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- Expand the equation K = m(γ−1) in aTaylor series, and find the first two nonvanishingterms. Explain why the vanishing terms are theones that should vanish physically. Show thatthe first term is the nonrelativistic expression forkinetic energy.In this problem you will consider the balance of thermal energy radiated and absorbed by a person. Assume that the person is wearing only a skimpy bathing suit of negligible area. As a rough approximation, the area of a human body may be considered to be that of the sides of a cylinder of length L=2.0m and circumference C=0.8m. For the Stefan-Boltzmann constant use ?=5.67SOLVE PLEASE
- The Newton–Raphson method for finding the stationary point(s) Rsp of a potential energy surface V is based on a Taylor-series expansion around a guess, R0. Similarly, the velocity Verlet algorithm for integrating molecular dynamics trajectories [xt, vt] is based on a Taylor-series expansion around the initial conditions, [x0, v0]. Both of these methods rely strictly on local information about the system. How many derivatives do we need to compute in order to apply them?The difference of the scalar potential squared and the modulus of the vector potential squared, Φ2 - |A|2, is Lorentz invariant (a Lorentz scalar). why the statement true?A particle experiences a potential energy given by U(x) = (x² - 3)e-x² (in SI units). (a) Make a sketch of U(x), including numerical values at the minima and maxima. (b) What is the maximum energy the particle could have and yet be bound? (c) What is the maximum energy the particle could have and yet be bound for a considerable length of time? (d) Is it possible for a particle to have an energy greater than that in part (c) and still be "bound" for some period of time? Explain. Responses
- One cycle of the signal on the oscilloscope screen has width of 2.8 cm (1 division = 1 cm). The setting on the Horizontal TIME/DIV control is 2 us. The period of the signal is us. Write your answer in the tenths place. Only the numerical value will be graded. One cycle of the signal on the oscilloscope screen has width of 2.8 cm (1 division = 1 cm). The setting on the Horizontal TIME/DIV control is 2 us. The frequency is kHz. Write your answer in the tenths place. Only the numerical value will be graded.Let's say we have a particle in motion. If f(x) represents the function of the particle's velocity, what does the integral of f(x) represent?