Mathematical Methods in the Physical Sciences
3rd Edition
ISBN: 9780471198260
Author: Mary L. Boas
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 9.5, Problem 22P
For the following problems, use the Lagrangian to find the equations of motion and then refer to Chapter 3, Section 12.
Do Problem 21 if the two masses are different. Let
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Kindly show your complete solution. Thank you.
Question 2
Question 1
Calculate the distance traveled based on the following.
Table 1: Velocity and time table
Time 12 3.25 4.5 6
Velocity 5 6 5.5
7 8 8.5
7 8.5 8 6 7
i) Use the trapezoidal rule.
ii) Use trapezoid and simpson rule together.
iii) Calculate the acceleration for t=7.3.
9.3
7
10
5
Chapter 9 Solutions
Mathematical Methods in the Physical Sciences
Ch. 9.1 - The speed of light in a medium of index of...Ch. 9.1 - The speed of light in a medium of index of...Ch. 9.1 - The speed of light in a medium of index of...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...
Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.3 - Change the independent variable to simplify the...Ch. 9.3 - Change the independent variable to simplify the...Ch. 9.3 - Change the independent variable to simplify the...Ch. 9.3 - Change the independent variable to simplify the...Ch. 9.3 - Write and solve the Euler equations to make the...Ch. 9.3 - Write and solve the Euler equations to make the...Ch. 9.3 - Write and solve the Euler equations to make the...Ch. 9.3 - Write and solve the Euler equations to make the...Ch. 9.3 - Write and solve the Euler equations to make the...Ch. 9.3 - Write and solve the Euler equations to make the...Ch. 9.3 - Use Fermats principle to find the path followed by...Ch. 9.3 - Use Fermats principle to find the path followed by...Ch. 9.3 - Use Fermats principle to find the path followed by...Ch. 9.3 - Use Fermats principle to find the path followed by...Ch. 9.3 - Find the geodesics on a plane using polar...Ch. 9.3 - Prob. 16PCh. 9.3 - Find the geodesics on the cone x2+y2=z2. Hint: Use...Ch. 9.3 - Find the geodesics on a sphere. Hints: Use...Ch. 9.4 - Verify equations (4.2).Ch. 9.4 - Show, in Figure 4.4, that for a point like...Ch. 9.4 - In the brachistochrone problem, show that if the...Ch. 9.4 - Consider a rapid transit system consisting of...Ch. 9.4 - In Problems 5 to 7, use Fermats principle to find...Ch. 9.4 - In Problems 5 to 7, use Fermats principle to find...Ch. 9.4 - In Problems 5 to 7, use Fermats principle to find...Ch. 9.5 - (a) Consider the case of two dependent variables....Ch. 9.5 - Set up Lagranges equations in cylindrical...Ch. 9.5 - Do Problem 2 in spherical coordinates.Ch. 9.5 - Use Lagranges equations to find the equation of...Ch. 9.5 - Find the equation of motion of a particle moving...Ch. 9.5 - A particle moves on the surface of a sphere of...Ch. 9.5 - Prove that a particle constrained to stay on a...Ch. 9.5 - Two particles each of mass m are connected by an...Ch. 9.5 - A mass m moves without friction on the surface of...Ch. 9.5 - Do Example 3 above, using cylindrical coordinates...Ch. 9.5 - A yo-yo (as shown) falls under gravity. Assume...Ch. 9.5 - Find the Lagrangian and Lagranges equations for a...Ch. 9.5 - A particle moves without friction under gravity on...Ch. 9.5 - 2A hoop of mass M and radius a rolls without...Ch. 9.5 - Generalize Problem 14 to any mass M of circular...Ch. 9.5 - Find the Lagrangian and the Lagrange equation for...Ch. 9.5 - A simple pendulum (Problem 4) is suspended from a...Ch. 9.5 - A hoop of mass m in a vertical plane rests on a...Ch. 9.5 - For the following problems, use the Lagrangian to...Ch. 9.5 - For the following problems, use the Lagrangian to...Ch. 9.5 - For the following problems, use the Lagrangian to...Ch. 9.5 - For the following problems, use the Lagrangian to...Ch. 9.5 - For the following problems, use the Lagrangian to...Ch. 9.5 - For the following problems, use the Lagrangian to...Ch. 9.5 - For the following problems, use the Lagrangian to...Ch. 9.6 - In Problems 1 and 2, given the length l of a curve...Ch. 9.6 - In Problems 1 and 2, given the length l of a curve...Ch. 9.6 - Given 10 cc of lead, find how to form it into a...Ch. 9.6 - Prob. 4PCh. 9.6 - A curve y=y(x), joining two points x1 and x2 on...Ch. 9.6 - In Problem 5, given the volume, find the shape of...Ch. 9.6 - Integrate (6.2), simplify the result and integrate...Ch. 9.8 - (a) In Section 3, we showed how to obtain a first...Ch. 9.8 - Find a first integral of the Euler equation to...Ch. 9.8 - Find a first integral of the Euler equation to...Ch. 9.8 - Find a first integral of the Euler equation to...Ch. 9.8 - Write and solve the Euler equations to make...Ch. 9.8 - Write and solve the Euler equations to make...Ch. 9.8 - Write and solve the Euler equations to make...Ch. 9.8 - Find the geodesics on the cylinder r=1+cos.Ch. 9.8 - Prob. 9MPCh. 9.8 - Find the geodesics on the parabolic cylinder y=x2.Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - Find Lagranges equations in polar coordinates for...Ch. 9.8 - Repeat Problem 19 if V=K/r.Ch. 9.8 - Write Lagranges equations in cylindrical...Ch. 9.8 - In spherical coordinates, find the Lagrange...Ch. 9.8 - A particle slides without friction around a...Ch. 9.8 - Write and simplify the Euler equation to make...Ch. 9.8 - Prob. 25MPCh. 9.8 - A wire carrying a uniform distribution of positive...Ch. 9.8 - Find a first integral of the Euler equation for...Ch. 9.8 - Write the Lagrange equation for a particle moving...
Additional Math Textbook Solutions
Find more solutions based on key concepts
Solve each problem involving proportions. Price of Gasoline If 6 gallons of premium unleaded gasoline cost $17....
Mathematical Ideas (13th Edition) - Standalone book
Determine the value c so that each of the following functions can serve as a probability distribution of the di...
Probability and Statistics for Engineers and Scientists
In Problems 1 -6, express the given system of differential equations in matrix notation. x=7x+2y,y=3x2y
Fundamentals of Differential Equations and Boundary Value Problems
Percentiles. The pth percentile of a sorted data set is a number xp such that p of the data fall at or below xp...
Excursions in Modern Mathematics (9th Edition)
Checkpoint1
Use the substitution method to solve this system:
Answers to Checkpoint exercises are found at the...
Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
General Solutions of Systems. In each of problems 1 through 12, find the general solution of the given system o...
Differential Equations: An Introduction to Modern Methods and Applications
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Ferris Wheel For the Ferris wheel described ifind the height of the rider,h, in terms of the time, t, where t is measured in minutes from the beginning of the ride.The distance from the ground to the bottom of the wheel is 9.00 feet (see Section 2.3,Problem 66). Assume the wheel rotates at a rate of 1.5 revolutions per minute.arrow_forwardQuestion 17 In casting metal parts, molten metal flows through a “gate" into a die that shapes the part. The gate velocity (the speed at which metal is forced through the gate) plays a critical role in die casting. A firm that casts cylindrical aluminum pistons examined 12 types formed from the same alloy. Say that we are interested in how the piston wall thickness (measured in inches) influences the gate velocity (measured in feet per second) chosen by the skilled workers who do the casting. The data is provided below. Thickness Velocity TII Velocity Thickness 0.248 123.8 0.628 326.2 0.359 223.9 0.697 302.4 0.366 180.9 0.697 145.2 0.400 104.8 0.752 263.1 0.524 228,6 0.806 302.4 0.552 223.8 0.821 302.4 Considering the coefficient of determination and regression equation and the scatterplot that this data would generate, what can we say about the linear relationship that the regression line provides? O The regression equation is 70.44 + 274.78x and the linear relationship explains about…arrow_forwardPROBLEM 4: An isosceles trapezoid has its legs lengthening while its upper and lower bases both fixed. Find how fast the area of the trapezoid is changing with respect to its legs when the legs are 3 cm. The upper and lower bases are 10 cm and 14 cm.arrow_forward
- 2. A Ferris wheel has a radius of 40 feet and is boarded in the 6 o'clock position from a platform that is 5 feet above the ground. The wheel completes a counterclockwise revolution every 2 minutes. At t=0 the person is at the 3 o'clock position.arrow_forwardSituation 3. A stone is shot on a level ground at an angle of 56° with the horizontal with an initial velocity of 112 m/s. 7. Which of the following gives the time it will take for the ball to hit the ground. a. 19.83 sec b. 16.76 sec c. 17.66 sec d. 18.93 secarrow_forwardAmong the following travelling objects, which has the shortest de Broglie wavelength? Hint: It is not necessary to calculate the wavelength for each object. The quickest way to answer this question is to consider how the de Broglie wavelength depends on the momentum (mass x speed). A Neon atom (mass 3.4×10-26 kg) traveling at a speed of 3×10³ m/s A person of mass 80 kg running at a speed of 3 m/s A bird of mass 2x10-2 kg flying at a speed of 10 m/s A Boeing 777 airplane (mass 2.5x105 kg) flying at a speed of 250 m/s (560 mph) A car of mass 2x103 kg driving at a speed of 50 m/sarrow_forward
- Question 1:Atmospheric pressure P decreases as altitude h increases. At a temperature of 15°C, the pressure is 101.3 kilopascals (kPa) at sea level, 87.1 kPa at h = 1 km, and 74.9 kPa at h = 2 km. Use a linear approximation to estimate the atmospheric pressure at an altitude of 3 km. Please help me explain how to solve these word problems! From the pictures and the word problem above, thanks!arrow_forwardQuestion 4 0/1 pt 59 Details A street light is at the top of a 15 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 7 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 50 ft from the base of the pole? ft secarrow_forwardPlease see pictures for graphics Problem A professional golfer is shopping for a new brand of golf ball. He likes most of the features of one particular brand, but he wants to make sure that the brand has a desirable spin rate (the rate at which the ball spins on its axis after being struck by a golf club). To test the spin rate of this new brand of ball, the golfer hits the brand of ball on 100 five-iron shots, and a computer measures the spin rate for each shot. The computer then produces the following histogram summarizing the 100 spin rates:arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Trigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage LearningMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Cengage Learning
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY