Harmonic Motion 2: Sally & Mommy Ride the Least Exciting Carnival Ride

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SUMMARY

The discussion revolves around a carnival ride modeled as a spring-mass system, where the spring has a force constant of k = 225 N/m. Little Sally oscillates with a period of 1.78 seconds, while riding with her mother results in a combined period of 3.32 seconds. Using the formula for the period of a mass-spring system, the mass of Sally's mother can be derived from the change in oscillation period when both are on the sling. The analysis leads to the conclusion that the mass of Sally's mother is approximately 45.5 kg.

PREREQUISITES
  • Understanding of harmonic motion principles
  • Familiarity with the formula for the period of a spring-mass system
  • Basic knowledge of mass and force constants
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study the formula for the period of a spring-mass system: T = 2π√(m/k)
  • Explore the concept of effective mass in oscillating systems
  • Learn about energy conservation in harmonic motion
  • Investigate real-world applications of harmonic motion in engineering
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Students in physics, educators teaching harmonic motion, and anyone interested in the practical applications of oscillatory systems.

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The world's least exciting carnival ride consists of a cloth sling (of negligible mass) hanging by a spring of force constant k = 225 N/m. Children sit in the sling and bob up and down slowly. How exciting ...

Little Sally tries the ride. She gets into the sling, and, after Cletus the Carny gives her a bit of a push, oscillates up and down with a period of 1.78 seconds.

"Mommy, mommy, help, it's scary!" cries Sally. Her mother replies, "Don't worry, dear, you can sit on my lap and we'll ride together."

Together, Sally and her mother bob up and down with a period of 3.32 seconds.

Cletus scratches his head for a moment, then derives the mass of Sally's mother. What is it?
 
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