Maximum speed before Rope Breaks

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SUMMARY

The maximum uniform speed at which a mass can be swung on a rope before it breaks is determined by analyzing the forces acting on the mass at the bottom of the swing. The equation T - Fg = m(V^2/R) is used, where T is the tension in the rope, Fg is the gravitational force, m is the mass, V is the speed, and R is the radius of the circular path (length of the rope). The maximum tension occurs at the bottom of the swing, where both gravitational force and tension act in opposite directions, leading to a higher resultant tension compared to the top of the swing.

PREREQUISITES
  • Understanding of circular motion dynamics
  • Familiarity with Newton's laws of motion
  • Knowledge of gravitational force calculations
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study the concept of centripetal force in circular motion
  • Learn how to derive tension in ropes under varying conditions
  • Explore the effects of mass and length on the maximum speed in pendulum systems
  • Investigate real-world applications of tension in ropes, such as in amusement park rides
USEFUL FOR

Physics students, educators, and engineers interested in mechanics, particularly those focusing on dynamics and forces in circular motion.

proness26
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Homework Statement


A mass of m is placed on the end of a rope of length l and swung in a vertical plane. The rope can withstand a maximum tension of P N(Newtons), after which it breaks. What is the maximum uniform speed that the object can be swung at, before the rope breaks?

Homework Equations



T-Fg=m(V^2/R)

The Attempt at a Solution



At which point on the vertical plane would I check to get maximum uniform speed?
Would I check the top where both Fg and T will be accelerating the object towards the center of the circle? Or would I check the bottom where T and Fg will be acting in opposite directions?
 
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proness26 said:

Homework Statement


A mass of m is placed on the end of a rope of length l and swung in a vertical plane. The rope can withstand a maximum tension of P N(Newtons), after which it breaks. What is the maximum uniform speed that the object can be swung at, before the rope breaks?

Homework Equations



T-Fg=m(V^2/R)

The Attempt at a Solution



At which point on the vertical plane would I check to get maximum uniform speed?
Would I check the top where both Fg and T will be accelerating the object towards the center of the circle? Or would I check the bottom where T and Fg will be acting in opposite directions?

Well, at which of these two situations would the tension be larger? The rope must not break at any point in the cycle, which means it must be able to withstand the largest tensile force that it will be subjected to.
 
Ohh ok I got it then. Bottom. Seems like a silly question now that I look at it haha
 

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