What is Two dimensions: Definition and 143 Discussions

Two-dimensional space (also known as 2D space, 2-space, or bi-dimensional space) is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point). The set ℝ2 of pairs of real numbers with appropriate structure often serves as the canonical example of a two-dimensional Euclidean space. For a generalization of the concept, see dimension.
Two-dimensional space can be seen as a projection of the physical universe onto a plane. Usually, it is thought of as a Euclidean space and the two dimensions are called length and width.

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  1. Euge

    POTW Gaussian Integrals in Two Dimensions

    Let ##a, b##, and ##c## be real numbers such that ##a## and ##c## are positive and ##ac > b^2##. Evaluate the double integral $$\int_{-\infty}^\infty \int_{-\infty}^\infty e^{-ax^2 - 2bxy - cy^2}\, dx\, dy$$
  2. ohwilleke

    I Trying To Conceptualize Two Dimensions Of Time

    Some BSM theories, often but not exclusively string theory inspired, have an extra time dimension, as well as extra spatial dimensions. I'm trying to make sense of what it even means to have more than one time dimension, ideally, with a concrete example that illustrates how the second time...
  3. S

    Motion in two dimensions: Launching up an incline

    But it seems to get too complex and am not sure whether it is correct.. my solution got a bit messy + incorrect Thanks in advance!
  4. C

    Can I improve the sinc interpolation?

    Hello everyone. I am working with mathematica, where I have developed a two-dimensional shannon interplation, just as can be seen in the slides 15 to 18 of this presentation. The code is as follows: savedX = Table[XposX = mat[[All, 1]]; YposX = mat[[All, 2]]; windXVal = mat[[All, i]]...
  5. mustafamistik

    Throwing Objects - Motion in Two Dimensions

    I stuck on part c and d. My attemption is attached.
  6. Diracobama2181

    Classical Canonical Partition Function in Two Dimensions

    For a single particle, $$Z=\frac{1}{h^2}\int_{-\infty}^{\infty} e^{-\beta \frac{P^2}{2m}}d^2p \int e^{-U(r)}drd\theta= \frac{1}{h^2}(\frac{2\pi m}{\beta}) 2\pi [\int_{0}^{r_0}e^{U_0}dr+\int_{r_0}^{R}dr]$$ $$ =\frac{1}{h^2}(\frac{2\pi m}{\beta}) 2\pi [e^{U_0}(r_0)+(R-r_0)]=\frac{\pi...
  7. E

    Work in two dimensions

    Since we don't know how far does it move in y-axis, I assumed that only x-component does work. a) W=Fx*Δx = 50N*(-6m) = -300 J b) Θ = arctan(12/50) = 13.5° But, I'm not sure that did I do this in right way...h
  8. T

    Can I Combine X and Y Components in the Work Equation?

    I don't know how to combine the x,y components with the equation of work.
  9. N

    Ideal Gas Law in Two Dimensions

    I am creating a two-dimensional model of an ideal gas, and I was wondering how I should determine initial velocity. Ideally, I would like for the simulation to reach a point where the velocity distribution resembles that of the maxwell-boltzmann curve — will this be achieved if I, say, assign...
  10. G

    How would you adapt the laws of physics for two dimensions of time?

    So imagine there are now two dimensions of time, instead of the one dimension which we're used to. The laws of physics which we're used to won't make anymore sense unless they're adapted for the two dimensions of time. How would you adapt them?
  11. CVRIV

    Help with a problem involving motion in two dimensions

    I attached an image with problem and the associated illustration. I don't know what the relevant equations are for this problem. Each and every time I read the problem I keep drawing a right triangle to represent the velocity components. The problem says the river is flowing east at 5km/h. I...
  12. K

    Conservation of momentum in two dimensions

    Homework Statement A bomb initially at rest is exploded into three pieces on a smooth, horizontal surface. Two pieces fly off at a 60° angle to each other, a 2.0 kg piece at 20 m/s and a 3.0 kg piece at 12 m/s. The third piece flies off at 30 m/s with an unknown direction. Determine the...
  13. MathematicalPhysicist

    Renormalization in Two Dimensions

    Homework Statement I am looking for references for the scalar field theory in one-space, one-time dimension defined by: $$\mathcal{L}=-\frac{1}{2}(\partial_{\mu}\phi)^2-\frac{1}{2}m_{2,0}^2\phi^2-\frac{1}{4!}m_{4,0}^2\phi^4-\frac{1}{6!}m_{6,0}^2\phi^6$$ That explains why the only divergences...
  14. R

    Circular motion in one or two dimensions

    I and my teacher argued whether a uniform circular motion in polar coordinates is considered to be a motion in one dimension or it's a motion in two dimensions.
  15. Specter

    Impulse and momentum in two dimensions - Finding velocity

    Homework Statement In a physics lab, 0.30 kg puck A, moving at 5.0 m/s [W], undergoes a collision with a 0.40 kg puck B, which is initially at rest. Puck A moves at 4.2 m/s [W 30 N] . Find the final velocity of puck B. Homework Equations Conservation of momentum Pythagorean theorum The...
  16. C

    Coefficient of restitution in two dimensions

    Homework Statement A ball of mass m hits the floor with a speed v making an angle of incidence theta with the normal. The coefficient of restitution is e. Find the speed of the reflected ball and the angle of reflection of the ball. The Attempt at a Solution I know that momentum is conserved...
  17. S

    Impulse and momentum in two dimensions - velocity question

    Homework Statement Sorry for another question so soon, I am not sure if there is a limit on how many I can ask. I try to keep it to a minimum but sometimes I can't figure it out on my own. Question: In a physics lab, 0.30 kg puck A, moving at 5.0 m/s [W], undergoes a collision with 0.40 kg...
  18. I

    Elastic Collision in two dimensions question

    Homework Statement [/B]A 2.0 kg ball moving with a speed of 3.0 m/s hits, elastically, an identical stationary ball as shown (The first ball is traveling to the right). If the first ball moves away with angle 30° to the original path, determine the speed of the first ball after the collision...
  19. H

    Coulomb's Law in Two Dimensions

    Homework Statement Three charges, q1, q2, and q3, lie in a plane, as shown below. Find the net force on charge q2 (please refer to attachment for diagram) Homework Equations F= k x q1q2/R^2, knowledge of trig functions and separating x and y components The Attempt at a Solution So I found the...
  20. S

    I Gaussian integral in two dimensions

    I am trying to evaluate the following integral. ##\displaystyle{\int_{-\infty}^{\infty}f(x,y)\ \exp(-(x^{2}+y^{2})/2\alpha)}\ dx\ dy=1## How do you do the integral above?
  21. BrainMan

    Dynamics in two dimensions problem

    Homework Statement Homework Equations xf = x0 + v0cos(θ)t + (1/2)axt2 yf = y0 + v0sinθt - (1/2)gt2 F = ma The Attempt at a Solution [/B] I first tried to find the acceleration in the x direction so I could solve for the force xf = x0 + v0cos(θ)t + (1/2)axt2 In order to find the time I used...
  22. K

    Places to learn kinematics in one and two dimensions W/Calc

    Im not sure where to find a good place to learn kinematics in one and two dimensions. Using calculus
  23. Square1

    Adding vector components in two dimensions

    Homework Statement A plane flies 600km/h south. The plane encounters a southwestern wind of 100km/h. Homework Equations What is the velocity (magnitude and direction) of the plane The Attempt at a Solution What I did was break the 100km southwestern vector into its components. 100*cos45 =...
  24. C

    Inelastic collision in two dimensions

    I am a programmer trying to simulate some 2D balls bouncing about and colliding with each other. I have both the ball's velocity components before the collision and I am trying to solve for them. I went to wikipedia to find a formula to satisfy my needs and ran into this section...
  25. shanepitts

    Find work done using force in two dimensions

    Homework Statement Homework Equations ∫F⋅dr=W The Attempt at a Solution
  26. G

    Possibility of violations of Born's rule in two dimensions?

    Hi, Gleason's theorem fails if the dimension of the Hilbert space is two. Does this allow for violations of Born's rule in two-dimensional systems? Or can you somehow tensor the system with the (ever-present and infinite-dimensional) Hilbert space of the rest of the universe, apply Gleason's...
  27. P

    Motion in two dimensions: Launching up an incline

    1. Homework Statement (The following is taken from Sears and Zemansky’s University physics with modern physics, thirteenth edition by Young Freedman. Chapter 3 bridging problem: Launching up an incline at page 95. You fire a ball with an initial speed ##v_0## at an angle Φ above the surface...
  28. I

    'forces in two dimensions' problem

    Homework Statement hello guys, that's the problem, when i tried to solve it using soh cah toh and Pythagoras law it resulted in answers e' and f', which make sense to me because both result it 54.6N and both relevant in directions so i am a bit confused.[/B] Suppose that a force with a...
  29. kostoglotov

    Impulse problem: how can these two angles be different?

    Homework Statement A baseball weighing 140g is traveling to the right at 35 m/s, makes contact with a baseball bat, and then leaves the bat at 55 m/s to the left at an angle 25 degrees from the horizontal. I got the right answer, I how how the solution works mathematically. The answer is...
  30. M

    Motion in Two Dimensions

    Question: In an anniversary celebration of Marilyn Bell's 1954 feat- she was the first person to swim across Lake Ontario- a swimmer set out from the shores of New York and maintained a velocity of 4m/s (N). As the swimmer approached the Ontario shore, she encountered a cross-current of 2 m/s...
  31. K

    Kinematics in Two Dimensions

    Homework Statement I need to find velocity v from the drawing. Homework Equations Equations of kinematics The Attempt at a Solution I found that v=12.134 m/s . I need to know is it correct. [/B]
  32. L

    Equilibrium in two dimensions

    Homework Statement a boy on whom the force of gravity is 400 N hangs on to the middle of a rope stretched between two trees. The rope sags in such a way that it makes an angle of 170 degrees at the boys hands. what force does the rope exert on each tree? Homework Equations F=ma The Attempt at...
  33. A

    Momentum: Mass & Velocity - Get Answer to 2dHW

    Homework Statement The problem is stated here (from brilliant.org) http://i.imgur.com/MkWwnjT.png Homework Equations momentum = mass * velocityThe Attempt at a Solution My attempt at a solution can be found here: http://i.imgur.com/Zsco86W.jpg I get the answer 0.035kg, but that is not an...
  34. RJLiberator

    Calculus based kinematics (two dimensions) question

    Homework Statement A soccer ball is kicked from the ground at an angle of 30◦ with speed 30m/s. Determine the duration of the flight, range and maximal height of the trajectory. Homework EquationsThe Attempt at a Solution 1. Break down the velocity vector into x and y components: 30cos(30) =...
  35. K

    Relative position and velocity question (Two dimensions)

    Homework Statement A freight train is moving at a constant speed of 10 m/s. A man standing on a flatcar throws a ball into the air and catches it as it falls. Relative to the flatcar, the initial vellocity of the ball is 15 m/s straight up. a. What are the magnitude and direction of the...
  36. AlphaA

    A question about Motion in One & Two Dimensions

    < Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown > A balloon going upwards with a velocity of 12 m/s, is at a height of 65m from the Earth at any instant. Exactly at this instant a packet drops from it. How much time will the packet take in...
  37. S

    Motion in two dimensions Help

    Motion in two dimensions! Help! Homework Statement The coordinates of an object moving in the xy plane vary with time according to the equations x =-5.00 sin (vt) and y= 4.00 - 5.00 cos (vt), where v is a constant, x and y are in meters, and t is in seconds. (a) Determine the components...
  38. T

    Motion in Two Dimensions Question

    Homework Statement Two thin rods are fastened to the inside of a circular ring as shown in the figure below. One rod of length D is vertical, and the other of length L makes an angle θ with the horizontal. The two rods and the ring lie in a vertical plane. Two small beads are free to slide...
  39. P

    Net Force in Two Dimensions

    Homework Statement Two tugboats are pulling a large log, as shown in the following diagram. The log has a mass of 250 kg and is initially at rest. How far have the tugboats moved the log after 10 s? http://imgur.com/GS7Y80x Homework Equations c^2=a^2 + b^2 -2ab cosC sin A/ a= sin...
  40. T

    Acceleration in Two Dimensions (Vector)

    Homework Statement A bird flies from Lesser Slave Lake in northern Alberta to Dore Lake in northern Saskatchewan. The birds displacement is 800.0 km [E 7.5deg S]. The bird then flies from Dore Lake to Big Quill Lake, Saskatchewan. This displacement is 400.0 km [E 51deg S]. The total time of...
  41. E

    Dynamics in Two Dimensions Question

    Homework Statement During baseball practice, you go up into the bleachers to retrieve a ball. You throw the ball back into the playing field at an angle of 42° above the horizontal, giving it an initial velocity of 15 m/s. If the ball is 5.3 m above the level of the playing field when you...
  42. S

    Energy conservation in two dimensions

    In an experiment, one of the forces exerted on a proton is F = −αx^2i , where α = 14.4 N/m2. (a) How much work does F do when the proton moves along the straight-line path from the point (0.10 m, 0) to the point (0.10 m, 0.5 m)? (b) Along the straight-line path from the point (0.09 m, 0) to...
  43. P

    Laplace's equation in two dimensions.

    Hi all, Had a doubt regarding Laplace's equation. In many textbooks, the general solution to the two dimensional Laplace's equation is mentioned as: \Phi(\rho,\phi) = A_{0} + B_{0}ln(\rho) + \sum_{n=1}^{\infty}\rho^n(A_ncos(n\phi) + B_n sin(n\phi)) + \sum_{n=1}^{\infty}\rho^{-n}(C_n cos(n\phi)...
  44. Y

    Classical Nucleation theory two dimensions

    Hi everyone, I'm having trouble understanding a problem on CNT in 2d. I'm given the equation \Delta G = \frac{4}{3} \pi R^3 \rho_s \Delta \mu + 4\pi R^2 \gamma for nucleation in 3d. Here mu is the difference in chemical potential between the solid and liquid phase, R is the radius...
  45. T

    Acceleration in two dimensions. Hockey puck question

    Problem: A hockey puck rebounds from a board as shown in figure 16. The puck is in contact with the board for 2.5 ms. Determine the average acceleration of the puck over the interval. t = 0.0025 s |vi|= 26 m/s |vf| = 21 m/s aav = ? *v and a are vectors* I have made several attempts to...
  46. T

    [Analysis] Derivative in Two Dimensions.

    Homework Statement Let f : ℝ2 -> ℝ be some function that is defined on a neighborhood of a point c in ℝ2. If D1f (the derivative of f in the direction of e1) exists and is continuous on a neighborhood of c, and D2f exists at c, prove that f is differentiable at c. Homework Equations...
  47. Q

    Motion in two dimensions please?

    A worker works in a roof and let's a hammer fall over the roof with the speed 4m/s.The roof forms an angle 30 degree related to the horizon and its lowest point its 10meters from the ground.What is the horizontal displacement of the hammer from the moment he leaves the roof to the moment he...
  48. M

    Collision in two dimensions problems

    1. On a table (defining the x,y-plane laying 3 identical coins A,B and C with identical diameter of 18.00mm. The coordinates of their centers are Z(0,0), Y(60.0,0), X(60.0, 45.0) all given in mm. Under what angle relative to the x-axis one has to push Z against Y so that Z performs after the...
  49. L

    Momentum: Collision in two dimensions

    Homework Statement Fast Eddie McSpeedy is a receiver for the Kennesaw Kilowatts in the Metro Metric Football League and Big Bobby Clobber plays defense in the rival Marietta Megatons. Eddie has a mass of 85 kg and Bobby has a mass of 140 kg. Eddie catches the ball and runs eastward at 2.4 m/s...
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