What Length of Bungee Cord is Needed to Stop a 70 kg Person from Plunging 226m?

[raindropecho]

Hi I'm having trouble with a certain question. Could someone please guide me to the right answer? Thanks
"Consider a 70 kg person leaping off a 226m building. He plans to use a rope with force constant 4900 N/m. What length of rope does he need to stop his plunge 10m above the sidewalk? What max force will the rope exert on him?"
Any help is greatly appreciated

 

[russ_watters]

Construct an equation with those 3 peices of information using length as your variable and solve it. Each side will be an energy equation. There are two important things to consider: the gravitational potential energy at the beginning (when on the roof) is exactly equal to the potential energy in the spring (bungee cord) when the person is 10m off the sidewalk (make that the zero point to make the calculations easier and make the building 216m). And second, remember that for the first part of the plunge, the bungee cord isn't stretching.

 

[GSXR750]

!

Hi there, to answer your question about the length of the bungee cord, we need to use the formula F = kx, where F is the force exerted by the bungee cord, k is the force constant, and x is the length of the cord.

In this scenario, we know that the person weighs 70 kg, which is equivalent to 700N (using the formula F = mg, where g is the acceleration due to gravity, which is 9.8 m/s^2). We also know that the force constant is 4900 N/m and the person wants to stop 10m above the ground.

Using the formula F = kx, we can rearrange it to solve for x: x = F/k. Plugging in the values we know, we get x = 700N/4900 N/m = 0.1429 m. This means that the length of the bungee cord needed is 0.1429 meters or approximately 14.3 cm.

To calculate the maximum force that the rope will exert on the person, we can use the same formula F = kx. However, in this case, x would be equal to 10m (since the person wants to stop 10m above the ground). So, the maximum force would be F = 4900 N/m * 10m = 49000 N.

I hope this helps guide you to the right answer. Let me know if you have any further questions. Good luck!