What physics can we learn from Sheldon and Wolowitz's debate in The Big Bang Theory (Season 8, Episode 2)
In the Tv series, "The Big Bang Theory", characters Sheldon Cooper (a physicist) and Howard Wolowitz (an engineer) always play a tug of wars with each other, proving the superiority of physicists over engineers and vice versa. In the latest season's 2nd episode, Sheldon presented Howard with a set of questions to prove if he was smart enough to take a graduate level physics class, which Sheldon was teaching. They questioned each other to prove their knowledge of the subject. In the following text we try to explain what did they try to ask each other and what was its answer.
Sheldon: “are you familiar with the Brachistochrone problem? And how it relates to the calculus of variations?”
Howard: “It's an inverted cycloid.”
The Brachistochrone problem is to find the fastest (not shortest) path, for a point like body, from one point to another under the action of gravity. The solution to this problem is an inverted cycloid. It is demonstrated in this GIF below.Video Courtesy: YouTube.com
A shortest path between two points is a straight line, but the fastest point between two points is an inverted cycloid.
Howard: “how do you quantify the strength of materials?”
Sheldon: “Young's modulus.”
Young's Modulus allows to calculate the change is the dimensions of a material under tensile or compressive loads. It predicts how much a material sample extends under tension or shortens under compression.
Howard: how do you prevent eddy currents in a transformer?
Sheldon: Laminate the core material.
Eddy currents are induced with in a conductor due to the changing magnetic field within it. These currents cause an opposition to the magnetic field that created it and also dissipates energy as heat in the material. Eddy currents are a source of energy loss in AC motors, transformers, inductors, generators etc.
Laminating the conductor parallel to the magnetic field lines can greatly reduce eddy currents in a conductor.
Howard: How does the flow rate in a pipe depend on its diameter?
Howard: What's the matter smart guy? Don't know Poiseuille law.
Poiseuille law gives the pressure drop in a fluid flowing through a cylindrical pipe. The flow is directly proportional to the diameter of the pipe. Infact it is directly proportional to d4, if the diameter of the pipe is halved the flow through it reduces to one-sixteenth (1/16th ).Here ΔP is the pressure loss L is the length of pipe μ is the dynamic viscosity Q is the volumetric flow rate r is the radius d is the diameter π is the mathematical constant Pi
Leonard: how long is a galactic year?
Raj: 250 million years!
A galactic year is the time required by our solar system to orbit around the center of the milky way galaxy. The estimates of the time required to complete this orbit is around 225 to 250 million years. The solar system is travelling around the milky way galaxy at an average speed of 828,000 km/h (230km/s). At this speed, an object could circumnavigate around the earth in 2mins and 54 secs.Image Courtesy: astronaut.com
Howard: Which Archimedean solid has 20 regular triangular faces, 30 square faces, 12 pentagonal faces, 60 vertices and 120 edges?
The Rhombicosidodecahedron in a flat out view.
Sheldon: How would you determine the ground state of a quantum system with no exact solution?
Howard: I would guess a wave-function and then vary its parameters until I found the lowest energy solution.
A wave function or wavefunction (also named a state function) in quantum mechanics describes the quantum state of a system of one or more particles, and contains all the information about the system considered in isolation.
Sheldon: Do you know how to integrate X squared times e to the minus X, without looking it up?
Howard: I'd use Feynman's trick differentiate under the integral sign.
The following document explains very clearly the Feynman's trick of differentiating under the integral sign.
Sheldon: What is the correct interpretation of quantum mechanics?
Howard: Since every interpretation gives exactly the same answer to every measurement, they are all equally correct. However, I know you believe in the Many Worlds Interpretation, so I'll say that.
The Many Worlds Interpretation is an interpretation of quantum mechanics tries to explain the interaction of everyday objects (photons of lights) with the quantum system (an electron). It presents the idea that the quantum system doesn't decide the outcome of the interaction of the everyday object with the quantum system, rather whenever such interaction happens the time-line of history divides and both possibilities happen at the same time in alternate parallel branches or worlds.