The motion of n planets (Po, P₁,..., Pn-1) is governed by the set of 6n first order ODEsnr₁ = V₁_and_vi' = Σ Gm;j=1jirj - rid¾3(5.10)where mi, ri(t) and vi(t) are the mass, position vector and velocity of the planet Pi, respectively.The scalar dij = dji = ||r¡—ri|| is the distance between the two planets Pi and Pj. The gravitationalconstant, G, can be taken equal to 1 without loss of generality.

The text in the image describes the motion of n planets subjected to gravitational forces exerted by…

Answered: The motion of n planets (Po, P₁,...,…

C++ for Engineers and Scientists

4th Edition

ISBN:9781133187844

Author:Bronson, Gary J.

Publisher:Bronson, Gary J.

Chapter1: Fundamentals Of C++ Programming

Section: Chapter Questions

Problem 2PP: (Conversion) An object’s polar moment of inertia, J, represents its resistance to twisting. For a...

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(Conversion) An object’s polar moment of inertia, J, represents its resistance to twisting. For a cylinder, this moment of inertia is given by this formula: J=mr2/2+m( l 2 +3r 2 )/12misthecylindersmass( kg).listhecylinderslength(m).risthecylindersradius(m). Using this formula, determine the units for the cylinder’s polar moment of inertia.
(Numerical analysis) Here’s a challenging problem for those who know a little calculus. The Newton-Raphson method can be used to find the roots of any equation y(x)=0. In this method, the (i+1)stapproximation,xi+1,toarootofy(x)=0 is given in terms of the ith approximation, xi, by the following formula, where y’ denotes the derivative of y(x) with respect to x: xi+1=xiy(xi)/y(xi) For example, if y(x)=3x2+2x2,theny(x)=6x+2 , and the roots are found by making a reasonable guess for a first approximation x1 and iterating by using this equation: xi+1=xi(3xi2+2xi2)/(6xi+2) a. Using the Newton-Raphson method, find the two roots of the equation 3x2+2x2=0. (Hint: There’s one positive root and one negative root.) b. Extend the program written for Exercise 6a so that it finds the roots of any function y(x)=0, when the function for y(x) and the derivative of y(x) are placed in the code.
(Mechanics) The deflection at any point along the centerline of a cantilevered beam, such as the one used for a balcony (see Figure 5.15), when a load is distributed evenly along the beam is given by this formula: d=wx224EI(x2+6l24lx) d is the deflection at location x (ft). xisthedistancefromthesecuredend( ft).wistheweightplacedattheendofthebeam( lbs/ft).listhebeamlength( ft). Eisthemodulesofelasticity( lbs/f t 2 ).Iisthesecondmomentofinertia( f t 4 ). For the beam shown in Figure 5.15, the second moment of inertia is determined as follows: l=bh312 b is the beam’s base. h is the beam’s height. Using these formulas, write, compile, and run a C++ program that determines and displays a table of the deflection for a cantilevered pine beam at half-foot increments along its length, using the following data: w=200lbs/ftl=3ftE=187.2106lb/ft2b=.2fth=.3ft
(Thermodynamics) The work, W, performed by a single piston in an engine can be determined by this formula: W=Fd F is the force provided by the piston in Newtons. d is the distance the piston moves in meters. a. Determine the units of W by calculating the units resulting from the right side of the formula. Check that your answer corresponds to the units for work listed in Table 1.1. b. Determine the work performed by a piston that provides a force of 1000 N over a distance of 15 centimeters.
(Heat transfer) The formula developed in Exercise 5 can be used to determine the cooling time, t, caused only by radiation, of each planet in the solar system. For convenience, this formula is repeated here (see Exercise 5 for a definition of each symbol): t=Nk2eAT3fin A=surfaceareaofasphere=4r2 N=numberofatoms=volumeofthespherevolumeofanatom Volume of a sphere sphere=43radius3 The volume of a single atom is approximately 11029m3 . Using this information and the current temperatures and radii listed in the following chart, determine the time it took each planet to cool to its current temperature, caused only by radiation.
One way to determine how healthy a person is by measuring the body fat of the person. The formulas to determine the body fat for female and male are as follows: Body fat formula for women: A1 = (body weight x 0.732) + 8.987 A2 = wrist measurement (at fullest point)/3.140 A3 = waist measurement (at navel) x 0.157 A4 = hip measurement (at fullest point) x 0.249 A6 = forearm measurement (at fullest point) x 0.434 B = A1 + A2 A3 A4 + A5 Body fat = body weight - B Body fat percentage = body fat x 100/body weight Body fat formula for men: A1 = (Body weight x 1.082) + 94.42 A2 = wrist measurement x 4.15 B = A1 A2 Body fat = body weight B Body fat percentage = body fat x 100/body weight Write a program to calculate the body fat of a person.
(Civil eng.) Modify the program written for Exercise 9 to determine the maximum load that can be placed at the end of an 8-foot I-beam, shown in Figure 2.21, so that the stress on the fixed end is 20,000lbs/in2. Use the fact that this beam’s rectangular moment of inertia is 21.4 in4 and the value of c is 3 in.
(Chemistry) a. Determine the final units of the following expression, which provides the molecular weight of 1.5 moles of hydrogen peroxide: 1.5moles34.0146grams/mole b. Determine the final units of the following expression, which provides the molecular weight of 5.3 moles of water: 5.3moles18grams/mole
(Civil eng.) The maximum load that can be placed at the end of a symmetrical wooden beam, such as the rectangular beam shown in Figure 2.20, can be calculated as the following: L=S1dc L is the maximum weight in lbs of the load placed on the beam. S is the stress in lbs/in2. I is the beam’s rectangular moment of inertia in units of in4. d is the distance in inches that the load is placed from the fixed end of the beam (the “moment arm”). c is one-half the height in inches of the symmetrical beam. For a 2” × 4” wooden beam, the rectangular moment of inertia is given by this formula: I=baseheight3=12=24312=10.674 c=(4in)=2in a. Using this information, design, write, compile, and run a C++ program that computes the maximum load in lbs that can be placed at the end of an 8-foot 24 wooden beam so that the stress on the fixed end is 3000lb/in2. b. Use the program developed in Exercise 9a to determine the maximum load in lbs that can be placed at the end of a 3” × 6” wooden beam so that the stress on the fixed end is 3000lb/in2.
(For thought) a. A token of a computer language is any sequence of characters, with no intervening characters or white space, that taken as a unit has a unique meaning. Using this definition of a token, determine whether escape sequences, function names, and the keywords listed in Table 2.1 are tokens of the C++ language. b. Discuss whether adding white space to a message alters the message and whether messages can be considered tokens of C++. c. Using the definition of a token in Exercise 4a, determine whether the following statement is true: “Except for tokens of the language, C++ ignores all white space.”
(Oceanography) The pressure, P, exerted on an underwater object can be determined by this formula: P=gh is the density of water, which is 1.94slug/ft3 . g is the acceleration caused by Earth’s gravity, which is 32.2ft/sec2. h is the object’s depth in the water in feet. a. Determine the units of P by calculating the units resulting from the right side of the formula. Check that your answer corresponds to the units for pressure listed in Table 1.1. b. Determine the pressure on a submarine operating at a depth of 2500 feet.

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