Confused Definition and 1000 Threads

Homework Statement Two electrons separated by a large distance are fired directly at each other. The closest approach in this head-on collision is 4.0 * 10-14 m. One electron starts with twice the speed of the other. Assuming there is no deflection from the original path, determine the initial...

Hello there! Sorry for the dumb question, but for years I have been very curious and confused about this: I just read that they discovered a galaxy 13.7 Bn light-years away -- therefore its light was emitted 13.7 Bn years ago and traveled 13.7 Bn light-years in some line. But, 13.7 Bn years...

I just got my first official introduction to relativity in my textbook (I'm equivalent to a high school senior student). It is part of a chapter on modern physics.It first mentions the two basic postulates and then briefly introduces what length contraction, time dilation, increase in mass...

Hi guys I was wondering after reading some other stuff on the web.. How much is (-1)^{2/6} It is (-1)^{\frac{2}{6}}=(-1)^{\frac{1}{3}}=\sqrt[3]{-1}=-1 OR (-1)^{\frac{2}{6}}=\sqrt[6]{(-1)^2}=\sqrt[6]{1}=1 I'm really confused with this... Any suggestions? Thanks João

Recently I have been having issues knowing when to use the work energy principal vs. impulse momentum or using F=ma and integration. I seem to default with all problems to integrating work done over a path but then messing it up or that not being the proper approach. The issue seems to be...

And now for the long story. I'm a first time poster, long time reader. A little bit about me, I am in my third year of undergrad studying way too many subjects yet not studying at all. I have jumped from philosophy, to physics, to bio, to economics, and now math. During this time...

Homework Statement A 2.30 kg mass on a spring has displacement as a function of time given by the equation x(t) = (7.40 cm)cos[(4.16)t-2.42] a) Find the time for one complete vibration. The back of the book had this same equation but a different mass, so I was able to figure out...

Homework Statement What is the probability the 3 men take the same test? A driving exam has 5 different written driving tests to give to drivers. Two women and three men take the test. What is the probability of each event? a) the 3 men take the same test b) exactly 3 people take the same...

What is the value of \lim\limits_{n\rightarrow\infty}\sup \left\{\frac{n}{x^n}:x\in\left( 1; \infty\right)\right\} It seems to be 0, but what if x = 1+\frac{1}{n}? In that case x^n = e and the above limit is then +\infty, isn't it? I have a feeling I'm somehow wrong, but if I'm not, for what x...

confused!..system stability and linearity 1)-Is y(n)=cos{x(n)} a stable system?? and is the condition s=Ʃ|h(k)|<∞ for stability valid only for LTI systems? actually my book solves the given problem using the above method..but according to me the given system is not LTI SINCE ZERO I/P...

I am a bit confused about laurent series. I know the definitions where the coefficients are expressed as integrals. However, I am confused about how to actually find the laurent series in practice, for analytic functions. The information I can find online is just terrible, some of them do solve...

Homework Statement Determine whether the following sets form subspaces of ℝ2: (a) {(x1, x2)T | x1 + x2 = 0} (b) {(x1, x2)T | x1 * x2 = 0}Homework Equations The Attempt at a Solution I know that a is a subspace and b is not, but I would like to know why. For part A, I let x=[c, -c]T ∂[c,-c]=...

Homework Statement The Lick Observatory has one of the largest refracting telescopes, with an aperture diameter of 36 in. and a focal length of 56 ft. Determine the radii of the first, second, and third bright rings surrounding the Airy disc in the diffraction pattern formed by a star on the...

Confused about voltage induced across inductors :( Hi, As you may have gathered from the topic title, I'm rather confused about inductors :rolleyes: I have another topic going regarding boost converter design, which involves an inductor, but as this confusion/question/observation is really...

OK, so let me start from the beginning... Ive always loved Maths and Physics and I've always got really good grades in olevel and alevel. However i was never sure what i wanted to do. i ended up choosing architecture since it looked cool and involved maths and physics. However i got to know...

The problem statement is "each of the four uniform links has a mass m. determine the horizontal force P required to hold them in place in the vertical plane as shown." I attached the solution, but I don't get when a force causes a +/- virtual work.

Confused about transistor "saturation" region I don't understand why the saturation region is called the saturation region. Take a look at the graph below: According to that graph, the "saturation" region is where the current changes most rapidly, which is the exact opposite of the...

Here is a diagram to help understand what I'm talking about: My textbook had a similar diagram that depicted the beam traveling between the two magnets as hydrogen atoms. Here is how my textbook describes it: "When a beam of atoms that have one or more lone electrons passes through a...

Confused with the use of the word "smooth". [Multi-Variable Calc course] A couple weeks ago we went over the Fundamental Theorem of Line Integrals, which requires "smooth" simple connected curves. My professor's definition of smooth was a curve having "no corners". Now, with Green's Theorem...

A fraction obviously stays the same if you multiply top and bottom by the same constant. If you integrate two equal functions, surely you should get the same answer? By applying the rule in the title, you can get different answers. I'm very confused. Example: 2x/x^2=6x/3x^2 The integral of...

Homework Statement A = 2i + 3j B = -5i + 6j Calculate (draw vector diagram) A + B A - B Homework Equations actually we're just confused as to whether we need to use the angles to answer this or just answer it directly, meaning that for A + B the answer would be -3i + 9j The...

I'm being asked to choose my specialization in ME (for the last 2 years of the BEng) and I'm not sure what to take--I LOVE EVERYTHING. The options are: (a) Thermo-fluids and propulsion (b) Design, manufacturing and materials science (c) Mechatronics Although I didn't like E and M too...

Hi, I've been listening to a Professor Jim Al-Khalil's scipod on time travel. I think this guy is bloody excellent by the way. http://reader.mac.com/mobile/v1/http%3A%2F%2Fwww.jimal-khalili.com%2Fpodcast%2Fjim.rss Anyway, He said to an observer on the Earth a clock on a...

F = Gmm'/r^2 Does this explain the sum or total gravitational force between two bodies?

This seems to contradict the very tools we use to perform the scientific method. Immediately after performing any experiment, the measurement becomes a historical event, and this says that we cannot say that any historical event has actually occurred. Thus, I cannot actually say that I...

So E=vB and {E}={v}cross{B} but if I have for instance v=5j and B=-1k, then E is in the positive i direction. Shouldn't it be in the negative direction? Thanks.

Homework Statement Hello everybody, I have a question that is tied into my lab report regarding centripetal force. The question asks if the frequency of rotation were to increase how would the radius r and the centripetal force change? Homework Equations 2\pif = v/r rearrange for...

Just some general questions as I'm confused with when to use chain rule when not to. For instance, to find the derivative of e^sqrt(x), the right answer is to use chain rule to get e^sqrtx*the derivative of sqrt(x). BUT, isn't there a formula that: d/dx K^x = In(K)*K^x? K for constant and x...

Homework Statement A boat floating in fresh water displaces water weighing 34.7 kN. (a) What is the weight of the water that this boat displaces when floating in salt water of density 1.10 x 10^3 kg/m3? Homework Equations The Attempt at a Solution I am utterly confused. They...

Homework Statement suppose that the dollar cost of producing x washing machines is c(x)= 2000 + 100x-0.1x6^2 a) find the average cost of producing 100 washing machines. b) find the marginal cost when 100 washing machines are produced. Homework Equations c(x)= 2000 + 100x-0.1x6^2: the...

While discussing Taylor's theorem, my professor pointed out that for n=2, Taylor's Theorem says: f(x) = f(x_{0}) + f'(x_{0})(x - x_{0}) + O(|x - x_{0}|^{2}) He then emphasized that O(|x - x_{0}|^{2}) is a much better approximation than o(|x - x_{0}|). But how is O(|x - x_{0}|^{2}) a...

I'm a sophomore math major. I've always liked math, and started college with a double major in chem and math, but now I have decided to drop chem and focus on math. I'm taking calc 3, proofs, and linear algebra ( not the proof-based one) this semester. However, these past days I have had some...

Confused on receiving just one K value for elongation and oscillation Homework Statement Ok. For lab, I had to place 5 different masses on a spring and calculate its initial and final position. I did this with a small, medium and large spring. Then after I gathered my values, I made a...

I'm confused by this problem. Is the answer 1 or 0 OR 1/2? If the series is upto n, then the answer is 1 if the number is odd and 0 if even. If you assume that the answer is x, then 1-x = x and the answer is 1/2. Is the answer 1 or 0 OR 1/2? or simply indeterminate?

\nabla_a[(-g)^{\frac{1}{2}}T^a] = T^a\nabla_a[(-g)^{\frac{1}{2}}]+(-g)^{\frac{1}{2}}\nabla_aT^a I just realized that I don't quite understand how a tensor density behaves when multiplied by a vector. I'm trying to find some clues in D'Inverno's book but I'm getting more confused. Thanks in...

Homework Statement This is a problem from an old exam I am reviewing for practice. Find a good approximation, for x large and positive to the solution of the following equation: y''-(3/x)y'+(15/(4x^2)+x^(1/2))y=0 Hint: remove first derivative term Homework Equations The...

Homework Statement I know that progressive waves are waves moving through a medium causing disturbance, transmitting energy. However, I'm confused over some concepts: 1)When the source emits out energy in the form of waves, if it passes through a medium such as water, the energy moves at v...

Hello, I'm a high school senior from Turkey,and I will be applying to US (and possibly Canadian) institutions this year. Ok, this post is going to be a bit long,but as an international applicant,I have many questions about the admissions process even after hours of Googling,and I'm hoping that...

emission and absorption?? confused! hiii, I am just wondering if anybody can give me a very simple definition of each of the two terms, and what the main difference is. Is emission when a wave enters a denser medium (from air to water)? and absorption when a wave enters a medium of lower...

In chemistry class today, we learned how to determine atmospheric pressure using a mercury barometer, and the pressure of a confined gas using a mercury manometer. I understood how to used the equations fine, but I did not know where they came from. I thought it would be a relatively simple...

Homework Statement Find the formula Σ[n, i =1](2i - 1) = 1+3+5+...+(2n-1) Homework Equations The Attempt at a Solution When I look at the back of the book , I got this solution which is 1, Sigma(2i - 1) = 1+3+5+...+(2n-1) 2, = 1+2+3+...+2n-2(1+..+n) 3, = ((2n)(2n+1)) /2...

Relative energy of simple 2 particle system (confused!) Ok so I have a simple question which I feel I should know the answer to: Setup: Two particles of different mass.. say M and m (where M > m) are moving past each other by some constant velocity. If we view the energy of the system from...

Homework Statement A point particle has a charge equal to –3.64 nC and a velocity equal to 2.75 10^3 m/s i. Find the force on the charge if the magnetic field is (d) 0.75 Ti + .75Tk The solution manual had a positive number. I thought it was a typo until I saw the next problem where they...

I don't get it, is the north pole of a magnet the north seeking; having in mind that like poles repel? Please help.:confused:

Currently, I'm doing some self studying on series, and I'm a bit confused regarding c (the value that the series is expanded about). For example, does the Maclaurin series expansion of Sin(x) and the Taylor series of Sin(x) about c = 1 both converge to Sin(x)? If so, what does the value...

Homework Statement Consider scalar functions u = u(x). Compute the gradients ∇u for: u(x) = (x, y, z) u(x) = (y, z, x) u(x) = (x^2y, 10, z + x) Homework Equations This is a question on my homework for undergraduate Fluid Mechanics. The teacher has been assigning math problems in topics...

Homework Statement A particle's position is given by x = 3.00 - 12.00t + 3t2, in which x is in meters and t is in seconds. Where is the particle when it momentarily stops? Homework Equations The Attempt at a Solution I tried plugging in m and s, like m= 3 - 12s +3s^2 and...

Homework Statement http://kellykemnitz.com/college/Spring%202011/PHYS%20214/PhysicsSolution/Chap%2022%20SM.pdf Problem #22 They chose dq to be in the 1st quadrant, what if I chose dq in any of the other quadrants? Wouldn't that be right also? But that would change the signs of the answer.

Homework Statement This is perhaps the most confused I've ever been. \int sin^{3}7x dx Homework Equations The Attempt at a Solution First, I let u = 7x. du = 7 dx Here's where the trouble begins. \frac{1}{7}\int sin^{3}U dU Now my book claims the following: \int...

Hello! I am confused as always, but this time about the following: In a physics textbook, the following happens: From Newtons second law, V is the velocity and is a function of time, t is time, i is initial and f is final. \begin{equation} m\frac{d}{dt}(v) = F(t) \end{equation}...