Exercise Definition and 578 Threads

Exercise is any bodily activity that enhances or maintains physical fitness and overall health and wellness.It is performed for various reasons, to aid growth and improve strength, preventing aging, developing muscles and the cardiovascular system, honing athletic skills, weight loss or maintenance, improving health and also for enjoyment. Many individuals choose to exercise outdoors where they can congregate in groups, socialize, and enhance well-being.In terms of health benefits, the amount of recommended exercise depends upon the goal, the type of exercise, and the age of the person. Even doing a small amount of exercise is healthier than doing none.

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  1. P

    Understanding Central Charges in Weinberg's Book

    Hi all, I'm having trouble solving problem 3 at page 105 in Weinberg's book, The Quantum Theory of Fields, Vol. 1: Derive the commutation relations for the generators of the Galilean group directly from the group multiplication law (without using our results for the Lorentz group). Include the...
  2. T

    Solve Calculus Exercise: Find Perpendicular Tangent Line to y=x^3-1

    Homework Statement Find the equation of a tangent line to the curve y = x³ - 1, that is perpendicular to y = -x (I mean the tangent line should be perpendicular to y=-x, sorry for my bad english). Homework Equations The Attempt at a Solution y = x^3 - 1; \;\; y' = 3x^2 If the tangent line...
  3. L

    Basic exercise for finding a Lagrangian from the Landau's Mechanics

    Basic exercise for finding a Lagrangian from the Landau's "Mechanics" Hello everyone! Homework Statement I've just started preparing for the classical mechanics course using only Landau & Lifgarbagez, so I'm doing everything according to their formulation. And so I solved an exercise...
  4. A

    Solve Arctan 2Arctan(1/3) + Arctan(1/7) = π/4: What's Wrong?

    2Arctan(1/3) + arctan(1/7) = π/4 I try to solve it like this: = sin(2arctan(1/3)) + sin(arctan(1/7) = sin(π/4) But this isn't correct What have I done wrong?
  5. M

    Real Analysis (Rudin) exercise with inequalities

    Homework Statement Suppose k>2, x, y in R^k, |x-y| = d > 0, and r > 0. Prove if 2r > d, there are infinitely many z in R^k such that |z-x| = |z-y| = r (In Principles of Mathematical Analysis, it is problem 16(a) on page 23.) Homework Equations |ax| = |a||x| |x-z| < or = |x-y| + |y-z|...
  6. V

    Help with Linear Algebra exercise

    Homework Statement Hi guys, I am new to this forum. I got a final exam tomorrow and the professor told us to solve some exercise before it. I came up with one exercise that I don't know how to do, at all. Hope you guys can give me some light. Here it goes. Know that the multiplication of...
  7. E

    Finding Eigenstates and Energies in Quantum Mechanics Exercise

    Homework Statement Let there be 3 particles with mass m moving in the 1D potential: \frac{k}{2}[(x_1-x_2)^2 + (x_2-x_3)^2 + (x_1-x_3)^2] where x_i is the coordinate of the particle i. 1)Show that with the following coordinat change the Schroedinger equation is easy to solve: y_1=x_1-x_2...
  8. E

    Solvable Group: Need Help Understanding Fraleigh's Exercise

    Hello... I have a question about the solvable group. I read a Fraleigh's 'A first course in abstract algebra', there is a question in sec56, exercise3. It says "The Galois group of a finite extension of a finite field is solvable." is true... I can't figure out why it's true. I think this...
  9. G

    Internat. Math Olympiad exercise. Weird function.

    Homework Statement A friend of mine tried to classify for the IMO a few days ago (he didn't do so well). A problem he had to solve was: f(x + xy + f(y)) = (f(x) + 1/2)(f(x) + 1/2) I didn't really understand what he said later. First he told me to find the values of X and Y for which...
  10. M

    Is M_n(K) isomorphic to K \otimes_F M_n(F) as F-algebras?

    So this is supposed be an introductory problem for tensor products that I was trying to do to verify I am understanding tensor products...turns out I'm not so much Show that M_n(K) is isomorphic as an F-algebra to K \otimes_F M_n(F) where F is a field and K is an extension field of F and...
  11. J

    Law of Total Probability Exercise

    Homework Statement Avril has certain standards for selecting her future husband. She has n suitors and knows how to compare any two and rank them. She decides to date one suitor at a time randomly. When she knows a suitor well enough, she can marry or reject him. If she marries the suitor, she...
  12. S

    Why don't muscle cells burst when you exercise?

    One way muscle grows is muscle hypertrophy where sarcoplasmic fluid increases inside the muscle cell. Wouldn't this burst the cell membrane, I can understand how organelles can replicate but what about the cell membrane. I know this sounds like a stupid question but please help. Thanks :smile:
  13. P

    FEMM Exercise for Electrical Engineering Student Maria

    Hello, I am a student of electrical engineering of Madrid (Spain).. And I need to present a simple but original exercise with the program Femm. I have done a workshop of 10 hours and more or less I control the basic thing, have done some exercise as bobbins, condensers, etc... I was...
  14. K

    Differential Forms Integration Exercise

    Hi all, I posted this awhile back in the homework sections of the forums and received only one reply, which suggested that I post it here instead, though I understand that it belongs in the homework section. The fundamental problem is not this particular exercise but about integration of...
  15. K

    General relativity, integration over a manifold exercise

    Homework Statement The problem I am facing is 2.9 in Sean Carroll's book on general relativity (Geometry and Spacetime) I should note that I am not studying this formally and so a full solution would not be unwelcome, though I understand that forum policy understandably prohibits it. The...
  16. J

    Vector force conceptual exercise help.

    Homework Statement This was a problem I needed help on. A train is traveling up a 3.73 degree incline at a speed of 3.25 m/s when the last car breaks free and begins to coast without friction. a). how long does it take for the last car to come to rest momentarily? b). how far did the...
  17. T

    Szabo, A.; Ostlund, N. S. (1996). MODERN QUANTUM CHEMISTRY Exercise 3.21

    Homework Statement "Use definition (3.219) for the STO-1G function and the scaling relation (3.224) to show that the STO-1G overlap for an orbital exponent zeta = 1.24 at R = 1.4 a. u., corresponding to result (3.229), is S12 = 0.6648. Use the formula in Appendix A for overlap integrals. Do...
  18. M

    Linux command exercise - help a total noob?

    Firstly, I've literally never used a Linux machine in my life. My phys prof thought it would be a good idea to get us acquainted with the system, but didn't want to actually teach it... The following is an exercise in Linux. I'm having a lot of trouble finding the commands to accomplish this...
  19. C

    Medical How to Incorporate Vigorous Exercise into Your Routine

    http://online.wsj.com/article/SB10001424052748704350304574638331243027174.html Doesn't sound like vigorous exercise to me at all. How on Earth can biking at a speed of 10 miles an hour be vigorous exercise? :confused:
  20. T

    Verifying Sylow-p Groups of Sp: A Homework Exercise

    Homework Statement This question is about sylow-p groups of Sp. I've proved these parts of the question: A. Each sylow p-sbgrp is from order p and there are (p-2)! p-sylow sbgrps of Sp. B. (p-1)! = -1 (mod p ) [Wilson Theorem] I need your help in these two : C. 1) Let G be a group...
  21. D

    Very simple - noobish physic exercise.

    Homework Statement Note that am a beginner in physics,hardy know any,so be gentle (: There are three particles in a line below. The question is where must we put Q3 so it will get 0 total power. Q1=6 mC Q2=15 mC Q3= -8 mC In a line of 2 meters like this...
  22. E

    Exercise Program Homework: Calculating Jumps & Time Needed

    Homework Statement A 75kg person is put on an exercise program by a physical therapist, the goal being to burn up to 500 food calories in each daily session. Human muscles are about 20% efficient in converting energy into mechanical energy. The exercise program consists of a set of consecutive...
  23. Z

    Is it Possible to Rescue a Stranded Crew Member on a Spinning Space Station?

    If a crew member were stranded on space station, due to spin, would he be rescuable? For example if an extended part bent or broke, putting the ship into a spin or tumble. If it were a one axis spin, perhaps a large mass, attached at a distance would change moment of inertia sufficient to...
  24. S

    How Does Gauss's Law Apply to Nested Spherical Shells with Charges?

    Homework Statement A small conducting spherical Shell (#1) with inner radius a and outter radius b is concentric with a larger conducting spherical shell (#2) with inner radius C and outter radius d. The inner shell has a total charge (-3Q), and outter shell has a charge ( +5 Q). a) Use...
  25. T

    Cohen-tannoudji exercise solutions

    So I am in a quantum course and as a reference text we have cohen's quantums mechanics volume 2. I've been using it to practice and study for the midterm, I've been doing the exercises but not sure if I'm doing them right, does anyone know if there are solutions to the exercises in this book...
  26. Q

    Why Does \(\nabla_{c} E_{ab} = 0\) Follow from the Anti-Symmetry of \(E_{ab}\)?

    Homework Statement Problem 2, chapter 3 of Wald's General Relativity. The details don't matter much, but it is given a totally anti-symetric tensor field Eab such that EabEab=2(-1)^(s), s being the signature of the metric. I have checked a solution to the exercise, and somewhere during the...
  27. Q

    What is the Position Vector of an Electron Moving in a Helix?

    Homework Statement An electron moves in a helix : \vec{r}(t)=v_{z}t \hat{z}+a e^{i\omega_{0}t}(\hat{x}-i\hat{y}), where a is the radius of the helix and v_{z} the relativistic z-component of the velocity. 1) Find the position vector of the electron in a system of reference that is moving...
  28. I

    QM Collision Exercise: Find Gamma Ray Wavelength in CMS

    Homework Statement A 2 MeV (kinetic energy) positron collides with an electron at rest. Find the wavelength of the resulting two gamma rays in the center of mass system. use the fact that E^{2} - p^{2}c^{2} = m^{2}c^{4} is invariant between frames of reference for any system)Homework...
  29. C

    Medical Why Isotonic Drinks are Better After Exercise

    Hi guys, i am not sure if its here i should post this but couldn't find a better category. Just wondering, after exercising, we're often thirsty and drinking isotonic drinks is better than drinking normal water, why is that so?
  30. T

    Do what? exercise may make you gain weight?

    i don't see how this makes any sense at all. http://www.time.com/time/health/article/0,8599,1914857,00.html
  31. R

    Problem, exercise, anomalous magnetic moment interaction

    I need to solve an exercise on Quantum Field Theory that reads as follows: Supousse that the electron has an anomalous magnetic moment, which makes the QED Lagrangian (density) to have an additional term: L'_I(x) = \frac{2ie}{m} \bar{\psi}(x) \sigma^{\alpha\beta} \psi(x) F_{\alpha\beta}(x)...
  32. B

    How Does Torque Relate to RPM in a Gyroscopic Exercise Tool?

    I want to know the relationship between the resistive forces of a gyroscopic exercise tool and the revolutions per minute of the rotor.
  33. B

    Designing a Ramp for Exercise Equipment Delivery

    You are designing a delivery ramp for crates containing exercise equipment. The crates weighing F_1 will move at a speed of v at the top of a ramp that slopes downward at an angle \phi. The ramp exerts a kinetic friction force of F_2 on each crate, and the maximum static friction force also has...
  34. T

    Solving Simple Homework Problems: An Exercise in O(x^4) Analysis

    Homework Statement Hi, I have been having huge problems with dealing with these kinds of problems, I would appreciate atleast some guidance in dealing with these sorts of problems, I think the major problem is just how I learned to solve them, I have been looking for resources on the net, but...
  35. H

    Help with modal logic exercise

    I'm teaching myself modal logic, and I'm curious about the following exercise, taken from this book... Homework Statement Prove T:\; \Box A \rightarrow A using the following rules: Homework Equations Given the structure M=<W,R,P> in which W and P are as they are in a model, and R...
  36. P

    Ideas for a physics related programming exercise

    I'm a physics student and need to come up with an idea for a relatively simple program for a programming exercise. The scope of the work is 5 ECTS credits which translates to about three weeks full time work. The program should probably include a simple gui so part of the effort goes into...
  37. K

    Temperature Changes During and After Exercise: What Causes the Difference?

    Hi, Does anyone know how much your temperature increases after exercise? and why the difference?
  38. Z

    Calculating Speed After a Collision: An Exercise in Momentum

    Homework Statement There are 2 identical boxes. One box is stationary. Another box is moving towards the other box at 6 m/s. After the collision what is the speed of the originally stationary box? Give a numerical answer in m/s. Homework Equations p=m1v1 W=K2-K1 The Attempt at a...
  39. L

    Exercise Ball Recall: 3M Fitness Balls Recalled by CPSC

    http://abcnews.go.com/Business/WellnessNews/story?id=7354193&page=1 If there was 1 piece of exercise equipment that Evo would buy, ... hmm.
  40. F

    Exercise bike that produces electricity

    Ok. Folks, first off this is my first post, and I am looking for some answers to some questions I have. I hope someone has the time to answer them :) First off, I'm no expert in physics. I know a billion times more than any of my friends but believe me that is not saying much. I have never...
  41. L

    Strang's book, question about exercise

    Hello, now I'm reading G.Strang's book Linear algebra and its Applications, chapter about Hermitian matrices and complex matrices. In one of the exercises, there's a sentence: "The real part of z=a+\mathrm{i}b is half of z+\overline{z}, and the real part of Z is half of Z+Z^H." I know...
  42. S

    Exercise 56 in chapter 1 of Lang's algebra

    Hi, I have been puzzled by this exercise for some time. I won't repeat it here as the hint refers to other exercises, so I would be copying a whole page of the book. My question is as follows. After having defined the sets S_i and picked a complex number s not belonging to any of the S_i...
  43. D

    Understanding Exercise c: Is the Flux Q an Integral?

    Homework Statement http://img528.imageshack.us/img528/3623/47021164uu2.png http://img18.imageshack.us/img18/8634/21260108gr1.png The Attempt at a Solution I have a question about exercise c. The flux Q is the integral, isn't it? So why do they use the word "then"?
  44. U

    Is There an Exercise Bike That Generates Heat?

    Hi all, I was wondering if there was such thing as a heat creating exercise bike. Made for the purpose of creating heat. It's really cold and the power bill is going up and I am wondering if this idea is stupid or has it already been tried. I would buy one. Any thoughts?
  45. D

    Proving That T Has a Supremum: A Mathematical Exercise

    Homework Statement Let S be a set of positive real numbers with an infimum c > 0 and let the set T = {\frac{1}{t} : t \in S}. Show that T has a supremum and what is it's value. The attempt at a solution Ok, so the value must be \frac{1}{c}. But I'm unsure how to start proving...
  46. J

    Exercise on Posets, Chains and upper bounds

    Homework Statement Suppose X and Y are sets. Let P be all pairs (A,f) where A is a subset of X and f is a function from X to Y. Then P is a poset with the relation (A,f)=<(B,g) iff A is a subset of B and f is the restriction of g to A. Show that if C={(Ai,fi)|i in I} is a chain in P, there is...
  47. R

    Solving Exercise 8.9 from ECE 3025 Lecture Notes

    Homework Statement http://img168.imageshack.us/my.php?image=eightss5.png Homework Equations I have the lecture notes that is 14pages long that covers this particular chapter and the lecture note provided by my professor does not mention anything with switchs in the lecture note...
  48. P

    Ideal Gas Exercise: Homework Statement & Solution

    Homework Statement A cylinder with a frictionless piston is placed horizontally in an atmosphere pressure 1 * 105 N/m2. A gas in the cylinder is initially at a temperature of 300K with a volume of 6.0 * 10-3 m3. Then the gas is heated slowly to 400K. How much work is done by the gas in the...
  49. arivero

    Breaking SU(3)xU(1) to SU(2) Exercise: A Search for Solutions

    Can anyone provide a pointer to the exercise of higgs breaking SU(3)xSU(2)xU(1) down to SU(2)? I expect it to be solved somewhere in the web...
  50. S

    What would you put in a survival guide for the end of the world?

    Well I thought it'd be nice to do a little thought exercise. Earlier today I was thinking about how much knowledge & wisdom we've acquired over the years, and was wondering what would happen if something truly disastrous was to happen to the planet... Now I'm going to set up a situation and...
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