# Conservation of energy and vertical circular motion

• tubworld
In summary: B) to make it around the loop if there was no friction. then realize that the block uses up additional energy doing work against friction.In summary, the block needs sufficient energy to overcome resistance to continue the loop at its highest point. It uses up additional energy doing work against friction.
tubworld
Thanx! Appreciate that!

Last edited:
Realize that the block must have a certain amount of kinetic energy (at point B) to make it around the loop if there was no friction. (Hint: How fast must it be going at the very top to stay in contact with the track?) Then realize that the block uses up additional energy doing work against friction. (How much? Consider the definition of work.)

I agree that it's to have sufficient enrgy to overcome resistance to continue the loop at its highest pt, but what has energy got to do with force? I only remember that force * displacement of force = energy. But in this case. the frictional force doesn't travel on a st line, making it hard to calculate the ans. I can't possibly take the diameter as the displacement right? Neither can I take the perimeter of half a circle as the displacement? I am seriously lost here. The second equation seems really hard to form, especially involving the circular motion.

tubworld said:
I agree that it's to have sufficient enrgy to overcome resistance to continue the loop at its highest pt, but what has energy got to do with force? I only remember that force * displacement of force = energy.
You just answered your own question. Work = Force x Displacement (parallel to the force).

But in this case. the frictional force doesn't travel on a st line, making it hard to calculate the ans. I can't possibly take the diameter as the displacement right? Neither can I take the perimeter of half a circle as the displacement?
The problem tells you the average frictional force is F. So all you need is the distance the block travels in getting up to the top. (Yes... it's half the circumference. It's that simple.)

Ohh... ... I see... but now that i have this value, where does the centripetal acceleration come to place? i don't seem to have any use for it in this question...

You'll need to use centripetal acceleration to figure out the minimum speed the block must have to maintain contact with the track as it reaches the very top. (That minimum speed is not zero!) Apply Newton's 2nd law.

Just one question that is bugging me though, is there a need for calculus in this question?

No calculus is needed to solve this problem.

thanx!
i got it solved! appreciate that!

## 1. What is conservation of energy and how does it apply to vertical circular motion?

Conservation of energy is a fundamental law in physics that states energy cannot be created or destroyed, only transferred or transformed. In the context of vertical circular motion, this means that the total energy (kinetic and potential) of an object remains constant throughout its motion.

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

As the object moves through its circular path, the conservation of energy states that the total energy (kinetic and potential) must remain constant. This means that as the object moves up and down, its potential and kinetic energies will change, but their sum will remain the same. Therefore, the speed of the object will also change, but its total energy will remain constant.

## 3. How does the radius of the circular path affect the conservation of energy in vertical circular motion?

The radius of the circular path does not directly affect the conservation of energy. However, it does affect the speed of the object, which in turn affects the kinetic and potential energies. A smaller radius will result in a higher speed, while a larger radius will result in a lower speed.

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

No, the conservation of energy is a fundamental law of physics and cannot be violated. In vertical circular motion, the total energy of the object must remain constant throughout its motion.

## 5. How is the conservation of energy related to the concept of work in vertical circular motion?

The conservation of energy and the concept of work are closely related in vertical circular motion. Work is defined as the transfer of energy from one form to another. In this case, the work done by the gravitational force on the object is converted into kinetic energy as the object moves. The conservation of energy states that the total energy remains constant, so the work done by the gravitational force must equal the change in kinetic and potential energies of the object.

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