# Calculating Conical Acceleration for a Rotating Object on a Table

• teresat628
In summary, the conversation discusses the maximum load a light string can support before breaking and the range of speeds that a 3.60 kg object can have while rotating on a frictionless table attached to the string. The conversation also suggests writing down relevant equations and showing an attempt at a solution.
teresat628

## Homework Statement

A light string can support a stationary hanging load of 25.0 kg before breaking. A 3.60 kg object attached to the string rotates on a horizontal, frictionless table in a circle of radius 0.800 m, while the other end of the string is held fixed. What range of speeds can the object have before the string breaks?

## The Attempt at a Solution

Hi teresa! Welcome to PF!

Write down the relevant equations first (equations for force, equations for acceleration, conservation equations, etc).

They are the tools you have to work with …

Then show us your attempt at a solution.

To calculate the range of speeds that the object can have before the string breaks, we can use the equation for centripetal acceleration, a= v^2/r, where v is the velocity of the object and r is the radius of the circle. We can also use Newton's second law, F=ma, to determine the maximum force that the string can support before breaking.

First, we can calculate the maximum centripetal acceleration that the string can support by setting the force equal to the tension in the string, which is equal to the weight of the object, 3.60 kg * 9.8 m/s^2 = 35.28 N. This gives us a maximum acceleration of 35.28 N / 25.0 kg = 1.4112 m/s^2.

Next, we can use the equation for centripetal acceleration to solve for the maximum velocity of the object. Plugging in the maximum acceleration and the given radius, we get v^2 = 1.4112 m/s^2 * 0.800 m = 1.129 m^2/s^2. Taking the square root of both sides, we get a maximum velocity of v = 1.062 m/s.

Therefore, the range of speeds that the object can have before the string breaks is 0 m/s to 1.062 m/s. Any speed above 1.062 m/s would exceed the maximum acceleration that the string can support and result in the string breaking.

## 1. What is conical acceleration and how is it related to a rotating object on a table?

Conical acceleration is the change in direction of an object's velocity due to its circular motion. When a rotating object is placed on a table, it experiences conical acceleration as it moves in a circular path.

## 2. How is conical acceleration calculated for a rotating object on a table?

Conical acceleration can be calculated by dividing the tangential velocity of the object by the radius of the circular path. This can be represented by the equation a = v^2/r, where a is the conical acceleration, v is the tangential velocity, and r is the radius of the circular path.

## 3. What factors affect the conical acceleration of a rotating object on a table?

The conical acceleration of a rotating object on a table is affected by the tangential velocity, radius of the circular path, and the mass of the object. Additionally, the coefficient of friction between the object and the table can also impact the conical acceleration.

## 4. How does the direction of conical acceleration change as the object moves along the circular path?

The direction of conical acceleration is always perpendicular to the velocity of the object, pointing towards the center of the circular path. As the object moves along the path, the direction of conical acceleration changes along with the velocity, always remaining perpendicular to it.

## 5. Can conical acceleration be negative and what does it indicate?

Yes, conical acceleration can be negative in some cases. This indicates that the direction of the acceleration is opposite to the direction of the velocity. In other words, the object is slowing down as it moves along the circular path.

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