Max Tension in Rope Supporting Bungie Jumper

[lovemake1]

Homework Statement

Find the maximum Tension in the rope that supports the bungie jumper.
mass of the jumper is 75kg. neglet air resistance.

Homework Equations

would it be Fnet = ma
Fgravity - F Tension = ma

The Attempt at a Solution

I am not sure how to approach this.
i know that when the jumper reaches the bottom. the rope flicks and for a moment it gains quite a bit of tension i believe? how would you approach this problem?
is it possible to find out ?

 

[ideasrule]

No, it's not possible to find out without more information. Think about it this way: if you jump down from somewhere really high up, you stretch the bungie farther, so it exerts a greater force.

 

[kerimek]

I would first clarify the scenario and gather more information. Is the bungee jumper jumping off a bridge or a platform? What is the length and material of the rope? Is the bungee jumper attached to the rope at their waist or ankles? These details can affect the calculation of maximum tension.

Assuming the bungee jumper is jumping off a platform and attached to the rope at their waist, we can use the equation Fnet = ma to calculate the maximum tension in the rope. As the bungee jumper falls, the force of gravity (Fgravity = mg, where m is the mass of the jumper and g is the acceleration due to gravity) will accelerate them downwards. At the same time, the rope will stretch and exert an upward force on the jumper, creating tension.

At the bottom of the jump, when the jumper reaches the maximum velocity, the net force will be equal to zero (Fnet = 0), as the jumper is no longer accelerating. This means that the tension in the rope (Ftension) must be equal and opposite to the force of gravity (Fgravity) at this point. Therefore, the maximum tension in the rope can be calculated as:

Ftension = Fgravity = mg = (75 kg)(9.8 m/s^2) = 735 N

However, this is a simplified calculation and does not take into account the stretching and recoiling of the rope, as well as the potential energy of the bungee jumper. To get a more accurate calculation, we would need to use more complex equations, such as the spring force equation and conservation of energy.

Overall, the maximum tension in the rope supporting a bungee jumper depends on various factors and can be calculated using different methods. As a scientist, it is important to consider all the relevant variables and use appropriate equations to accurately determine the maximum tension in the rope.