# Conservation of Energy + circular motion

• anotherghost
In summary, the conversation discusses the concept of using conservation of energy to calculate the minimum initial velocity for a mass hanging from a string to make it around a circle. While the equation can determine the minimum velocity for one full rotation, it does not account for energy loss from friction and air resistance, making it impossible for the mass to continue rotating indefinitely.
anotherghost
Quick question:

I'm having trouble understanding a concept: say you've got a mass hanging from a peg by a string. Using conservation of energy, you can figure out what the minimum velocity is that the mass has to have initially so that it goes around the circle: at the top, mv^2/r = mg, so it just makes it around once. However, I'm having trouble with this - how do you calculate the minimum initial velocity so that it goes around the circle twice?

Confusion.

Say it goes around once. If mechanical energy is truly conserved, then it should go around the circle twice, thrice, four times and so on. In other words, if it has enough kinetic energy at the bottom to make it through the top and energy is not lost anywhere, then it will keep on going forever. However, in real life, energy is lost to friction and air resistance so this does not happen

Hi there,

It's great that you are exploring the concept of conservation of energy and circular motion. To answer your question, the minimum initial velocity required for the mass to go around the circle twice can be calculated using the same principles of conservation of energy.

At the top of the circle, the centripetal force required for the mass to move in a circular path is equal to its weight, which is given by Fc = mv^2/r = mg. To go around the circle twice, the mass needs to cover twice the distance, which means it will need twice the amount of energy. Therefore, the minimum initial velocity can be calculated by equating the initial kinetic energy (1/2mv^2) to twice the potential energy (mgh) at the top of the circle. This will give you the minimum initial velocity required for the mass to go around the circle twice.

I hope this helps clarify your confusion. Keep exploring and asking questions, as that is the essence of science. Best of luck!

## 1. What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, it can only be transformed from one form to another. This means that the total amount of energy in a closed system remains constant.

## 2. How does conservation of energy apply to circular motion?

In circular motion, an object is constantly changing direction and therefore constantly accelerating. According to the law of conservation of energy, this change in direction requires a change in velocity, and therefore a change in kinetic energy. However, the total energy of the object (kinetic energy + potential energy) remains constant as the object moves in a circular path.

## 3. What is the relationship between kinetic and potential energy in circular motion?

In circular motion, kinetic energy and potential energy are constantly being exchanged as the object moves. When the object is at the top of its circular path, it has maximum potential energy and minimum kinetic energy. When it reaches the bottom of its path, it has maximum kinetic energy and minimum potential energy.

## 4. How does conservation of energy affect the speed of an object in circular motion?

As the object moves in a circular path, its speed changes due to the exchange of kinetic and potential energy. However, the total energy of the object remains constant, so the speed will always remain within a certain range. The object's speed will increase as it moves towards the bottom of its path, and decrease as it moves towards the top.

## 5. Can the conservation of energy be violated in circular motion?

No, the law of conservation of energy is a fundamental principle in physics and cannot be violated. However, in real-world scenarios, there may be small losses of energy due to factors such as friction and air resistance. In these cases, the total energy of the system will decrease slightly, but the law of conservation of energy still holds true.

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