Length Definition and 1000 Threads

Here is a problem that showed up on my exam that I couldn't find any variation online. A stick of length L is depth D in the water. The stick is parallel to the surface of the water, and the viewer (in air) is looking down in the water right over the middle of the stick. What is the apparent...

Is it possible to magnify an object if the magnifier is sitting directly on top of the object (a focal length of zero)? How can this be accomplished if it is not possible with a traditional magnifier?

Homework Statement frequency, Tension, mass, mode of vibration Homework Equations v = sqrt(T/μ) The Attempt at a Solution length of string is 2.14m weight .00247kg mass per unit length (μ) .00089 However, I need to confirm this graphically. I solved for mass per unit length μ = T/V^2 or...

Homework Statement [/B] A spaceship is approaching Earth from the far side of the sun. The Earth and sun are 8 light minutes apart and the ship is traveling at .8c. Two events are indisputable. 1) the ship is at the sun 2) the ship is at the earth. Assume that the Earth and sun are at rest...

Homework Statement if displacement is the shortest distance between two point then that would also meant that it is equivalent to the hypotenuse when using phytogaras theorem right?. but why isn't displacement the shortest length between two point ?because Xinitial - Xfinal couldn't posibly be...

I'm trying to understand special relativity well enough to explain it to others, ANY others, including myself. I am trying to use Robert Resnick's Introduction to Special Relativity to inform my thinking. In introducing length contraction, he introduces L' as the length measured by an observer...

There's a section in my astronomy book on relativity. The image shows a train traveling at a slow speed and a second image of the train approaching the speed of light. The text says the second train is length contracted, but only in the horizontal direction. In the vertical direction the train...

Homework Statement An object is at a very large distance from a concave mirror of focal length 40cm. Find the distance from the image to the mirror. Is the image real or virtual? Homework Equations 1/u + 1/v = 1/f The Attempt at a Solution [/B] 1/u + 1/v = 1/40 The image has to be real...

Homework Statement Board ##A## is placed on board ##B## as shown. Both boards slide, without moving w.r.t each other, along a frictionless horizontal surface at a speed of ##6 \text{m/s}##. Board ##B## hits a resulting board ##C##, "head-on". After the collision, board ##B## and ##C## stick...

Dear PF Forum, Perhaps it's not a question, just a light discussion. Time From this, we get the standard time https://en.wikipedia.org/wiki/Caesium_standard, it's 9,192,631,770 ticks per second. I think this number should be discreet. No need to tune it to some figures after decimal point. Is...

Homework Statement Consider the path r(t) = <10t,5t2,5ln(t) defined for t >0. Find the length of the curve between (10,5,0) and (20,20,5ln(2)) Homework Equations L= ∫ab |r'(t)|dt The Attempt at a Solution r'(t) = <10, 10t, 5/t> t values are 1 and 2 based on the x values for the points...

how have we figured out plank length of the universe ?and know its that size ?

For a research problem, I'd like a way to find the distance of each of 4 lines perpendicular to one of 4 walls connected to a point that is within a box of known dimension. I know the distance from the center of each wall to the point of interest (C1 to C4), but I do not know the angle this...

In the trapezium ABCD shown in the figure, AB = (x + 3) cm, DC = (2x − 3) cm and BE = EC. If the area of the trapezium is 15 cm2, find the length of DC to the nearest first decimal place. Take $\sqrt{19}$ = $4.36$ Have I done correctly, Okay first we know that area of a trapezium $15 =...

Here is a quote from this website: My question is: is this derivation of length contraction considered to be sound and correct today? Are they treated in modern textbooks?

I was wondering if it is possible to work out the maximum amount of energy an object with mass can have using the length contraction equation (i.e. "actual" length divided by Lorentz factor). The way I thought of doing this was by rearranging e = mc^2 to get c^2 = e/m. Then, substitute e/m into...

Homework Statement in the notes , i was told that ∂A is the resistance of aluminium rod...I'm wondering the change length of steel rod that we can 'see' is ∂ st or ∂T(st) ? Homework EquationsThe Attempt at a Solution I think the change length of steel rod that we can 'see' is ∂ st ?

Homework Statement The bar has a mass of 3 grams/cm. When a mass of 15 grams is hung on the left side, the system is balanced. Calculate the length of the bar. Homework Equations F1*r1 = F2*r2 The Attempt at a Solution I thought that the moment on the left should be equal to the moment at the...

Suppose that frame O' moves at speed v = 0.6c relative to frame O. A rod with two balls is attached to its ends is 10 meters long in its rest frame, O'. Length contraction will tell you that in frame O, the rod is 8 meters long. But aren't the two balls at the ends "events"? They are clearly...

Would Planck's length be subject to length contraction if an object hypothetically of the length had a velocity near c? I suspect that it won't becuase Planck's length is defined by the invariant, physical constants of G, c and the reduced Planck's constant. Thus, Planck's length would not be...

Homework Statement Let P be the set of (x,y,z)^t in R^3, which satisfies the following inequalities: -2x+y+z <=4 x-2y+z<=1 2x+2y-z<=5 x>=1 y>=2 z>=3 Homework Equations I want to find the vector in the set with the maximal length. The Attempt at a Solution I have transformed the linear...

A particle travels along a circular arc segment centered at the origin of the Cartesian plane with radius R, a start angle θ1 and an end angle θ2 (with θ2 ≥ θ1 and Δθ = θ2 - θ2 ≤ 2π). The total distance traveled is equal to the arc length of the segment: L = R(Δθ). I would like to find the...

I was uncertain wether to put this in the general physics forum, but I decided against it. How do length adjustable gas springs(like for example in office chairs)work ? I know how gas springs work and i even have an idea how length adjustable ones could work. Since you hear a "gas flowing...

There are several unreasonable assumptions in the formulation of the Prandlt Mixing Theory. However, it works reasonably well for simple 1-D flow. An attempt to explain why is given by Davidson in his book 'Turbulence', on page 122 - 124, section 4.1.4. It's stated that it still works because...

I've recently been reading this paper (a free version is available here). I've been trying to work out how they came to the 128m length, but I just can't. Feel like it's been just beyond my grasp for a long time and it's been driving me mad. Any help would be appreciated. Thanks in advance.

Homework Statement A double slit apparatus is held 1.2 m from a screen. (a) When red light (λ = 600 nm) is sent through the double slit, the interference pattern on the screen shows a distance of 12.5 cm between the first and tenth dark fringes. What is the separation of the slits? (b) What...

According to this video the length of basis is r. It grows as we further from the origin . Why?

Hi, First: I'm pretty sure my question has been asked numerous times, so I'm absolutely happy with links to other threads. I've used search but it didn't come up with satisfying responses, probably mainly because I don't really know what search terms to use. So the question is: How can a...

Imagine there are two space ships, Ship A and Ship B. Ship A sees Ship B traveling at 0.865c towards him. (And of course vice versa) From Ship A's FOR there is a marker 9,000,000 km away which is at rest wrt Ship A. The marker, Ship A and the path of Ship B therefore form a straight line. When...

Homework Statement Homework Equations D = rt The Attempt at a Solution [/B] This is my attempt let d= length of the circuit 60/a mph --- speed for walking 60/b mph ----speed for riding 60/c mph ---- speed for driving d=(60/a)t1+(60/b)t2+(60/c)t3 From here I cannot continue. Kindly help...

Homework Statement Sam, whose mass is 75 kg, stands at the top of a 12-m-high, 100-m-long snow-covered slope. His skis have a coefficient of kinetic friction on snow of 0.07. If he uses his poles to get started, then glides down, what is his speed at the bottom? Homework Equations v =...

I have heard a claim that looks a little odd to me and I am hoping that someone can help. In the gym there are foam rollers people use, some of them are 36 inches long and some are 16 inches. The claim is that the shorter ones can withstand greater weight than longer ones and will have less...

Please excuse any stupidity, but I'm under the impression that objects that travel "along" 3- dimensional" space (therefore the objects are three dimensional) with velocity v are subject to length contraction. However would objects of 3+ dimensions and with velocity v still be subject to length...

Hello, I would think that it would, because if the wire is longer there is more of a chance of their being foreign objects interfering, which could cause resistance, right? Or no?

An army of soldiers is marching down a road at 5 mi/hr. A messenger on horseback rides from the front to the rear and returns immediately, the total time taken being 10 minutes. Assuming that the messenger rides at the rate of 10mi/hr, determine the distance from the front to the rear. Can you...

This article is posted on twitter with the byline: "You, me, and even aliens from Alpha Centauri could arrive at the same Planck units." but does not explain why. http://www.symmetrymagazine.org/article/the-planck-scale I believe I have read (but cannot find the reference now) the following...

If you are in a space ship, traveling near light speed, will length contraction enable you to se astronomical events lightyears away, before it is possible to see them from earth? This because the distance is shorter for you in the spaceship and light speed is constant. Example: A star 100 ly...

Homework Statement A telescope has a focal ratio of f/7.5. You wish to use it with a spectrometer that requires a f/10 beam as its input. Compute the focal length of a 50mm diameter lens that, when inserted into the beam 150mm in front of the unmodified focal plane, produces the required beam...

Quick question: what's the calculation required for working out the day length (i.e. rotational period) of a double planet, where both planets are tidelocked to each other? Do just need to make adjustments to Kepler's Third? I've got a spread sheet set up to allow me to calculate orbital...

Homework Statement A biconvex lens, L_1, with focal length of magnitude \left| f_1 \right| = 15 cm is used with a second biconvex lens, L_2, with focal length of magnitude \left| f_2 \right| = 25 cm to form a compound lens system. If the two lenses are placed in mutual contact what is...

Homework Statement Evaluate the length of the spiral with parametric equation ψ(t) =< 2 cost, 2 sin t, π/t >, with t ∈ [0, 2π]. Homework Equations Line integral ∫C f(x,y) dS The Attempt at a Solution f(x,y) = z = π/t ∫C π/t dS [0, 2π] are the lower and upper bounds of integration dS=...

Homework Statement Homework Equations 1/do+1/di=1/f The Attempt at a Solution I tried finding the distance of image at 27m and then at 30.5m and taking the difference but that didn't work.

Homework Statement Homework Equations T=2pi√(L/g) The Attempt at a Solution I am just making sure I am doing these right. For the first one, I used the equation to determine the length it would be on Earth. The length I got was g/pi^2 = 0.993 m. I thought that it would have to stay the same...

Homework Statement The plano-convex lens has a diameter of 200 mm and the central thickness of 20 mm. The edge thickness is zero and the refractive index of glass is 1.5. Find the following parameters of the lens: (i) the back focal length Homework Equations N/A The Attempt at a Solution I've...

Find the arc length of $$f (x)=(1/3)(x^2 +2)^{3/2}$$ On the interval [0, a] The parametric I got $$y=t$$ $$x=\sqrt{(3t)^{2/3}-2}$$ I proceeded but didnt get the answer of $$a+\frac{a^3}{3}$$

Hello, in ice I have read that the average bond length of the hydrogen bond is about 2 Angstroms. This is roughly twice the O-H (covalent) bond length. My question is what really determines the length of the hydrogen bond? Why wouldn't the hydrogen be drawn closer to the next water...

Does length contraction means the contraction of space time?

Hey, I’m currently stuck at my research and I’d like to ask for some help. First I’ll try to introduce the measurement and the setup and then I’ll get straight to the problem. The goal is determining the diffusion length of charge carriers quantitatively in different materials. For this...

Hello! We are 3 students working on a bachelor thesis rigth now, with the purpose to determine the efficiency for different nozzle designs. We have done several practical tests, where we have logged the water pressure and the flow out from the nozzle, and calculated the nozzle efficiency based...

Homework Statement Imagine another planet with an acceleration of 10m/s^2 at its equator when ignoring the rotation of the planet. The radius of the planet is 6.2 x 10^6m. An object dropped at the equator yields an acceleration of 9.70m/s^2. Determine the length of one day on this planet...