What Range of Speeds Can an Object Have Before a String Breaks?

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SUMMARY

The discussion centers on calculating the maximum speed of a 3.00kg object rotating in a circle with a radius of 0.800m, using a string that can support a stationary load of 25.0kg before breaking. The key equation used is F = (m*v^2)/r, where the tension in the string must not exceed the weight of the hanging load, calculated as 25.0kg multiplied by gravity (9.81 m/s²). The maximum speed can be derived by rearranging the formula to v = sqrt((F * r) / m), leading to a definitive numeric answer for the maximum rotational speed before the string fails.

PREREQUISITES
  • Understanding of circular motion dynamics
  • Knowledge of tension in strings and forces
  • Familiarity with gravitational force calculations
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Calculate the maximum tension in a string using F = m*g
  • Explore the implications of varying mass and radius on rotational speed
  • Learn about centripetal force and its applications in real-world scenarios
  • Investigate the effects of friction in circular motion systems
USEFUL FOR

Students studying physics, particularly those focused on mechanics and circular motion, as well as educators seeking to clarify concepts related to tension and forces in rotational systems.

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Homework Statement



A light string can support a stationary hanging load of 25.0kg before breaking. An object of mass m = 3.00kg attached to the string rotates on a frictionless, horizontal table in a circle of radius r = 0.800m, and the other end of the string is held fixed. What range of speeds can the object have before the string breaks?

Homework Equations



F = (m*v^2)/r


The Attempt at a Solution



I seem to only be able to solve this question in terms of F. As in, the max velocity can be:

v = (F*0.800/25)^0.5

Yet there is an actual numeric answer to this question.

I'm not sure what to do with the '3.0kg' given. Any hints would be appreciated!
 
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when you spin this 3kg mass, there is a certain amount of tension in the string. The tension in the string cannot exceed 25kg * gravity. So what is the maximum speed you can spin a mass of 3kg so the tension in the string doesn't exceed 25kg * gravity?
 
Ohh, this is the definition of "hanging load"? I understand now! Thank you.
 
shawli said:
Ohh, this is the definition of "hanging load"? I understand now! Thank you.

You're very welcome:smile:
 

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