Plane Definition and 1000 Threads

How does the object slide down the surface (With friction negligible)

Hello, I saw an applet awhile ago during a late-night mathematical web-surfing marathon that used the addition of plane waves at different angles to generate aperiodic tilings (like the penrose tiling.) I haven't been able to find it again. I'm trying to make my own version of it, using the same...

$\tiny{s6.194.4.12.4.29}$ $\textsf{a. Find a nonzero vector orthogonal to plane through the points: }$ $\textsf{b. Find the area of the triangle PQR}$ \begin{align} \displaystyle &P(1,0,0)& &Q(0,2,0)& &R(0,0,3)\\ %&=\color{red}{\frac{1209}{28} } \end{align} $\textit{do what first?}$

Homework Statement A mass ##m_1## is attached to a second mass ##m_2 > m_1## by an Acme (massless, unstretchable) string. ##m_1## sits on a frictionless inclined plane at an angle ##\theta## with the horizontal; ##m_2## is hanging over the high end of the plane, suspended by the taut string...

Hello, I have a few questions regarding the osculating plane, which I understand to be the plane generated by the Principal unit tangent vector and principal unit normal vector (both are orthogonal), and the inertial Cartesian z-axis. Ultimately, I plan to understand the geometric/kinematic...

Homework Statement 2 masses are connected by a spring. They are on a frictionless plane inclined relative to the horizontal by ##\alpha##. The masses are free to slide, rotate about their center of mass, and oscillate. 1. Find the Lagrangian as a sum of the Lagrangian for the COM motion and a...

Homework Statement I am asked to find the Hamilton equations for a block on an inclined plane (no friction) Homework EquationsThe Attempt at a Solution Please ignore the fact that my steps are written in French (sorry!) I am no longer sure of what I'm doing when it comes to finding the...

Say i Have 1. A perfectly spherical and perfectly rigid Ball 2. A perfectly flat and perfectly rigid wall Say i throw the ball at my FLAT wall also giving the ball a linear velocity The only contact with the wall and the ball is a point... a POINT ! So, I can as well forget about the rest of...

Homework Statement An intensity current I descends down the z-axis from z = \infty to z = 0, where it spreads out in an isotropic way on the plane z = 0. Compute the magnetic field. Homework Equations The only relevant equation I can think of is Ampere's Law, \oint_\gamma \vec{B} \cdot...

Homework Statement I am about to do an experiment where we masure the average speed of a cart released from the top of an inclined plane that has little friction (air track). The speed measurement is done by a photo gate. This is repeated a hundred times. Homework Equations I need to come up...

for a disck rolling on a horizontal plane the kinetic energy should be the kinetic energy of the CM of the disk with respect to the origin plus the kinetic energy due to the rotation of the disc about his CM so T= 1/2 (M V^2) +1/2(I ω^2) where M is the mass of the disk and V is the velocity of...

Are all planets in our Solar System in the same plane ? :))

Homework Statement find the vector in R3 that is a unit vector that is normal to the plane with the general equation x − y + √2z=5 [/B]Homework EquationsThe Attempt at a Solution so the orthogonal vector, I just took the coefficients of the general equation, giving (1, -1, √2)[/B] then...

Homework Statement A block of mass m1 is at rest on an inclined plane that makes an angle (theta) with the horizontal. The coefficient of static friction between the block and the inclined planed is µs. A massless, inextensible string is attached to one end of the block, passes over a fixed...

Homework Statement I am given the following figure: These are converging rays that appear to be going to a point F convert to a plane wave upon hitting the boundary between n2 and n1, and I am asked to find the equation for the boundary between n1 and n2 that perfectly accomplishes this...

Homework Statement I have a question that came up during a mechanics problem. (I put my question towards the end of the post) A particle slides on a smooth inclined plane whose inclination ##\theta## is increasing at a constant rate ##\omega##. If ##\theta(t=0)=0## at which time the particle...

Ran into a question in my amateur research. Been waaay too long since college physics, and I've exhausted searches. This is the theoretical question: Assume a non-conducting, infinite plane charged to +10 kV. An electron leaves perpendicular to the surface with an energy of 10 keV. How far...

Homework Statement Find the centroid of solid enclosed by surface z= y^2 , plane x=0 , x = 1 and z =1 . The density is 1 Homework EquationsThe Attempt at a Solution Here's my working . Centoird = mass of inertia / mass So , i find the mass first . It's clear that the circle is on zx...

I've just had my first batch of lectures on complex numbers (a very new idea to me). Algebraic operations and the idea behind conjugates are straightforward enough, as these seem to boil down to vectors. My problem is sketching. I have trouble defining the real and imaginary parts, and I don't...

Homework Statement Find the surface portion bounded by plane 2x +5y + z = 10 that lies in cylinder (x^2) +(y^2) = 9 ... I have skteched out the diagram and my ans is 5sqrt(30) instead of 9sqrt (30) as given by the author ... Anything wrong with my working ? Homework EquationsThe Attempt at a...

Homework Statement ##\vec { \dot { r } } =(t+1)\vec { A } +(1-sint)\vec { B } \quad \vec { r(0) } =\vec { C } ## a. Find an equation of the tangent line to the curve at ##\vec { r(0) } =\vec { C } ##. b. Use a definite integral to find ##\vec { r(t) } ## c. If ##A## and ##B## are non...

Homework Statement As shown in the figure below, small object A is projected upward along a smooth slope forming angle α with the horizontal plane, with initial speed v0 in the direction of angle θ from the horizontal within the slope’s plane. The object continues to travel along the surface...

Homework Statement Mass 1 of 1 kg is resting on an inclined plane of 30 degrees. A string is attaached to the mass and ran through a pulley at the top of the plane and attached to a suspended mass 2 of 2 kg. How far must the inclined plane be rotated until mass 1 starts to move down the...

Homework Statement During a flume ride the boat plunges 54 feet down a 43 degree incline. Assuming coefficient of friction .12 determine the acceleration of the boat.[/B]Homework Equations I'm really not sure, no mass is given or force. All of the equation I know involve mass or force. The...

Homework Statement r(t) = < 2e^t - 5 , e^t +3t^2 , 4t^2 +1> Is a curve that lies within a plane. Find the equation of this plane. The Attempt at a Solution I am not sure if my approach is correct. These are my results: x=2e^t - 5 y = e^t +3t^2 z = 4t^2 + 1 z = 4t^2 + 1...

The problem I am trying to write the equation for the plane on the following form ## ax + by + cz + d = 0 ## $$ \begin{cases} x = 1 + s - t \\ y = 2 - s \\ z = -1 + 2s \end{cases} $$ The attempt ## s, t ## are the parameters for the two directional vectors which "support" the plane. $$...

Homework Statement Force F = 460 N acts perpendicular to the inclined plane Determine the moment produced by F about point A. Enter the x, y, and z components of the moment separated by commas. Homework EquationsThe Attempt at a Solution r(CA)=4j-3k u(CA)=4/5j-3/5k r(CB)=-3i+4j...

Homework Statement A current of 3 A flows down each of two long vertical wires, which are mounted side by side 5 cm apart. Show on a diagram the magnetic field pattern in a horizontal plane, indicating clearly the direction of the magnetic field at any point. What is the magnitude and direction...

Homework Statement 7. A boy drags his 60.0-N sled at constant speed up a 15.0° hill. He does so by pulling with a 25.0-N force on a rope attached to the sled. If the rope is inclined at 35.0° to the horizontal, (a) What is the coefficient of kinetic friction between sled and snow? (b) At the...

Homework Statement Function is ##f(x,y)=((x-1)y)^\frac{2}{3}##,##\space\space(a,b)=(1,0)## a) Calculate ##f_{x}(a,b)## and ##f_{y}(a,b)## at point ##(a,b)## and write the equation for the plane. Homework EquationsThe Attempt at a Solution So...

Homework Statement If a, b and c are coplanar vectors related by λa+μb+νc=0, where the constants are non-zero, show that the condition for the points with position vectors αa, βb and γc to be collinear is: λ/α + μ/β + ν/γ = 0 Homework Equations Dot product Cross product Tripple product Vector...

Homework Statement A boy drags his ##60.0N## sled at constant speed up a ##15.0°## hill. He does so by pulling with a ##25.0N## force on a rope attached to the sled. If the rope is inclined at ##35.0°## to the horizontal, (a) What is the coefficient of kinetic friction between sled and snow...

Homework Statement Suppose that you have the following information concerning a differentiable function ##f##: ##f(2,3)=12##, ##\space## ##f(1.98,3)=12.1##, ##\space## ##f(2,3.01)=12.2## a) Give an approximate equation for the plane tangent to the graph of ##f## at ##(2,3,12)##. b) Use the...

Homework Statement For a plane, monochromatic wave, define the width of a wavefront to be the distance between two points on a given wavefront at a given instant in time in some reference frame. Show that this width is the same in all frames using 4-vectors and in-variants. Homework...

Homework Statement I have to find for which values of the real parameter ##b## the following plane is orthogonal to the following line: ##\pi : 5x + (2b - 1)y - (1 + 8b)z + 3 = 0## ##s : \begin{cases} x + z - 4 = 0 \\ x - 3y + z + 2 \end{cases}## Homework EquationsThe Attempt at a Solution For...

Fermat’s principle states that light follows the path of least time. In textbooks, a specific formulation of Fermat’s principle is about the optical path between two points, A and B: How can a ray of light, emitted from point A, reach point B? Suppose that there is a plane wave in free space...

Hi, I'm recently reading an introductory text about particle physics and there is a section about the Dirac equation. I think I can understand the solutions for rest particles, but the plane wave solutions appear to be a bit weird to me. For instance, when the upper states are (1 0), the lower...

Hi all, I have a very simple question. Will an object dropped from a plane moving at a constant velocity ever achieve purely vertical motion? (Make sure we're not taking air resistance into account) Thanks

Homework Statement Find for what real parameters the line ##r## is parallel to the plane ##\pi##. ##r: \begin{cases} x - 3y + 3 = 0 \\ 2y + z - 5 = 0 \end{cases}## ##\pi : 6x - (a - 1)y + 3az - 11 = 0## Homework EquationsThe Attempt at a Solution So, the only method I know is to put the three...

Homework Statement I have a block of mass M attached to a cord of mass m on an inclined plane of angle θ . A force F is pulling the cord & block up the plane. I have to find the force exerted on the block by the cord. The surface is frictionless Homework Equations F = ma The Attempt at a...

Homework Statement Finding yourself in a nearly empty airplane, you take a seat other than your allotted seat. Soon, an air hostess comes up to you and requests you to occupy a different seat. What may be the reason? A) The plane momentum can change if the passengers change their position...

Homework Statement A travel agency knows from experience, that 5% of passengers who have booked a ticket will not show up for the flight. Therefore the company sells 260 tickets for a plane that can only take 255 passengers. What is the probability that all of the passengers arriving for the...

Homework Statement there is a frictinless slope. And there is a box sliding down the slope. let's say that the slope slides from right, towards the down and left. object's mass is unknown value m. angle of the slope is 35deg. calculate the absolute value of the acceleration that the box has...

Here is the problem: I am sure I can use pythagorean theorem of quadratic equation to solve but to be honest I'm blanking ridiculously. I have tried setting it on a coordinate grid and finding the resultant, but I have had no luck! I know I've done this problem before in high school but I'm...

I found the following problem on the 2009 F = ma exam. 24. A uniform rectangular wood block of mass M, with length b and height a, rests on an incline. The incline and the wood block have a coefficient of static friction, μs. The incline is moved upwards from an angle of zero through an angle...

Homework Statement Homework Equations f = mu_k * N F=ma The Attempt at a Solution

Homework Statement The figure below shows a closed loop of wire that consists of a pair of equal semicircles, of radius 7.0 cm, lying in mutually perpendicular planes. The loop was formed by folding a flat circular loop along a diameter until the two halves became perpendicular to each other...

Homework Statement Suppose r:R\rightarrow { V }_{ 3 } is a twice-differentiable curve with central acceleration, that is, \ddot { r } is parallel with r. a. Prove N=r\times \dot { r } is constant b. Assuming N\neq 0, prove that r lies in the plane through the origin with normal N. Homework...

Homework Statement my notes gave that in a 3d cubic , plane stress is state of stress in which two surfaces are free of stress ... Homework EquationsThe Attempt at a Solution Does it mean the we only consider the stresses in xy plane only ? because the object is too thin, so we assume it's 2...

Hello guys, How can i check if coordinantes A,B,C and D are in the same plane? 3D space(x,y,z) Can i take the cross product: AB x AC and check if its perpendicular to for example DC x DB. and then check if the crossproducts are parallell? but i guess this can give me two parallell vectors in...