# Conservation of Energy & circular motion

• nrahim
In summary, the problem attached is a classical one that the poster is struggling with. They have posted their attempted solution and are asking for guidance. The problem involves finding the total energy in a system and the conditions imposed. A solution is provided by another user.

#### nrahim

The problem is stated on the sheet i have attached along with my attempt to the possible solution. This is a proof and i am very bad at working with proofs. This seems to be a classical problem so I'm sure some of you guys might have seen it, please guide me!

http://img22.imageshack.us/img22/1405/53811275.th.jpg [Broken]

I have posted the problem with what i have tried... as you can see i was stuck, please guide me if my logic or math is wrong

Last edited by a moderator:
Welcome to PF.

Consider the conditions imposed.

Total energy in the system is m*g*L

To complete a circle then with Vt the velocity at the top of the circle about x

m*Vt2/(L-x) = m*g

m*Vt2 = m*g*(L-x)

So ... at the top of that loop

1/2*m*Vt2 + m*g*(2*(L-x)) = m*g*L

Substituting ...

1/2*m*g*(L-x) + m*g*(2*(L-x)) = m*g*L

thanks a lot my friend.. you saved me a lot of hassle:D

## 1. What is the conservation of energy in circular motion?

The conservation of energy in circular motion refers to the principle that the total energy of a system remains constant as long as there are no external forces acting on it. This means that the kinetic energy and potential energy of the system will remain constant as it moves in a circular path.

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

Conservation of energy applies to objects in circular motion because the energy of the system is constantly being exchanged between kinetic energy and potential energy, but the total energy remains the same. This is because the work done by the centripetal force is equal to the change in kinetic energy, resulting in a constant total energy for the system.

## 3. What is the role of centripetal force in conservation of energy?

The centripetal force is responsible for maintaining the circular motion of an object and constantly changing its direction. In terms of conservation of energy, the centripetal force is responsible for converting the potential energy of the object into kinetic energy, and vice versa, resulting in a constant total energy for the system.

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

The speed of an object in circular motion does not affect conservation of energy as long as there are no external forces acting on the system. This is because the kinetic energy of the object will increase as its speed increases, but the potential energy will decrease by the same amount, resulting in a constant total energy for the system.

## 5. What happens to the conservation of energy if there is friction present in circular motion?

If there is friction present in circular motion, the energy of the system will decrease over time due to the work done by the frictional force. This means that the total energy of the system is not conserved and will continuously decrease until the object comes to a stop.