Length Definition and 1000 Threads

two wires A and B made from two different materials have temperature coefficient of resistance equal to 0.0025 and 0.0005 ohm per degree Celsius respectively. It is desired to make a coil of wire having a resistance of 1200 ohms with a temperature coefficient of 0.001, using a suitable length of...

I'm thinking about a very basic scenario in special relativity, but I've got something backwards, and I could use help understanding why it's wrong. Suppose a rod R is moving past an observer O at speed v. The observer wants to know how long the rod is, so he starts his stopwatch as soon...

EDIT: Okay now that the admin has cleaned up my mess, please scroll down to see the correct image and the question on the 3rd post in this thread.

find the arc length function for the curve $y=2x^{3/2}$ with starting point $P_{0}(1,2)$. how do i do this? this is what I've done so far. $y'=3\sqrt{x}$ $1+(3\sqrt{x})^2=9x+1$ $\int_{a}^{b} \ \sqrt{9x+1},dx$ what's my a and what's my b?

$y^2=4(x+4)^3$ $0 \le x \le 2$ $y=2(x+4)^{3/2}$ $y'=3(x+4)^{1/2}$ $\int_{0}^{2} \ \sqrt{1+9(x+4)},dx = 13.5429$ is that right?

Hello all, My lab recently purchased a deformable lens, which can change its focal length from 140 mm to 40 mm and anywhere in between, based on current applied to it. I'm wondering how to use a beam profiling camera to measure the focal length of this lens at various current levels. We...

Hi Im trying to increase the length of a movement of a rope so when one rope is pulled the other rope movement is increased x 2 (it is attached across). So far i have tried gears whice has somewhat worked but it increases the force as well. Is there any other way to achieve this amplification...

how do i use the nspire to find arc length?

If so, is 'its half' also not a real size of space? What I am asking is pretty much; what is the meaning of the notion of a 'smallest possible' 3d area? What is the meaning of that cusp between 2d and 3d? Almost like asking what is in between 1.999999999999(repeating) and 2. Must...

Is there a way to map time-like curves in Minkowski space to curves in a Euclidean space such that the length of the curve in the Euclidean space is equal to the proper time of the curve in Minkowski space?

I can't figure out why the length the a pipe (L) increases the change in driving pressure with respect to this law: Delta P = (8*mu*L*Q)/(pi*(r^4)) I would think that delta P wouldn't change because the fluid is incompressible. Does anyone have a conceptual explanation for the simple...

Homework Statement We take a sphere (1mm) which has a parabolically changing refractive index, which is given in a function. Homework Equations Depending on the gradient of the refractive in the sphere, how does it correlates with the focal length. The Attempt at a Solution I...

Homework Statement The ##m = 75kg## man jumps off the bridge with ##v_1 = 1.5 m/s##. Determine the unstretched length ##l_0## of the cord in order that he stops momentarily above the surface of the water. The stiffness is ##k = 80 N/m##. Picture...

I'm building a telescope and one of the more important choices I'm making is what focal length to make the mirror, my understanding is the longer the focal length the closer you see far away stuff, but the field of view diminishes a bunch. I've seen both long tube dobsonians and short tube ones...

Hi, The focal length of the Plano-Convex lens as calculated by the lens maker equation: Does it work when light crosses the lens from the convex side, planar side, or both? Thanks.

After reading an article on Planck length, I began to wonder whether or not the theoretical limit implied that position could be quantized in whole integer multiples of Planck length? To demonstrate what my question is asking mathematically I hope you will scrutinize the equations below: If...

We are all taught that the TEM modes in coax have no low frequency cut-off. So this would suggest that nothing different happens for very long wavelengths that are longer than the coax itself. However, in this rather shocking paper here: http://vixra.org/pdf/1403.0964v5.pdf ...it is suggested...

prove the length of QR is fixed

So I'm designing a system that requires an extremely high amount of current for an extremely short pulse lengths. These pulses would be consecutively spaced at relatively large intervals from one another. I'm just wondering if there is some sort of instantaneous power limit to wires, even if the...

I learned in my calc 1 class that to calculate the arc length of a curve, we are to compute the integral of the function. For example, the integral of a function that describes the path of a thrown baseball would give the total distance traveled by the baseball (I hope I'm using the term arc...

Hello everyone! I am generating a signal as a function of time. This is an irregular signal generated by using the superposition principle and random phase. Thus I actually have already all the frequency components of the signal. And from the frequency components I know that there is also a...

a heavy bar, weights 0.6 Kg is used as a lever for pick up an object from 200 Kg situated 60 cm from the point of A support Calculate the length that should have the bar to lift the object with a minimum of effort answer 2 m ok we know 0.6x = 200.0.2 m But how can I continue?

Homework Statement Find the length of the curve r = cos(θ) - sin(θ), 0<θ<∏/4 Homework Equations L=∫ds ds=sqrt(r^2 + (dr/dθ)^2) The Attempt at a Solution r^2 = (cosθ - sinθ)^2 = cos^2(θ) -2cosθsinθ + sin^2(θ) =1-2cosθsinθ dr/dθ = -sinθ -cosθ (dr/dθ)^2 = 1+2cosθsinθ...

Suppose that a wheel is rotating around its axis in free space with no friction, with no external forces acting on it. In theory, the wheel will rotate forever with constant angular velocity. This velocity is assumed to be small (essentially non-relativistic). Now, consider an observer O...

Homework Statement A convex lens is used to project the image of an object on a screen with a magnification m1 . Leaving the lens fixed, the object is moved along the optical axis by a distance Δs and the screen is moved until the image is located again. If the new value of the...

As I've understood so far, there are theoretically many types of acceleration. In all cases except in the Born rigid acceleration the proper length of the object increases or decreases. If all parts of the object undergo the same acceleration simultaneously wrt to some IRF then the object...

Homework Statement Choose correct order of C-F bond length A)C-HF2<C-H2F<C-F3 B)C-F3<C-HF2<C-H2F C)C-F3<C-H2F<C-HF3 D)C-HF2<C-F3<C-H2FThe Attempt at a Solution What factors should I look for while measuring bond lengths?

Homework Statement Find the length of the curve r=cosΘ - sinΘ, 0≤Θ≤∏/4 Homework Equations Arc length = ∫|v| dt The Attempt at a Solution I found r'(θ), then used the arc length formula. Arc length = ∫ sqrt (sin^2 Θ + cos^2 Θ) = ∫ dΘ and integrated it to find ∫dΘ = ∏/4 The correct answer...

Consider a pole of 1 light second long in the ##y## direction (the vertical line(s) in the enclosed figure). It is moving in the ##-x## direction. According SR, the pole's length is not contracted because its length is not parallel to the propagation direction. However, given the time of flight...

1.) The problem is: Find the arc length of f(x)= x^3/3-1/(4x) from x=1 to 2 2.) Relevant formulas: ds = √(1+(dy/dx)) abs(L) = ∫ds 3.) My work so far: f'(x)= x^2+1/(4x^2) abs(L) = ∫(from 1 to 2) √(1+(x^2+1/(4x^2))^2 dx = ∫(from 1 to 2) √(1+(x^4+1/2+1/(16x^4)) dx = ∫(from 1...

A rod is made of two sections joined end to end. The sections are identical, except that one is steel and the other is brass. While one end is held fixed, the other is pulled to result in a change in length of 1.20mm. By how much does the length of each section increase ? I understand that E...

Homework Statement A metal rod of length L at temperature of 0°C is not uniformly heated such that the temperature is given by the distance x along its length measured from one end when: T(x) = T_0 \sin (\pi x/L) Accordingly, points at x = 0 and x = L are also zero temperature, whereas at x...

Hi! I have been pondering a scenario involving a paradox with length contraction. I brought it up with my physics professor, and I somewhat understand what is supposed to happen, but I'm still somewhat confused, so I was wondering if you could help me figure out what is going on. In this...

I understand why an object in a moving frame would be longer, but not why one in a stationary frame would be shorter. Wouldn't one in a stationary frame be the same as the object would be in the rest one? I understand the time dilation behind it, it's just that the rest of the reasoning makes no...

I am trying to get another insight in what I think is currently for me a contradiction. I have searched the forums, and the web but come to the following assertion: The coordinate distance is the computation of the proper distance times the gamma-factor, while the "coordinate" length is a...

Hello Physics Forums! I'll try to cut right to the chase. I'm studying both length contraction and time dilation in my physics class and it seems these two occurrences are mutually exclusive. That is, in any given situation, only time will be dilated or length will be contracted. This doesn't...

So here's a little background for the question: I have an arc that covers 3/4s of a circle (so it's not quite a full circumference) such that the radius from the center of the arc varies with respect to the angle (dR/d(theta)) (and it can be either positive or negative, but not constant). I am...

Homework Statement Determine the insulation resistance in a coaxial cable of length L, with conductivity, as shown in Figure assume that the current density J is radial direction. The Attempt at a Solution so i was wondering if this approach is correct, consider a sequence of...

Let's suppose that we have a rod which is 2 meters long in its rest frame. Its rest length can be defined as a set of points which do not occupy the same place, measured in a frame which is at rest with the rod as a whole. Now if we travel relative to the rod, it gets length contracted, I...

Homework Statement Here is the problem with the solution: I feel like the solution should be 10.74m. The maximum allowable length should be the lower one. This is because, for example, if we make the column 11m in length. The Pcr in the zy plane would decrease and since we are applying...

Since many authors call simultaneity between events a convention, and that under the specific set of rules we may choose a convention or a coordinate system relative to an IRF (or non-inertial) to describe space time, I wonder what's the relation between this and the effects of length...

Homework Statement A grandfather clock has a pendulum that consists of a thin brass disk of radius r and mass m that is attached to a long thin rod of negligible mass. The pendulum swings freely about an axis perpendicular to the rod and through the end of the rod opposite the disk, as shown in...

Let's say A and B are 2 vectors with length in cm and the angle between them is 170°. Obviously, the dot product of A and B will give cm2 as unit but since the value of cos(170) is negative, will the dot product be negative (something)cm2?

Homework Statement A double slit experiment is set up using a helium-neon laser (wavelength 633 nm). Suppose we add a small piece of glass (n = 1.50) over one of the slits. Then, the central point on the screen is occupied by what had been the m = 10 dark fringe. Determine the thickness t of...

why do we square the value of T ( time period) while plotting the graph of effect on time period of a pendulum with change in its effective length ? also while deriving the formula of T=2∏√(l/g) why do we take T^2 = 1/g. Whats the need for squaring the time period ?

Homework Statement Find the length of the curve x = 3 y^{4/3}-\frac{3}{32}y^{2/3}, \quad -64\le y\le 64Homework Equations Integral for arc length (L): L = \int_a^b \sqrt{1 + (\frac{dy}{dx})^{2}} dx The Attempt at a Solution Using symmetry of the interval and the above integral for arc length...

Homework Statement A relativistic conveyor belt is moving at speed 0.5c relative to frame S.Two observers standing beside the belt, 10 ft apart as measured in S, arrange that each will paint a mark on the belt at exactly the same instant (as measured in S). How far apart will the marks...

So in the infinite well Energy is proportional to 1/L^2, so I'm assuming in the finite well there is some sort of similar relation. So as the L decreases, the energy increases, so the wavelength decreases. Decreasing the wavelength means more energy, so it should penetrate further, but also if...

Trying to see the logic in deriving length contraction and time dilation using the Lorentz transformations and inverse Lorentz transformations. In the following treatise it leads to ambiguities. Given ##Δ\acute{t}=\gamma(Δt-\beta c^{-1}Δx)## (1) ##Δ\acute{x}=\gamma(Δx-\beta c Δt)##...

∫sqrt(x^4/4 + 1/(x^4) + 1/2) dx from x = 1 to 4 Could someone help me solve this? I can't seem to find a substitution that works, or find the square root of (x^4/4 + 1/(x^4). Any help would be very appreciated. Thanks in advance!