Ring moves on curved path faster

In summary, the conversation discusses the concept of a ring traveling on a curved path versus a straight line in the same amount of time. The question arises as to which principle can explain this phenomenon. The topic is related to the Brachistochrone problem, which involves finding the path of shortest time for an object to travel between two points under the influence of gravity. The solution typically involves using calculus of variations, but the resulting curve depends on the specific setup. Unfortunately, there is no diagram available to further illustrate the concept.
  • #1
apr
6
0
A ring on curved path (say on bent rod) will move longer distance than the one moves on straight line in same interval of time (the two rings are released simultaneously - one moves on curved path and other one moves horizontally) - How to explain? by which principle one can explain?
 
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  • #2
apr said:
A ring on curved path (say on bent rod) will move longer distance than the one moves on straight line in same interval of time (the two rings are released simultaneously - one moves on curved path and other one moves horizontally) - How to explain? by which principle one can explain?
Do you have a diagram to illustrate what you mean? Assuming I understand you correctly, why do you think the two rings taking different paths will travel from A to B in the same time?
 
  • #3
My guess is that the original poster question is similar to which path is best for gravity to pull a ring on a frictionless wire to get from point A to point B in the shortest time. If the goal is to get the same time as a straight line from A to B, then the path of shortest time could be modified in numerous ways to get the time to be the same.
 
  • #5
Sorry I don't have the diagram. The question asked me over the phone by a teenager - I replied as said by rcgldr in previous post here. But not satisfied really.
 

FAQ: Ring moves on curved path faster

1. How does a ring move on a curved path faster than on a straight path?

A ring moves on a curved path faster due to the centripetal force acting on it. When an object moves in a curved path, it experiences a change in velocity, which requires a force to act on it. In this case, the centripetal force is directed towards the center of the curve, causing the ring to move faster.

2. What is centripetal force?

Centripetal force is the force that acts on an object moving in a curved path, towards the center of the curve. It is responsible for maintaining the object's circular motion and is dependent on the object's mass, velocity, and the radius of the curve.

3. Can a ring move on a curved path faster without any force acting on it?

No, a ring cannot move on a curved path faster without any force acting on it. According to Newton's First Law of Motion, an object will continue to move at a constant speed in a straight line unless acted upon by an external force. In the case of a curved path, the centripetal force is required to maintain the object's motion.

4. How does the radius of the curve affect the speed of the ring?

The radius of the curve directly affects the speed of the ring. As the radius decreases, the speed of the ring increases, and vice versa. This is because a smaller radius requires a greater centripetal force to maintain the object's motion, resulting in a higher speed.

5. Is the speed of the ring on a curved path constant?

No, the speed of the ring on a curved path is not constant. The ring's speed will vary as it moves along the curve, with the highest speed occurring at the point closest to the center of the curve. This is due to the changing direction of the ring's velocity, which requires a changing centripetal force to maintain its motion.

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