Problem Solving Assignment 4 Read Chapter 5 In Text Due

Question

Problem Solving Assignment 4 Read Chapter 5 In The Text Due Wed Problem solving – assignment 4 (Read Chapter 5 in the text) (due Wed, Oct 11): 1. Please research the Umbilic Torus sculpture outside the Physics building at STONY BROOK UNIVERSITY. a. Who built it? Why? b. What is unusual about this 3D form? c. Estimate its surface area (Hint: Look up a shape called a deltoid, which is the shape of a cross section of the torus), and volume. Show how you did this. If you are really into math, you can calculate this based on the equations for an umbilic torus, but that is difficult. d. If it weighs 10 tons and is composed of bronze, is it solid? Why or why not? 2. Estimate the height and weight of the big Pagoda structure on top of the Charles B. Wang Center. Make sure you provide details about how you did this. (also, who is Charles B. Wang? What is he known for?) 3. a. What is the “SUNYLAB” structure standing behind the Heavy Engineering building? b. Based on its weight and dimensions (which you can rather easily find out (Hint – go look at it!)), calculate the resolved forces (perpendicular and parallel to the ground) on one of the three legs. c. How would you go about designing a lighter and more portable version of SUNYLAB – in other words, how would you solve the problem of creating a lighter and more transportable version of a structure that does what the SUNYLAB was designed to do (back in 1973!)? Describe your problem solving process.

Dr. Jack HW Helper · Accepted Answer

The assignment involves interdisciplinary exploration of engineering, architecture, and physics through three distinct problems centered on specific structures at Stony Brook University. The approach requires research, estimation, and theoretical calculations to understand the physical properties and design considerations of these structures, emphasizing problem-solving techniques rooted in physics and engineering principles. Analysis of the Umbilic Torus Sculpture The Umbilic Torus outside the Physics building at Stony Brook University was created by the artist Jürgen Meyer. Meyer, known for his sculptures that explore complex mathematical forms, designed the torus to illustrate the beauty of topology and mathematical symmetry. The torus's unusual 3D form is characterized by its smooth, continuous surface with a central hole, exemplifying a shape with genus one, meaning it has a single hole, unlike a sphere. The shape is a classic example of a mathematical surface known as a 'deltoid,' which refers to the cross-sectional shape used to approximate the surface. Estimating the surface area of the torus involves using the formula for a standard torus: $A = 4\pi^2 R r$, where R is the major radius (distance from the center of the tube to the center of the torus), and r is the minor radius (radius of the tube). Assuming measurements obtained visually or through known dimensions—say, R ≈ 3 meters and r ≈ 1 meter—the surface area calculates approximately as: $A ≈ 4 \pi^2 \times 3 \times 1 ≈ 37.7 \text{ m}^2$. Similarly, the volume of a torus is given by $V = 2\pi^2 R r^2$. Using the same estimated dimensions: $V ≈ 2 \pi^2 \times 3 \times 1^2 ≈ 59.2 \text{ m}^3$. These estimations rely on the assumption of uniform, smooth surfaces and enable a practical understanding of the scale of the sculpture. Considering the sculpture’s mass and material—bronze, with an estimated weight of 10 tons (about 9,070 kilograms)—we can assess if it is solid. The density of bronze is ap

Problem Solving Assignment 4 Read Chapter 5 In Text Due

Problem Solving Assignment 4 Read Chapter 5 In The Text Due Wed

Paper For Above instruction

Analysis of the Umbilic Torus Sculpture

The Pagoda Structure on the Charles B. Wang Center

The SUNYLAB Structure

Conclusion

References