Homework 5 Problem 3

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Sunday, February 28th, 2016

Marvel states Giant-Man can achieve a maximum height of 60 feet with his formula.

Giant-Man’s initial state is 6 foot tall with a mass of 100 kg an average density of 1 g/cm3 .

3a. Calculate the load in the vertebral body of Giant-Man as a function of height.  Use the same approach referenced in problem 2 above.

3b. Calculate the height at which Giant Man’s vertebral body will collapse under his own weight? Show evidence to defend your claim (back up your position with numbers).

 


2,111 thoughts on “Homework 5 Problem 3”

  1. Erik Hansen says:

    Just want to make sure I am understanding what is being asked:
    For 3a, are we supposed to calculate the load at the max height of 60ft?

    Also, the wording of the assumptions appear to me to be a little more complex than necessary. My understanding is that the radius increases by the same factor as the height. Does anyone have a different understanding?

    1. Myra Fabro says:

      This is how I’m understanding the problem:
      I believe we are to find the load in the vertebral body as a function of height since Giant-Man’s height can change from 6 ft to 60 ft. You don’t need to calculate an actual number but provide a function that would allow you to calculate the load if you were to plug in a height value.

      Like in Problem 2, we assume Giant-Man is modeled as a cylinder and since you know his mass and density, you can find the relationship between radius and height.

      1. Myra Fabro says:

        I should clarify…the relationship is proportional, using the initial height and radius

  2. Ryan Wesley Hoover says:

    Since the vertebral body also grows, we are to assume the strength increases as the Giant Man grows. If we assume strength is based on strain energy, then strength is a function of volume. However, if strength is merely a function of stress, then ultimate strength is a function of area. If we use volume as the strength increase factor, then everything tends to cancel itself out and the factor of safety remains constant. Therefore I think we are to assume that vertebral body strength increases based on torso area, such that as the height grows, the weight increases per volume but the verterbal strength only increases per area, therefore at some point fractures when Giant Man grows too tall. Confirm, disagree, agree?

    1. Erik Hansen says:

      If I interpreted your statements correctly, I agree. Since the radius and the area of the vertebral body increase proportionally with height, the area of the vertebral body and radius increases proportionally to each other and as the cross-sectional area of the cylinder increased the vertebral body area/strength increases.

  3. Ryan Wesley Hoover says:

    Is there a preferred method to select an ultimate strength based on the 2004 – 8126 N scatter of data presented in the paper. I’d like to use the high end of 8126 N. My reasons include posture and health of giant man.

    1. Erik Hansen says:

      I calculated using the max and min values and specified a range.

  4. Samantha Munoz says:

    Perhaps I worked through Problem 2 wrong but no matter how I do this problem or that one, I am getting R to cancel, which means I am unable to keep h in my equation & therefore cannot write an expression for load in terms of height. Can anyone provide some guidance? Maybe I’m just missing something obvious and can’t see it.

    1. Erik Hansen says:

      If I did this correctly….For this problem we are to assume that the radius scales with the change in height, so the radius at the chosen height would be: R=Ri*(h/hi). Ri does not cancel out in this case, so you may need to check your Fes` equation. Hopefully this helps.

    2. Nathan Shaw says:

      It canceled out in my equations too, at first. If his mass and density are constant then his radius would shrink as he grows. The problem only states that his density is constant. This was my problem. His mass will increase as he grows. So I agree with Erik, we need to redefine our radius equation from problem 2. Then it all works. If not, you get a flat line if you graph it.

    3. Gabriella Baldo says:

      Just like in problem two I had R cancels out. I used v=pi*r^2*h and m/D=v.
      Since the position relationships all scale and density remains the same, I use the BMI formula (kg/m^2) to relate height and weight…
      it allows me to write the mass in terms of h.

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