Calculate Force Constant for Safe Bungee Jumping: F=700N, x=9m, k=77.77 N/m

[Marc Briancon]

Bungee jumping- The unstretched length of the cord is 25.0m, the student weighs about 700N, and the balloon you start at is 36.0 m above the surface of the river below. Calculate the required force constant of the cord if the student is to stop safely 4.00m above the river.

So would I want to use F=kx, then set k=(F/x)...?

F=700 N
x=9 m
k=77.77 N/m

Is that right?

 

[tiny-tim]

Welcome to PF!

… Calculate the required force constant of the cord if the student is to stop safely 4.00m above the river.

So would I want to use F=kx, then set k=(F/x)...?

F=700 N
x=9 m
k=77.77 N/m

Is that right?

Hi Marc! Welcome to PF!

Isn't that when acceleration is zero?

You want the velocity to be zero.

 

[astrokreng]

Yes, you are correct. To calculate the required force constant for the bungee cord, we can use the formula F=kx, where F is the force (700 N), x is the distance (9 m), and k is the force constant. Rearranging the formula, we get k=F/x, which gives us a force constant of 77.77 N/m. This means that for every meter the bungee cord stretches, it exerts a force of 77.77 N.

To ensure a safe bungee jump, we also need to take into account the starting height and the desired stopping height. In this scenario, the student weighs 700 N and the starting height is 36.0 m above the river. To stop safely 4.00 m above the river, the bungee cord needs to stretch a total of (36.0-4.00) = 32.0 m.

Using the same formula, we can calculate the required force constant for the bungee cord to safely stop the student at a height of 4.00 m above the river. This would be k=F/x = (700 N)/(32.0 m) = 21.875 N/m. This value is lower than the initial force constant of 77.77 N/m, which makes sense as the bungee cord needs to stretch more to safely stop the student at a lower height.

In conclusion, the required force constant for safe bungee jumping in this scenario is 21.875 N/m. It is important for bungee jumping operators to carefully calculate and test the force constant of their bungee cords to ensure the safety of their customers.