Calculating Conical Acceleration for a Rotating Object on a Table

[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?

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

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.

 

[Moetasim]

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.