[Mechanics] Tension in bungee jumping

In summary, a bungee jumper of mass 60kg jumps from a bridge 24 m above the surface of the water. The rope is 12 m long and follows Hooke's law. To just reach the water, the spring constant of the rope should be 200 Nm^-2. This is calculated by using the height above the water to determine the initial gravitational potential energy.
  • #1
sushichan
12
1

Homework Statement


A bungee jumper of mass 60kg jumps from a bridge 24 m above the surface of the water. The rope is 12 m long and is assumed to obey Hooke's law. What should the spring constant of the rope be if the woman is to just reach the water?

Homework Equations


Ep=mgh
E=1/2 kx^2

The Attempt at a Solution


Energy conservation? I'm definitely doing something wrong here and not understanding something but I don't know what.

mgh = ½kx^2
(60)(10)(12) = ½k(12)^2
[I put the length of the unstretched part of the rope as my h value and x as the extension, which is 24-12=12]

k= 100 Nm^-1
[This is the answer I got]

But the answer is k=200 Nm^-2
 
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  • #2
sushichan said:
I put the length of the unstretched part of the rope as my h
To calculate the initial gravitational PE, use the height above the water.
 
  • #3
Doc Al said:
To calculate the initial gravitational PE, use the height above the water.
okay thanks!
 
  • #4
This is the key statement : The woman jumps from a bridge 24 m above the surface of water.
 

Related to [Mechanics] Tension in bungee jumping

1. What is tension in bungee jumping?

Tension in bungee jumping refers to the force that is exerted on the bungee cord or rope as it stretches and pulls against the weight of the jumper.

2. Is tension in bungee jumping dangerous?

Tension in bungee jumping can be dangerous if the bungee cord is not properly designed or if it is stretched beyond its capacity. It is important for jumpers to follow safety protocols and for bungee cords to be regularly inspected.

3. How is tension in bungee jumping calculated?

The tension in bungee jumping is calculated using Hooke's law, which states that the force exerted by a spring is directly proportional to the distance it is stretched. The formula for tension is T = kx, where T is the tension, k is the spring constant, and x is the distance the bungee cord is stretched.

4. What factors affect tension in bungee jumping?

The tension in bungee jumping is affected by several factors, including the length and elasticity of the bungee cord, the weight of the jumper, and the distance the jumper falls before the cord starts to stretch.

5. Can tension in bungee jumping be controlled?

Yes, tension in bungee jumping can be controlled by adjusting the length and elasticity of the bungee cord. This allows for a safe and thrilling bungee jumping experience for participants.

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