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!

 

[anathema]

Thank you for sharing your approach to designing a bungee ride. Your use of the conservation of energy principle is a good starting point for this problem. However, I would like to point out a few things that you may want to consider.

Firstly, the equation you have used is correct for finding the spring constant, but it does not take into account the fact that the bungee cord will stretch during the jump. This will affect the value of the spring constant and the final rebound height. To account for this, you can use the equation for the potential energy of a spring, which takes into account the displacement of the spring, instead of the stretched length.

Secondly, using a jump height of 165 feet and expecting the person to rebound to the full height may not be realistic. In real life, there will always be some energy lost due to friction and air resistance, so the person will not rebound to the full height. You may want to consider using a smaller jump height and taking into account the energy lost during the jump.

Lastly, your partner's approach using integrals may be more accurate as it takes into account the varying forces and displacement of the bungee cord during the jump. However, it does involve more complex calculations and may not be necessary for this simple problem.

In summary, your approach using the conservation of energy principle is a good starting point, but you may want to consider the factors mentioned above to make your design more accurate. Good luck with your project!

 

[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!