Oscillation:Mass dropped on Vertical Spring

In summary, a 60 kg woman bungee-jumping from a high bridge attached to an elastic rope with a natural length of 15m and spring constant of 220Nm falls a distance determined by the conservation of energy equation. The potential energy includes both gravity and the elastic force of the cord.
  • #1
thedefender7
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Homework Statement



A woman bungee-jumper of mass 60 kg is attached to an elastic rope of natural length 15m. The rope behaves like a spring of spring constant k= 220Nm. 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



a= -(omega)Acos((omega)t)
omega^2=k/m
E=Ep+Ek
Ep=1/2mv^2
Ek=1/2 mv^2

The Attempt at a Solution


I'm not sure anymore, please help
 
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  • #2
You can use conservation of energy but find the correct form of the potential energy. You have two forces, gravity and the elastic force of the cord, both of them contribute to the potential energy of the woman. ehild
 

FAQ: Oscillation:Mass dropped on Vertical Spring

What is oscillation?

Oscillation is a repetitive back-and-forth movement or motion of an object around a central point or equilibrium position.

How does a vertical spring create oscillation?

A vertical spring creates oscillation by storing potential energy when it is compressed or stretched, and releasing this energy as kinetic energy when it returns to its original position.

What is the relationship between mass and oscillation in a vertical spring?

The relationship between mass and oscillation in a vertical spring is that as the mass of the object increases, the period of oscillation also increases. This means that the object takes longer to complete one full cycle of oscillation.

How does dropping a mass onto a vertical spring affect its oscillation?

Dropping a mass onto a vertical spring will cause the spring to compress and stretch, storing potential energy. As the spring returns to its original position, this energy is released, causing the mass to oscillate up and down.

Can the amplitude of oscillation be changed in this system?

Yes, the amplitude of oscillation can be changed by altering the initial position of the mass or by changing the stiffness of the spring. A stiffer spring will result in a smaller amplitude, while a less stiff spring will allow for a larger amplitude of oscillation.

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