Length Definition and 1000 Threads

Mod note: Thread originally posted in a technical math section, so is missing the homework template. I am trying to solve this problem it states as follows "A piece of wire 24 cm long has the shape of a rectangle. (a) Given that the width is W cm, show that the area, A cm^2 of the rectangle is...

I was thinking about the special theory of relativity and how as one approaches the speed of light, ones length contracts. what I would like to know is: If I had an object and I accelerated it towards the speed of light and it contracts in the direction of travel, what happens when it reaches...

Object A goes horizontal line and object B diagonal line in 45 degrees angle (Fig 1). A and B have the same velocity ##v## in x-direction. In y-direction, B has velocity ##v##, A has none. The magnitude of ##v## is not very important, but the total speed of B must be below ##c##. In their own...

How does one get time dilation, length contraction, and E=mc^2 from the spacetime metric? Suppose all that you are given is x12 + x22 + x32 - c2t2 = s2 How do you derive time dilation, length contraction, and E=mc^2 from this? What is the most direct way to do this?

Hi, So I'm working through a bunch of problems involving gradient vectors and derivatives to try to better understand it all, and one specific thing is giving me trouble. I have a general function that defines a change in Temperature with respect to position (x,y). So for example, dT/dt would...

Homework Statement Find the arc length parametrization of the curve r = (3t cost, 3tsint, 2sqrt(2)t^(3/2) ) . Homework Equations s(t)=integral of |r'(t)| dt The Attempt at a Solution I was able to get the integral of the magnitude of the velocity vector to simplify to: s(t) = integral of...

Homework Statement what is the focal length of a plane glass ? Homework EquationsThe Attempt at a Solution place a plane glass in a plane and allow light to pass through it measure its focal length (i think its focal length is infinite )

In Sedra&Smith's microelectronic circuits they have the following expression for the drain current in a MOSFET in saturation iD = 1/2µpCox(W/L)Vov2(1+VDS/VA)But I don't see how this can be correct. Wikipedia also has another expression, see...

In Every measurement there must be uncertanity.In length or In time everything.Lets assume we have a ruler and a rope.If I measure the rope I get a result but I can't say this is exactly true because there's a unncertanity in measurement.Lets suppoe the rope is 100 cm minus or plus 0.5 mm.The...

The Lorentz transformation for motion in the same direction along the x-axis of two frames can be used to derive the length contraction formula. Say we are converting from dx to dx'. The t would obviously have to be 0. That would leave us with dx'=gamma(dx). My question is why dx here has to be...

Homework Statement Sally and Sheldon have identical meter sticks. Sally is on earth, and sheldon is in a spacecraft that moves at 0.5c relative to sally. Sheldon leaves the spaceship at 0.1c relative to the spacecraft in a launch pad, moving away from sally. according to sally, what is the...

Now i haven't checked yet whether or not this is correct, but the formula for the length of an arc that subtends a central angle can also be expressed this way: AC/360 Where: A: Central Angle C: Circumference Is this correct? Thank you for your help.

I've been reading "The Qualitative Theory of Ordinary Differential Equations, An Introduction" and am now stuck on an inequality I am supposed to be able to prove. I am pretty sure the inequality comes from linear algebra, I remember seeing something about it in my intro class but I let a friend...

Homework Statement Consider the diagram below. A 1000 kg block being suspended in equilibrium by cables c and a. Cable c is on a pulley which can vary the length of the cable. Write the constraints of equilibrium. Find the tension in each cable based on varying lengths of cable c between 1.2 m...

Homework Statement Find the exact length of the curve: y= 1/4 x2-1/2 ln(x) where 1<=x<=2 Homework Equations Using the Length formula (Leibniz) given in my book, L=Int[a,b] sqrt(1+(dy/dx)2) I found derivative of f to be (x2-1)/2x does that look correct? The Attempt at a Solution I found f'...

I've been asked to investigate the value of g. My graph shows that the gradient is around 4.4 as when the length was 0.27m, the squared time period was 1.18s (since this is a T2 against L graph). My question is, of course, why? If I am detecting g, which is 9.81 on earth, why did I get such...

Homework Statement A simple method for determining the focal length of a negative lens is shown below. Prove this is true. Homework Equations The Attempt at a Solution The linear magnification formula relates magnification, the distance from the lens to the image (i), the distance from...

I don't know if this can be calculated. I have tried for hours and days to isolate/calculate the radius and angles of the circle in order to be able to calculate length 1. I have tried using cos/sin-relation formulas and triangle formas - but Iam stuck. Any hints would be greatly appreciated...

I'm searching for a week from now and can't find out difference between optical and geometrical length in optical path. Can anyone explain or give me idea or how can I find it out?

Homework Statement A curve has the equation y2 = x3. Find the length of the arc joining (1, - 1) to (1, 1). Homework Equations The Attempt at a Solution I took the integral of the distance and tried to evaluate from -1 to 1. L = [intergral (-1 to 1) sqrt (1+(dy/dx x^3/23/2)2 dx] Evaluated I...

Homework Statement Find the length of the path traced out by a particle moving on a curve according to the given equation during the time interval specified in each case. The equation is r(t) = a(cos t + t sin t)i + a(sin t - t Cos t)j, 0</=t</=2pi, a>0Homework Equations Arc length =...

I am reading "Introduction to Ring Theory" by P. M. Cohn (Springer Undergraduate Mathematics Series) In Chapter 2: Linear Algebras and Artinian Rings, on Page 61 we find a definition of the length of a module. Some analysis follows, as does a statement of Theorem 2.5. I need help to understand...

Homework Statement An optical telescope with a 12mm eyepiece makes the Moon appear to have an angular diameter of 30 degrees. What is the focal length of the telescope's objective? Homework Equations magnification=focal length of objective/focal length of eyepiece The Attempt at a...

Hi! The question is simple, seemingly... Doubling the length of a wire, doubles the resistance of the wire... Why? There is one interesting point to it: Doubling the length of the wire also makes the ELECTRIC FIELD weaker TWO times. That automatically makes the current smaller two times...

Find the optimum frame length nf that maximizes transmission efficiency for a channel with random bit erros by taking the derivative and setting it to zero for the following protocols: (a) Stop-and-Wait ARQ (b) Go-Back-N ARQ (c) Selective Repeat ARQ My work has been uploaded I am a bit rusty on...

Homework Statement A traveler in a rocket of length 2d sets up a coordinate system S' with origin O' anchored at the exact middle of the rocket and the x' axis along the rocket’s length. At t' = 0 she ignites a flashbulb at O'. (a) Write down the coordinates t'_F, x'_F, and t'_B, x'_B for...

find the length of an arc of a helix r(t)=(sint,cost,t) from the point (0,2,0) to (0,5,2pi) would the interval when integrating be from 0 to 2pi because t in the case is (z=t)? please say yes. please say yes.

let C be the curve of intersection of the parabolic cylinder $x^2=2y$ and the surface $3z=xy$. find the exact length of C from the origin to the point (6,18,36). please help! this is the last question i have left from this assignment and i have no idea how to do it. i have grading to do and a...

Consider the following case: First frame S, which is earth. Second frame S', which is rest relative to rocket. Rocket are moving in speed of v relative to earth. Problem: Due to time dilation, from frame of S, the clock in rocket is running slower. Likewise, due to time dilation, from...

Homework Statement Find the arc length of one of the leaves of the polar curve r= 6 cos 6θ. Homework Equations L = ∫sqrt(r^2 + (dr/dθ)^2) dθ (I use twice that since the length from 0 to π/12 is only half the petal) The Attempt at a Solution I seem to get an integral that can't be...

Find the length of largest square accommodated in a right angled triangle whose perpendicular length is 16 m and base's length is 8 m. My attempt I have tried a lot to find the length but every time it comes in fraction , i think that the figure i have made is wrong . The answer I am getting is...

10. The average lifetime of a pi meson in its own frame of reference is 2.6 x 10^-8 s. If the meson moves with a speed of 0.95c, what is (a) its mean lifetime as measured by an observer on Earth and (b) the average distance it travels before decaying, as measured by an observer on...

Objects in motion relative to an inertial frame S are measured to have contracted lengths in S in the direction of motion. How does Special Relativity view this contraction physically? For a concrete example, suppose I have a bar of steel moving lengthwise and, as it moves past me (in frame...

Homework Statement Hi guys! Here is my problem: A Children's slide is 20 ft long and makes an angle 30° with the horizontal. If the coefficient of sliding friction is 0.05 and the child starts from rest at the top, with what speed does he reach the bottom? I want to say it is about...

Of course, I need to find the first derivative and integrate its norm. α'(t) = (1, 0, (1/2)t^2 - (1/2)t^-2) ∫ [1 + (1/4)t^4 + (1/4)t^-4]^(1/2) dt, t = 1 to t = 3. Have I simply forgotten useful integrals? α'(t) = (e^t, -e^-t, root2) ∫ [e^2u + e^-2u + 2]^(1/2) du, u = 0 to u = t.

Reposting to this section of the forum instead of the Introductory Physics homework section. So let's say a guy travels at 0.5c in a spaceship from planet 1 to planet 2. Am I right in saying that: proper time = time measured inside space ship proper length between planets = length the...

Hi, I am trying to derive the path length of a charged particle in a B-field. I am assuming the particle will travel a distance L along the applied field. Using the following equations for the path length of a helix and gyroradius: Helix defined as [a*cos(t),a*cos(t),b*t] for t on [0,T] has...

Hello! 1. The problem statement and all variables AIM: Calculating persistence length P of a single dsDNA molecule from a data set of force F (to the molecule) vs. extension x measurements. Experimental background: pN forces were applied to a single dsDNA molecule spanned between two...

Hello! From a data set of F-x measurements of a single dsDNA molecule I want to calculate the persistence length P . So I plotted \frac {1} {\sqrt{(F)}} vs. x and fitted these data points (linear). According to an interpolation formula the extension x of a worm like chain with contour...

All - my first post, and as a lay person interested in quantum physics, forgive me if my questions are naive or ill-informed. Is it possible that the Universe inflated then exploded into being from a singularity smaller than Planck length? If I understand the concepts properly, the Planck...

Hey! I just started study landsurveying and got a task i don't figure out how to get the right answer. My goal is to find the length of one of the sides in a triangle, but i can not use pytagoras formula. Here is the formula i am supposed to use (dont care about the text, its norwegian)...

Homework Statement for diagram 2 , i just can't understand why S1P -t + ut (upper ray ) is longer than the lower light ray (S2P) , ? if I take S2P minus ( S1P -t + ut ) , then i would get mt t (thickness ) is negative , which is indeed wrong! so it has shown that optical path of the upper...

Hi guys, I've been thinking about this experiment for the last few hours and I have a few questions which I am deeply confused about. 1) In the light clock experiment, where light clock is set up so that light travels vertically, and the train carrying the clock travels horizontally, wouldn't...

It seems self-evident that mathematics must keep uncertainty at arms length. For example, to deal with probability mathematics establishes a set of assumptions. The assumptions themselves are not probabilistic - i.e. the "laws" of probability are assumed to be true "all the time", not...

Homework Statement please refer to the photo, Homework Equations The Attempt at a Solution why can't I directly use the lens maker formula to get the ans ? my working is 1/f = ( (1.5-1.33) /1.33) x ( (1/20) + 0 ) ...finally , i get my f = -160cm. the radius of curvature of...

The at rest distance between Betty the astronaut and a flag in open space is 1 unit. If Betty approaches the flag at constant speed while laying out metre rulers, will she have laid out 1 unit of at rest rulers when she reaches the flag? Or will the number of rulers laid out exceed 1 due to...

In the field of acoustical physics the mathematical relationship (wavelength (lambda) = speed of sound (velocity) / frequency (cycles per sec)) indicates that lambda (wavelength) would increase if the speed of sound were increased while the frequency (cps) is held constant (e.g., 100 Hz)...

Homework Statement A converging meniscus lens is made of glass with index of refraction n = 1.55, and its sides have radii of curvature of 4.5 cm and 9 cm. The concave surface is placed upward and filled with carbon tetrachloride which has index of refraction n' = 1.46. Determine the focal...

Considering that speed of light is constant and finite, then why are the time dilatation and length contraction infinite to a frame of reference moving at the speed of light? We know that a moving frame of reference experiments time dilatation and length contraction from the point of view of a...

Hello, I am new here. I was reading Wangsness electromagnetic fields and he delves into a short discussion about poisson-boltzman equation/Debye length before introducing the point-form of Ohm's Law. Just wondering what the significance of this was and how these two things are related.