Length Definition and 1000 Threads

Homework Statement Suppose a harp string is tuned to middle C (C4) and is 0.56m long. If I want the tension to be 193.5 N, what mass per unit length do I need the harp string to be? Calculate your answer in kg.m Homework Equations Vs = sqrt(T/μ) V = fλ The Attempt at a Solution Having a very...

Homework Statement Let γ : [0, L] → Rn be arclength parametrized. Show that the distance between the endpoints of the curve can at most be L, and equality can only hold when γ is a straight line segment. Thus, the shortest path between two points is the straight line segment connecting them...

So I decided to try deriving a general formula for fun. Being a high school student, the calculus got scary very fast. At this point, I'm just curious as to what the best approach to this might be. The approach I used was finding y as a function of x and then inputting it into the arc length...

The debye length is the effective length over which electrostatic potential disturbances are "screened out" in a plasma. So if I drop a charged point particle in a plasma, then I expect after some Debye Length, D, from this point charge, I can see no difference between any other point in the...

I'm trying to design some novel cross bow designs and also trebuchet's with the trebuchet (similar to catapults to those who don't know) using springs or a combination of weight and springs. I'm looking into using linear springs and pullies for the crossbow depending on whether they can be...

Homework Statement [/B] This is a problem from my Differential Geometry course A velociraptor is spotting you and goes after you. There is a shelter in the direction perpendicular to the line between you and the raptor when he spots you. So you run in the direction of the shelter at a...

Homework Statement A muon is created in the atmosphere 3 km above Earth's surface, heading downward at speed 0.98c. It survives 2.2 * 10-6s in its own frame of reference before decaying. Relativistitically, according to the muon, what is the distance from the point in the atmosphere where the...

Homework Statement Show that the length of a curve γ in ℝn is invariant under euclidean motions. I.e., show that L[Aγ] = L[γ] for Ax = Rx + a Homework Equations The length of a curve is given by the arc-length formula: s(t) = ∫γ'(t)dt from t0 to tThe Attempt at a Solution I would imagine I...

Homework Statement The problem is described in the picture I've attached. It is problem number 6. Homework Equations Tangent line of a curve Length of a curve The Attempt at a Solution I don't know why I'm so confused on what seems like it should be a relatively straightforward problem, but I...

Homework Statement The problem statement is in the attached picture file and this thread will focus on question 7 Homework Equations The length of a curve formula given in the problem statement Take a polygon in R^n as an n-tuple of vectors (a0,...,ak) where we imagine the vectors, ai, as the...

Sorry community, I know I have another outstanding relativity question but something else is currently troubling me. What got me thinking was the question of muons moving towards earth. Now according to their half lives very few of them should make it through 12Km of atmosphere... ANALYSIS...

Hi All, Bob and Alice are both 21. I'm imagining a scenario where Alice starts on a journey at 0.8c towards a distant planet. Bob (stays still) says this planet is 16 light years away and that it takes Alice 16/0.8 = 20 years to get there (so Bob is 41 years old when Alice gets there). So Bob...

How to find the length of an angle bisector ($$BK$$) in a triangle $$A(1;4), B(7;8), C(9;2)$$. I calc $$BK$$: \frac{x-7}{\frac{1+\frac{\sqrt{13}}{\sqrt{10}} \cdot 9}{1+\frac{\sqrt{13}}{\sqrt{10}}} - 7} - \frac{y-8}{\frac{4+\frac{\sqrt{13}}{\sqrt{10}} \cdot 2}{1+\frac{\sqrt{13}}{\sqrt{10}}} -...

If an object was traveling fast enough relative to an observer such that it's length is contracted down to the Planck scale (as with time), I would imagine that any further increase in speed would result in no more observable relativistic effects? Please correct me if I'm wrong.

Homework Statement Given Ma = Mb =Mc and muk between c and the surface is 0.30 Homework Equations (rope length) = constant Maaa = Mag - T Mbab = Mbg - 2T Mcac = T - (mu)Mcg The Attempt at a Solution The equations I came up on my own and the answer key did as well. The problem is I also need...

Homework Statement An arrangement of four wires, in cross section, with θ=30° and u=5cm. Wire 2 and wire 4 carry the same magnitude of current (I2=I4=10mA) directed out of the page. Wire 3 carries current I3=25mA directed into the page. If the resultant force per unit length on wire 1 is zero...

1. Homework Statement An air coaxial transmission line has a solid inner conductor of radius a and a very thin outer conductor of inner radius b. Determine the inductance per unit length of the line. Homework Equations the book states the methodology to find the inductance as follows: 1)...

For a string in string theory, Energy = string tension * length So I'm wondering if it can increase its length with increasing its energy.

Does the length of a string depend on its energy, or does its energy depend on its length? Similarly, does the area of a d brane depend on its energy, or does its energy depend on its energy? Are these stupid questions?

Hello there, Suppose there are two inertial frames of reference ##S## and ##S'## with coordinates ##(x,ct)## and ##(x',ct')## such that ##S'## is moving relative to ##S## with velocity ##v##. Suppose ##v>0##, that implies ##\gamma >1##. We know that a Lorentz boost is given by: $$ x' = \gamma...

https://web.mst.edu/~numbere/CP/CHAPTER%203.htm I have trouble understanding why the length used in 3.1.1 is pir^2. My notes don't explain what length we use either.

Long shot, but has anyone applied to the GWU Physics PhD program? If so, how long was your Statement of Purpose? There is no information about it on the application, I ran across this page: https://www.programs.gwu.edu/graduate/physics. This says 250-500 words, but asks for "your academic...

Finding length of vector with unknown variable. Purely for study purposes. Find the smallest possible length of the vector →v . Let vector V = (-2/3,b,16/7) Equation for finding length of vector : Sqrt(a^2+b^2+c^2)Question would be quite straight forward had there been no unknown variable but...

I recently saw the derivation of length contraction in Special Relativity . At the end , it said x' = (x - vt) γ(gamma) x = (x' + vt') γ(gamma) Where γ(gamma) is Lorentz transformation . It is = 1/√(1- v²/c²) Then derivation continued , with expansion of x' = (x + vt)γ As t = 0 in this case...

The de Sitter group is often used as an extension of the Poincaré group, because its a simple group and preserves, in addition to a velocity c, a length L. A natural candidate for this length scale is the Planck length. Thus it seems to make sense to think about the invariant Planck length as...

I have fabricated a few biconvex lens (12mm diameter) for an experiment and am trying to find their focal lengths. My though is to set up three parallel lasers and find where the beams converge. However, even with the smallest laser diodes I could find, three beams surpass the diameter of the...

I've been given that in an electromagnetic calorimeter the radiation length of a material consisting of a single nucleus is: ##X_0 = \frac{716.4A}{Z(Z+1)\ln(287/\sqrt{74}}## Where ##X_0## is in g ##cm^{-2}##. How can it be in those units when everything in that expression is dimensionless? It's...

Homework Statement The problem is about calculating the error on the area of a rectangular field. What is known is that the sides of the rectangle are 120 m and 180 m, and they have been measured with a 10 m measuring tape. The tape has a sensitivity of 2 cm.Homework Equations Since the area...

You have 2 bikes. They only differ in 1 way. The length of the crank arm (where pedal attaches) https://en.wikipedia.org/wiki/Crankset How will these bikes differ when riding? Is one harder to pedal than the other? Why?

Homework Statement You are required to set up a light source, an object grid, a converging lens and a screen so that a quantitative investigation of object and image distances can be performed. Tabulate corresponding object and image distances (p and p' respectively). Also tabulate values of...

Homework Statement a= 0.3 m / s2 k = 10 000 N / m m = 1800 kg ( of the car that is being pulled) Ignore friction. A car is being pulled by another car by a rope ( stiffness = 10 000 N/m) with acceleration of 0.3 m/s2.. Find the change in length of the rope. Homework Equations F = ma F = kx (x...

Hello! I really don't understand this concept, and I have an example problem that I am working on that I just CANNOT figure out! Any help? Thanks so much in advance! A group of people get on a pirate ship ride at the fair. This ride is a swinging pendulum with a maximum swing angle of 65 degrees...

I thought I understood the concept of a correlation function, but I having some doubts. What exactly does a correlation function quantify and furthermore, what is a correlation length. As far as I understand, a correlation between two variables ##X## and ##Y## quantifies how much the two...

Hi, I would like to try and calculate the average distance traveled through a box of length ##w## by any straight path possible. As shown in the attached figure. Where the path through the box to an adjacent face is given by $$r_{adj}^2=\left(\frac{w}{2}-x\right)^2+y^2+z^2.$$ The average...

I don't remember seeing this solution to the question. Imagine an object of length d with a reflector on the far end (x=4). A moves past the object at speed a, emitting a signal at the origin in the positive x direction. A makes one pass in the +x direction, reverses and makes one pass in the...

Hi. I derived a formula for the length of the graph of e^x in the first quadrant between x=a and x=b. It is: sqrt(1+e^(2b)) - sqrt(1+e^(2a)) + (a-b) + log [(sqrt(1+e^(2b)) - 1) / (sqrt(1+e^(2a)) - 1)] I think it works because it gave a value of approx 2.003 units for a=0 and b=1. For a=0 and...

Which materials have high capillary length, and can be found easily? (above 1cm)

I'm coming across a contradiction that I can't resolve. Two points on the ground are separated by 30km. If you're in a moving frame at velocity +v relative to the ground and you view those two points on the ground, would those two points be greater or less than 30km apart? At first, I thought it...

Homework Statement Prove that, given a metric ##g_{ij}## such that ##ds^{2}=g_{ij}dx^{i}dx^{j}##, where ##x^{r} = x^{r}(\lambda)## , we have the following result for the arc length: $$ L(p,q) = \int_{p}^{q} ds = \sqrt{ g_{ij} \frac{dx^{i}}{d \lambda} \frac{ dx^{j}}{d \lambda} } d \lambda $$...

Homework Statement There is a triangle with sides $$ 3,3r,3r^2 $$ such that 'r' is a real number strictly greater than the Golden Ratio. Is this statement true or false...? Homework Equations $$Golden \space Ratio = \phi = 1.618... $$ The Attempt at a Solution Actually I have no clue at all...

Homework Statement A ball of mass 620 g hangs from a spring whose stiffness is 115 Newtons per meter. A string is attached to the ball and you are pulling the string to the right, so that the ball hangs motionless, as shown in the figure. In this situation the spring is stretched, and its...

Homework Statement Calculate the focal length of a planoconvex lens that produces a real image 2.5 times as big as the object if the object is 2.5 cm from the lens? Homework Equations The only one I can think of is 1/f = 1/v + 1/u The Attempt at a Solution [/B] My 'attempt' is 1/f = 1/62.5...

Recently I have had a lot of eye strain from excessive computer use. The problem is because your eye lenses re stuck in a fixed position. I wanted to know if it would be possible to make a screen that is 1m away look like it is 4m away for example. Would it be possible by making the screen out...

As I understand it, the proper length, ##L## of an object is equal to the length of the space-like interval between the two space-time points labelling its endpoints, i.e. (in terms of the corresponding differentials) $$dL=\sqrt{ds^{2}}$$ (using the "mostly plus" signature). Furthermore, this is...

A square $ABCD$ , each side with length 13, if points $E,F$ on $\overline{BC} ,\overline{AB} $ respectively,$\angle EDF=45^o,$and $\overline{EF}=11$ find length of $\overline{CE}=?$

Good Evening/Morning/Afternoon Everyone, Question: Why is it that demonstrations of Van de Graff generators use Leyden Jars in series to get bigger sparks? If a spark gap's size determined by voltage, and Leyden jars are simply to be treated as capacitors which wouldn't increase voltage, why...

Hello ansys users in ANSYS workbench, how can I plot the contact tool results (Frictional stress, sliding distance...etc) with length (500mm for example) in the "x-axis" instead of the default "by time" option?. the path method can not be used with this type of results "Contact tool results"...

Hi, I was doing an experiment with Neodymium magnets and a long copper pipe (3cm internal diameter) to see Lenz's Law in action. At first I used a long bar magnet (about 15cm long) and there was little resistance to the magnet falling through the pipe. It was only slightly slower than a...

Homework Statement Two identical spaceships are under construction. The constructed length of each spaceship is 1.5 km. After being launched, spaceship A moves away from Earth at a constant velocity (speed is 0.850c) with respect to the earth. Spaceship B follows in the same direction at a...

Homework Statement "An infnitely long hollow cylinder of radius ##a## has surface charge density ##σ_a##. It is surrounded by a coaxial hollow cylinder of radius ##b## with charge density ##σ_b##. The charge densities are such that the total confguration is electrically neutral. Using whatever...