Simple Harmonic Motion - bungee jumping

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SUMMARY

The discussion centers on a bungee jumping problem involving a 50 kg woman attached to a spring-like elastic rope with a spring constant of 220 N/m. The key equations used include the force of gravity (Fg = mg) and Hooke's Law (Fe = -kx). The correct approach to determine how far she falls before coming to rest is through conservation of energy, leading to a solution of 27.2 m, rather than equating forces which incorrectly assumes zero acceleration. The distinction between zero acceleration and zero velocity is crucial for solving this type of problem.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Knowledge of gravitational force calculations
  • Familiarity with conservation of energy principles
  • Basic concepts of kinematics and dynamics
NEXT STEPS
  • Study the conservation of mechanical energy in elastic systems
  • Learn about the dynamics of free fall and forces acting on falling objects
  • Explore advanced applications of Hooke's Law in real-world scenarios
  • Investigate the mathematical modeling of oscillatory motion in springs
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and energy conservation, as well as educators seeking to explain the principles of simple harmonic motion and bungee jumping dynamics.

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Homework Statement


A woman bungee-jumper of mass 50 kg is attached to an elastic rope of natural length 15 m. The rope behaves like a spring of spring constant k = 220 N/m. The other end of the spring is attached to a high bridge. The woman jumps from the bridge.

a) Determine how far below the bridge she falls, before she instantaneously comes to rest.

Homework Equations


Fe = -kx, Fg= m*g... Fg=Fe, -kx=m*g
OR
1/2kx^2=mgh

The Attempt at a Solution


Okay, so this is a question that appears in the Tsokos book and although I am aware of the solution and how to acquire it (through the use of the conservation of energy; equating the potential energy and elastic energy) by using the formula above, I would like to know why the task cannot be solved through the conventional equating of forces. Since the woman is in free fall, the only other force that could cause her to stop is the restoring force of elastic rope, hence the formula above: Fg=Fe. Through using this formula, however I have gotten that x=17.2 m and the answer seems to be 27.2 m and I do not know why I cannot solve it through equations of force.

Please, help.

Thanks.
 
Physics news on Phys.org
By equating the weight of the bungee jumper with the restoring force, you are creating the condition that the acceleration is zero.

In this problem you are not interested in when the acceleration is zero, you are interested in when the velocity is zero.
 

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