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 24P
For the following problems, use the Lagrangian to find the equations of motion and then refer to Chapter 3, Section 12.
Do Problem 23 if
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Question # 10 Calculate The Average Speed
Reference Q. 15261
Al and Bob, who live in North Vancouver, are Seattle Mariners fans. They regularly drive the 264 km from their home to the
ballpark in Seattle. On one particular day, Bob drove to the game. On the return journey Al was able to increase their average
speed by 10% and save 18 minutes on the travelling time.
Calculate the average speed at which Bob drove the game.
Calculate the time it took Al to drive back from the game.
biuov lout rbirw.(HO HDlonisrte bne H) anscue to asitenob n
ebor to Jriait nl
bne zenu nb ba nlera mont abnuogrnop uol or ot ascisv Hàso
2s alomsxe 1o) loutio elom eq pseh ar 0o2om to tedmun srir yd a
noimss ol negyxo to elom 1ag HA6 LODvig iweiT (onsrio tr
mot bezeelen sd nga ot nene to muons ar upda yse uea air a
Sanoibeg no
In the previous Problem Set question, we started looking at the position function s(t)st, the position of an object at time tt . Two important physics concepts are the velocity and the acceleration.
If the current position of the object at time tt is s(t)st, then the position at time hh later is s(t+h)st+h. The average velocity (speed) during that additional time hh is (s(t+h)−s(t))hst+h−sth . If we want to analyze the instantaneous velocity at time tt, this can be made into a mathematical model by taking the limit as h→0h→0, i.e. the derivative s′(t)s′t. Use this function in the model below for the velocity function v(t)vt.
The acceleration is the rate of change of velocity, so using the same logic, the acceleration function a(t)at can be modeled with the derivative of the velocity function, or the second derivative of the position function a(t)=v′(t)=s′′(t)at=v′t=s″t.
Problem Set question:
A particle moves according to the position function s(t)=e5tsin(7t)
Enclose…
Two ships are sailing in the fog and being tracked on a small screen. At some point in time, t=0, the first ship, the Andy Daria (AD), is at a point 900 mm from the bottom left corner of the screen along the lower edge. The other ship, the Helinski (H), is located at a point 100 mm above the lower left corner along the left edge. One minute later, the AD has moved to a location that is 3 mm west and 2 mm north of the previous location. The H has moved 4 mm east and 1 mm north. Assume that they will continue to move at a constant speed on their respective linear courses.
Create an illustration of the situation.
Create a parameterization for each of the vessels.
Will the two ships collide if they maintain their speeds and directions? If so, when and where?
Determine the minimum distance between the ships and the time at which they are the closest.
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
Prove sinh(x+y)=sinh(x)cosh(y)+cosh(x)sinh(y) by changing the expression to exponentials.
Calculus Volume 1
Negative equilibrium. Find equations for the two lines in the previous Mindscape and use them to solve for the ...
The Heart of Mathematics: An Invitation to Effective Thinking
The spring force F and displacement x for a close-wound tension spring arc measured as shown in Fig. P1.3. The ...
Introductory Mathematics for Engineering Applications
In each of problem 1 through 14, find a fundamental matrix for the given system of equations. In each case, als...
Differential Equations: An Introduction to Modern Methods and Applications
[T] In the following exercises, identify the value of x such that the given series n=0an is the value of the Ma...
Calculus Volume 2
10. Course Enrollments Suppose that all of the 1000 first-year students at a certain college are enrolled in a ...
Finite Mathematics & Its Applications (12th Edition)
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
- In Figure 208, gear A is turning at 120 revolutions per minute and gear B is turning at 3.6 revolutions per second. Determine the ratio of the speed of gear A to the speed of gear B.arrow_forwardFigure 219 shows a compound gear train. Gears B and C are keyed to the same shaft; therefore, they turn at the same speed. Gear A and gear C are driving gears. Gear B and gear D are driven gears. Set up a proportion for each problem and determine the unknown values, x, y, and z in the table. Round the answers to 1 decimal place where necessary.arrow_forwardIn the previous Problem Set question, we started looking at the position functions (t), the position of an object at time t. Two important physics concepts are the velocity and the acceleration. If the current position of the object at time is as (t), then the position at time h later is a (t+h). The average velocity (speed) during that additional time his (s(t+h)-s(t)) If we want to analyze the instantaneous velocity at time t, this can be made into a mathematical model by taking the limit as h→0. i.e. the derivative a' (t). Use this function in the model below for the velocity function (). h The acceleration is the rate of change of velocity, so using the same logic, the acceleration function a(t) can be modeled with the derivative of the velocity function, or the second derivative of the position function a(t) = ✔ (t) =" (t). Problem set question: A particle moves according to the position functions (t) = etsin (2). Enclose arguments of functions in parentheses. For example, sin…arrow_forward
- A hot-air balloon is released at 1:00 P.M. and rises vertically at a rate of 6 m/sec. An observation point is situated 100 meters from a point on the ground directly below the balloon (see the figure). If t denotes the time (in seconds) after 1:00 P.M., use an equation to express the distance d between the balloon and the observation point in terms of t.arrow_forwardTask 4: Newton's Law of cooling, which also can be applied to heating problems, states that "the time rate of change of the temperature of a body is proportional to the temperature difference between the body and its surrounding medium." If a tank of water has a temperature of 70° F and the air temperature is OF. After 35 minutes the temperature of the tank is 45° F. Assume: T: temperature of the body and Tm : temperature of the surrounding medium. (i) Formulate a differential equation to express the previous system. (ii) Solve this first order differential equation using Laplace Transform.arrow_forwardrandom sample of 100 families the variances of the savings is one quarter of the variance of the income and the coefficient of correlation between S, and Y, is found to be 0.40. Obtain the estimate of m.arrow_forward
- PS #3 7. Can a man hit a 208 - ft ceiling of an Astrodome if he is capable of giving a baseball an upward velocity of 100 fps from a height of 7 ft?arrow_forwardOnly #55. Use problem 54 to solve problem 55, and change the radius of the hole in problem 55 from 1 inch to 1 foot.arrow_forward2A.16 Please refer to the attached image for my question. Please show ALL your work. Thank you!arrow_forward
- How much time will it take them to travel there, and how much time could they save by going 80mph?arrow_forwardProblem 3 When a red blood cell is pumped it moves a distance s (in millimetres), in a given time, t, (in seconds) described by the following equation: s = 0.005t2 + vot In this equation, vo is the initial velocity, in mm s-1. Distance is measured in millimetres and time is measured in seconds. Use the equation to find how long it takes a red blood cell to travel a distance of 1000 mm. The cell had an initial velocity of 4 mm s1. -btV62 -4ac x = 2a (quadratic formula) To use the quadratic formula, the equation needs to be in form at? + bt +carrow_forwardFind the reference number for t=4arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
Points, Lines, Planes, Segments, & Rays - Collinear vs Coplanar Points - Geometry; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=dDWjhRfBsKM;License: Standard YouTube License, CC-BY
Naming Points, Lines, and Planes; Author: Florida PASS Program;https://www.youtube.com/watch?v=F-LxiLSSaLg;License: Standard YouTube License, CC-BY