Circular motion, grade 12 physics

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SUMMARY

The discussion focuses on calculating the period of oscillation for a bungee jump scenario and determining the spring constant for a mass oscillating on a spring. For the bungee jump, a 78.5 kg man experiences a period of oscillation of 4.54 seconds using the formula T = 2π√(m/k) with a spring constant of 150 N/m. In the second problem, a 5.00 kg mass oscillating at a frequency of 0.667 Hz results in a spring constant of 87.84 N/m, derived from the same oscillation formula and the relationship T = 1/f.

PREREQUISITES
  • Understanding of harmonic motion and oscillation principles
  • Familiarity with the formula T = 2π√(m/k)
  • Knowledge of frequency and its relationship to period (T = 1/f)
  • Basic algebra for rearranging equations
NEXT STEPS
  • Explore the concept of damping in oscillatory systems
  • Learn about energy conservation in spring-mass systems
  • Investigate the effects of varying spring constants on oscillation periods
  • Study real-world applications of harmonic motion in engineering
USEFUL FOR

Students in grade 12 physics, educators teaching oscillation concepts, and anyone interested in understanding the mechanics of bungee jumping and spring dynamics.

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Problem:
A 78.5kg man is about tocompletea bungee jump. If the bungee cord has a spring constant of 150 N/m, determine the period of oscillation that we will experience.

m= 78.5 Kg
k= 150 N/m
T=?

Relevant equations:
T= 2(pi)√(m/k)

The attempt at a solution
T= 2(pi)√(78.5kg/150 N/m)
I get, T=4.54s

.......................
2nd Problem:
A 5.00 kg mass oscillates on a spring with a frequency of 0.667 Hz. Calculate the spring constant.

m= 5.00 Kg
f= 0.667 Hz
k= ?

Relevant equations:
T= 2(pi)√(m/k)
T=(1/f)


The attempt at a solution
T= (1/0.667Hz)
T= 1.499s
T= 2(pi)√(m/k)
I rearange and get:
k=87.84 N/m

If anyone can confirm or let me know if I did something wrong it would be great!
Thanks in advance!
 
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