact wording of the original problem?

Are there external forces acting on the system? If they are, there is no conservation of energy.

gneill said:
Question: How can the speed not change? What happened to conservation of energy? Is this the exact wording of the original problem?

There would have to be some tangential forces being applied and modulated just so. However there is no law against it, and, assuming these extra forces are truly purely tangential, they don’t prevent you from answering the question. So it’s an unusual construct, but it makes answering the question very easy.

## 1. What is a vertical circle in circular motion?

A vertical circle in circular motion is a type of motion where an object moves in a circular path that is perpendicular to the ground. This means that the object is constantly changing direction as it moves in a vertical circle.

## 2. What are the forces acting on an object in a vertical circle?

The forces acting on an object in a vertical circle are the centripetal force and the force of gravity. The centripetal force is directed towards the center of the circle and keeps the object moving in a circular path, while the force of gravity pulls the object towards the center of the Earth.

## 3. How is the speed of an object in a vertical circle related to its radius?

The speed of an object in a vertical circle is directly proportional to its radius. This means that if the radius of the circle increases, the speed of the object also increases, and vice versa. This is because a larger radius means a larger distance to cover in the same amount of time, so the object must move faster to maintain the circular path.

## 4. What is the minimum speed an object needs to complete a vertical circle?

The minimum speed an object needs to complete a vertical circle is equal to the square root of the product of the acceleration due to gravity (g) and the radius of the circle (r). This can be calculated using the formula v = √(gr).

## 5. How does the angle of the circle affect the speed of an object in a vertical circle?

The angle of the circle has no effect on the speed of an object in a vertical circle. The speed is only dependent on the radius of the circle, the acceleration due to gravity, and the mass of the object. However, the angle of the circle can affect the tension in the string or other force keeping the object in motion, as well as the vertical and horizontal components of the velocity.

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