Designing a Bungee Ride: Calculating Energy & Springs

[audi476]

i realize that this is a common question, but i have a partner for this assignment and she's doing something different than me. i just want to make sure I'm not off base

the assignment is to design a bungee ride. the problem involves someone being launched from 150 ft above the ground and having to miss an obstacle 15 feet below the launch point

this is how i worked this:

i realize using conservation of energy, the man will jump from 150 and have some potential energy, and this potential energy should be converted into spring energy at the end of the jump. i also realize that i can't convert it all into spring energy or he'd smack into the ground, so i do have some potential energy left in the equation. but using this equation, he would ideally rebound to the full height, disregarding irreversibilities with the environment (i.e. friction).

what i did is i made the jump occur from 165 feet above the ground, and worked a COE equation to find a value of K (spring constant). the equation looked like this (with the weight of the man being 300 pounds).

mgh1 = mgh2 + .5kx^2
(300)(170) = (300)(10) + .5k(100^2)

"10" is the height i want him to stop above the ground (i realize i can eliminate this by taking this point to be the datum, but i don't want to), and "100" is the stretched length of the bungee.

so, for the man to rebound to a point 15 feet below the initial jump, i reworked the equation using a jump height of 150 (instead of 170) and found what the remaining amount of potential would be. the remaining amount is exactly equal to the amount of potential energy he loses in that 15 feet.

does this make sense? my partner did something using integrals, but i think that all might be a bit unnecessary

thanks a bunch!

 

[thepatientmental]

Your approach to designing a bungee ride using conservation of energy and spring energy is correct. By setting the jump height to 165 feet and solving for the spring constant, you have found the ideal amount of energy that needs to be stored in the spring in order for the person to rebound to the full height.

To ensure that the person safely misses the obstacle 15 feet below the launch point, you have correctly reworked the equation using a jump height of 150 feet and found the remaining potential energy. This remaining potential energy should be equal to the energy lost during the 15-foot descent, ensuring that the person safely stops above the ground.

Your partner's approach using integrals may be a more advanced method, but your method is still valid and effective. As long as you both reach the same conclusion and your calculations are accurate, both methods are acceptable. Good job on designing the bungee ride and considering the safety of the person jumping!