Length Definition and 1000 Threads

The reciprocal of the Planck length, ##\Lambda=1/l_P##, is used as a high-frequency cutoff in the particle-physics estimation of the vacuum energy. For example in "the cosmological constant problem" Steven Weinberg says that summing the zero-point energies of all normal modes of some field of...

Homework Statement A 16m long vessel moved passed you at a relative speed of 0.86c. What was the length of the vessel recorded by your measuring device? Homework Equations Speed = distance/time t=to/√1-v2/c2 L=Lo⋅√1-v2/c2 The Attempt at a Solution Ok, so I can just sub the 16m and 0.86c in...

Suppose an observer in the Earth frame set out to measure the length AB by measuring the time interval between the event "B coincides with D" (event BD) and the event "A coincides with D" (event AD), and then multiplying the time with ##v##. This observer argues that an observer in the train...

1. Homework Statement I have to find the length of a diagonal from bottom to top. I don't know which formula i would be using? Please see the attachment for more information. Homework Equations May be pythagorous theorem. But i don't know which sides i have to select The Attempt at a Solution...

while i understand what plank length is... Has it ever been measured on multiple axis? As an indicator of the granularity has the plank length (or second) been thus measured?

Imagine a cubic volume of space, defined today, with edges of the order of the Planck length. As cosmological time goes forward this volume expands so that the edges of the cube expand with the scale factor. This seems ok. However, as physics is time-reversible, it should be valid to imagine...

I'm asking many questions on inflation, I hope this is the last one... If inflation is correct, our observable Universe would have been a tiny homogeneous patch before inflation started (if it started at all). The length of that initial patch is estimated to be of the order of 1 Hubble length...

How much is the length of horizon that human's eye can see at sea level? How much is the length of horizon that human's eye can see at higher level? any formula? I am not sure i should use wide or length. i mean the rightest point of horizon to the leftest point of it for human' eye angles.

Homework Statement The width of a rectangle is increased by one tenth, but the area remains the same. By what fraction has the length of the rectangle been reduced? The Attempt at a Solution Length = x Width = x + 1/10 Set equation: L * W x *(10x + x) 10x^2 + x^2 I am stuck... Please help...

I'd like to get some conceptual clarification on whether or not length contraction is only apparent to an observer or if it's physically real in the sense that the object under contraction would experience compressive forces? My thinking on this has been along the lines of: I know that time...

Homework Statement Homework EquationsThe Attempt at a Solution a) t' = l0/c b) ct1 = l0 /ϒ - vt1 t1 = l0 /ϒ(c + v) c) t2 = l0 / (ϒ v) Is this correct?

Homework Statement Homework Equations 1) k.e. = (1/2)mv2, non- relatvistic 2)K.E. = m0 c2 (ϒ -1), relativistic 3) L=L0/ϒ , Length contraction The Attempt at a Solution (A) Taking 1019 eV to be the kinetic energy of the proton, Non- relativistic calculation (1/2)mv2 = 1019 eV = 1.6 v =...

what is the Length of a 60/40 soldering lead that is 0.453kg and 0.8mm in diameter? i could not find the volume of the thing so is there any other way to go around this? i could also not find the density of the 60/40 solder. so yeah I am asking here if anybody knows thank you

Hello all, I am in a total state of confusion with regard to this. Here is question. The length of a rod is [11.05 (+/-) 0.2]cm. What is the length of two rods? I want to know should the answer be reported like [22.1(+/-) 0.2] or [22.1(+/-) 0.4]. Regards:)

Homework Statement Question: An ant starts at one vertex of a solid cube with side of unity length. Calculate the distance of the shortest route the ant can take to the furthest vertex from the starting point. Now, in the answer, the cuboid is unfolded and a rectangle of side 1 and 2 is...

Homework Statement Hi Guys, I am a bit unclear regarding adding vectors and hoping someone can clear up the confusion for me. In the image below, we are adding two vectors and we used the vector components to find find x and y. Finally we then used x and y to get the resultant and the angle...

Problem : To measure length of a scale Rest frame : The frame w.r.t. which scale is at rest Moving frame : The frame w.r.t. which the scale is moving with speed v along +ve x-axis In rest frame ,the positions of the two ends of the scale are (measured simultaneously ) x1 and x2. So length L =...

some formula related I tried to draw the problem can anyone give me clue how to solve it?

The definition of the Planck length I have found is that it is the shortest length that has meaning. What is meant by that? Can someone give be a better definition of what it is?

By using particle physics natural units with ##\hbar=c=1## so that Planck's length ##l_P=(8\pi G)^{1/2}## we can express Einstein's field equations as $$G_{\mu\nu}=l_P^2\ T_{\mu\nu},$$ where ##G_{\mu\nu}## has dimension ##[\hbox{proper length}]^{-2}##, ##l_P## has dimension ##[\hbox{proper...

Homework Statement Note that this formula (##C=4 \pi \epsilon_0 R##) and the others we have derived for capacitance involve the constant multiplied by a quantity that has the dimensions of a length. Homework Equations ##\epsilon_0## has the following units in SI: $$\frac {C^2} {N \cdot m^2}$$...

Homework Statement This is a common massless string and pulleys problem. I'd just like to understand why, according to the solution, l_2 + 2l_1 = constant. It doesn't seem to me that two times the l_1 length is equivalent to l_2. Can somebody explain? Homework EquationsThe Attempt at a Solution

Homework Statement Estimate the total path length traveled by a deuteron in a cyclotron of radius 53 cm and operating frequency 12 MHz during the entire acceleration process. Accelerating potential between dees is 80 kV. mass m = 3.2e-27 kg charge q = 1.6e-19 C radius r = 0.53 m frequency f =...

I see various sources: 1. Karp- Cell biology 2. some papers 3. Michael M. Cox -...

Hello I would need help to continue. calculation problem: Given a right angled triangle with catheter lengths a and b length units, determine and indicate the length of the bisectris to the right angle. find: Xa^2 + b^2 = (y+z)^2X^2 + y^2 = a ^2X^2 + z^2 = b ^2

1. The problem statement, all variables and given/k nown data x = (sin(t))^2 y = (cos(t))^2 t goes from 0 to 3 pi Homework Equations ∫ \sqrt{ {(dx/dt)}^2 + {(dy/dt)}^2 } dt The Attempt at a Solution ∫ \sqrt{ {(2sin(t)cost)}^2 + {(-2cos(t)sin(t))}^2 } dt ∫ \sqrt{ 4(sin(t)cos(t))^2 +...

So I'm working on a project where we're deciding a new lens to use for our laser diode. I need to determine the appropriate focal length based on the equation: 1/ƒ = 1/μ + 1/σ where ƒ is our focal length, μ is the distance from the lens to image and σ is distance from lens to object. For the...

Hello! I have a small problem with a task professor gave us. I tried many options (you will see below) but I cannot seem to get the right solution. Any advice or guideline how to solve this would be really helpful. In advance I thank you for helping me. Homework Statement Our professor of...

Homework Statement Homework Equations Stress = force/ cross sectional area elongation = force x length / modulus of elasticity x cross sectional area The Attempt at a Solution The given solution is 0.149mm I assumed that the bar needs to be solved in two sections because of the hole...

So an object moving close to the speed of light will be length contracted. Does that mean the distance it covers also contracts in length? From the traveling object's point of view it's surrounding's would contract as he sees them moving along. In these scenarios wouldn't velocity be a...

Homework Statement : [/B]The correct relation is: A. x=y B. x>y C. x<y D. None. Please refer to picture attached.Homework Equations : [/B]As stability increases, bond length decreases. When a Π bond is delocalised i.e it takes part in resonance, stability increases.The Attempt at a Solution I...

Homework Statement Originally the statement: Find a length of two points on sphere. It was easy. ##\int \sqrt{g_{\phi\phi}}d\phi## I hope you agree :-) But I have idea, how to find a length of path which is NOT a part of arc (circle). For example sinusoid. Is possible to find length of sinusoid...

I am confused about time dilation. I understand that a common pedagogical device used is a light clock, in which a pulse of light flashes back and forth between two objects. I understand that when an observer in a vehicle carrying such a contraption is moving, to an external observer, as the...

A piece of wire is cut into two pieces. Each piece is then bent to form a square. If the sum of the areas of the two squares is 5L^2/128, how long is each piece of the wire? My Reasoning: I see the words square and sum of the squares. A = s^2, where s is side of the square. Sum of the areas...

Homework Statement UT has jumped over a wall and unfortunately for her, she forgot to bring her sword. Her friend SS decided to shoot the sword to her with a bow. He can bend a bow and arrow so that it gets a potential energy of 179 Nm. It seemed that Ut landed 9 meters behind the wall; a...

Does anyone know how long the lunar month was when the moon was formed? I can't get the equation to work. I'm looking for speed of the moon when it was created at about 1/10th the current distance from the earth. Thanks.

Does the orientation of a plan convex lens affect it's focal lenght? If I put il like in the first example in the photo and makeep the calculation using the lens maker equation I get f positive What happens if I turn the curved face on the right? Using the lens maker equation now the radius...

How would you approach a most accurate measurement of the "length" of a coastline?

Homework Statement Consider a mass attached to four identical springs, as shown in the figure. Each spring has a force constant k and an unstretched length lo, and the length of each spring when the mass is at equilibrium at the origin is a (not necessarily the same as lo). When the mass is...

(cos(s), sin(s)) gives an arc-length parameterization of the unit circle so that the speed is constantly 1, but the second derivative doesn't give zero acceleration which should be the case with constant speed?

When winding a coil around a magnetic core, if you wanted to tap the coil such that each half has the same AC voltage output, would you: A) wind each part at the same RPM for the same amount of time, to get the same number of turns for each, or B) wind the second part proportionally less, to...

Homework Statement A source having a half life of 5.27 years is calibrated and found to have an activity of 3.5*10^5 Bq.The uncertainty in the calibration is +- 2% Calculate the length of time in days after the calibration has been made for the stated activity to have a maximum possible error...

Two trains of equal length are on parallel tracks. One train is traveling at 40 km/h and the other at 20 km/h. It takes two minutes longer for the trains to completely pass one another when going in the same direction, than when going in opposite directions. Determine the length of each train...

ħello. Here is my question: Has the so-called "planck length" (~1.61622837 * 10^(-35) meters) been derived with mathematical rigor within standard quantum field theory? If so, I need help finding this proof. Any literature would be appreciated. Also: If it has, then doesn't this imply a...

Homework Statement You must complete the circuit of (Figure 1) in such a way that it draws a current of 0.450 A from the battery. The battery maintains a potential difference of 10.0 V with no load, but has an internal resistance of Rbatt = 15.0 Ω . The only material you have is 20.0 mm^3 of...

Homework Statement Show that integrated track length in EM-shower is proportional to ##E_0##. Homework Equations ##E(t)=\frac{E_0}{2^t}##, with radiation length, ##x_0##. Knowledge that shower terminates at ##E_c##. The Attempt at a Solution The total track length is naturally the total...

Homework Statement Let a is a complex vector given by a = 2π K - i ρ / α^2 , where ρ is a two dimensional position vector and K is the corresponding two dimensional vector in the Fourier space. In order to find magnitude of this vector, i found that it is 4π^2 K^2 + ρ^2 / α^4 . The logic...

If I understand correctly, the Planck length, or maybe a tenth of it, is considered the point at which quantum effects mess up any attempt to apply our present physical laws, and so one could not even in theory make a dependable measurement of something smaller. However, I was wondering what...

Homework Statement [/B] Calculate the work done by a force, against an electric field, to bring a charged particle (2 coulomb) from the point (2,0,0) to (0,0,0). Also calculate the work from (0,0,0) to (0,2,0). Finally calculate the work done going directly from (2,0,0) to (0,2,0) and...

I'm having trouble even beginning to figure out how to approach solutions for this. I begin with a unit cube, and imagine all the possible lines that intersect the cube. I am assuming there must be an average length of these intersections; I want to find that average length. Another way to...