# Centripetal Motion Homework: Mass of String/Spring Effect

• bjgawp
In summary, taking into account the mass of the string/spring in problems involving centripetal motion would affect the radius of the circular path. This is similar to a conical pendulum and can be demonstrated by imagining a heavy rod replacing the string. For the same energy, the heavy rod would revolve at a lower height.
bjgawp

## Homework Statement

When solving problems involving centripetal motion, say rotating a string/spring with an object attached to it, without taking into account of the mass of the string/spring. What effect would it have if we DID take it into account?

## The Attempt at a Solution

If we were to twirl the mass in a horizontal circle, I would think that the weight of the string/spring would lower the height of the circular path, like a conical pendulum - affecting the radius of its path. Am I going in the right direction .. ?

That's right. Think of a very heavy rod replacing the string. For the same energy, it would revolve at a lower height.

Your thinking is correct. Taking into account the mass of the string/spring would affect the radius of the circular path. This is because the string/spring has its own mass and therefore, has its own inertia. This inertia must be overcome in order for the object attached to it to move in a circular path. As a result, the radius of the circular path would be slightly smaller than if we did not take into account the mass of the string/spring. This effect would be more significant for objects with larger masses attached to the string/spring. Additionally, the tension in the string/spring would also increase due to the added mass, which would affect the centripetal force acting on the object. Overall, taking into account the mass of the string/spring would provide a more accurate and precise solution to problems involving centripetal motion.

## 1. What is centripetal motion?

Centripetal motion is the circular motion of an object around a fixed point. It is caused by a force directed towards the center of the circle, known as the centripetal force.

## 2. How is centripetal motion related to the mass of the string or spring?

The mass of the string or spring affects the centripetal motion by determining the strength of the force needed to keep the object in circular motion. Heavier strings or springs require a greater centripetal force to maintain the same circular velocity.

## 3. What factors affect the centripetal force in this homework?

The centripetal force is affected by the mass of the object, the velocity of the object, and the radius of the circular motion. In this homework, we are specifically looking at how the mass of the string or spring affects the centripetal force.

## 4. How do you calculate the mass of the string or spring in this homework?

To calculate the mass of the string or spring, you will need to measure the length and diameter of the string or spring, as well as its density. Then, you can use the formula: mass = density x volume, where volume = length x π x (diameter/2)^2.

## 5. Can the mass of the string or spring ever be ignored in centripetal motion?

No, the mass of the string or spring cannot be ignored in centripetal motion as it directly affects the centripetal force required to maintain circular motion. However, in some cases, it may be negligible compared to the mass of the object in motion.

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