Plane Definition and 1000 Threads

Homework Statement The cylinder x^2 + y^2 = 1 intersects the plane x + z = 1 in an ellipse. Find the point on the ellipse furthest from the origin. Homework Equations $f(x) = x^2 + y^2 + z^2$ $h(x) = x^2 + y^2 = 1$ $g(x) = x + z = 1$ The Attempt at a Solution $\langle 2x, 2y, 2z \rangle...

Homework Statement In the "Before" scenario, there is conductive plate in electrostatic equilibrium with uniform surface charge density +η (the plate has some thickness but the width and length are significantly larger). In the "After" scenario, an infinite plane of negative charge with fixed...

Homework Statement Hi ! :) I'm having some difficulties with the question below, in which there are numerous steps and I am unsure in which part(/s!) I have gone wrong. The question is as below; you must via integration calculate the shaded volume of a perfect cylinder of radius R and height...

Not exactly homework in my case but I guess it fits the level. We know that a = v dv/dx holds when moving on a line. Does it hold when moving on a plane? If yes, what would be the exact formulation of the statement. I mean, I read a = v dv/dx as a(x) = v(x) dv/dx(x) (or are they functions of...

Homework Statement So I am trying to accomplish the above by using spherical coordinates, I am aware the problem may be solved using dv=dxdydz= zdxdy were z is known but I would like to try it using a different approach (using spherical coordinates). Any help would be greatly appreciated...

I want to rotate an inclined plane to achieve a flat surface. I think I can use the Euler angles to perform this operation. Using following data: and following rotation matrix I think you can make the plane flat by following rotations: 1: rotation around x-axis by 45° 2: rotation around...

Homework Statement A warehouse worker pushes a crate of mass 24 kg up a ramp. Assume that the friction between the crate and ramp can be ignored. a) Determine the component of gravitational force directed along the ramp's surface. b) Calculate the force required to move the crate at a...

I have a problem with conceptualising what happens to an object as it travels down an incline slope. Online resources say that as the gradient of the slope increases the acceleration increases, but isn't this incorrect in a sense. Shouldn't it be said that as the incline of a plane increases...

Hello! I've read on several pages that plane mirrors have an infinite amount of focal points. I don't understand? I thought plane mirrors have no focal points because the rays are parallel and don't focus in the first place. Why does a plane mirror have infinity focal points and what does it mean?

My teacher says that "N" has no plane of symmetry(POS). But shouldn't the plane shown with blue be POS? I understand that a plane of symmetry bisects a molecule into halves that are mirror images of each other. For this reason, this plane shown here should be the POS. Where am I...

Conventionally we have the following equation of a plane ax+by+cz=d where d = ax0+by0+cz0. Where (x0,y0,z0) is a known point on the plane. Now if we try to find the distance between a point P and a plane we take any point on the plane Q (x,y,z) and find the vector from Q to P and project on...

Homework Statement I am doing my IB Physics Individual Investigation on how mass affects the stopping distance of a small cart when colliding with an open box at the bottom of an inclined plane. I wanted to know the relationship mass has with the stopping distance, similar to how a train...

http://www.stuff.co.nz/world/middle-east/78357212/egyptair-plane-hijacked-with-82-passengers-on-board.html Obviously this is a developing situation, and information is scarce. It seems the plane has landed, going by the tweet by @AviationSafety -- "We are investigating reports about a possible...

Homework Statement a) A charge q is released a distance d above a grounded infinite conducting plane. It's non relativistic velocity is v. Find the induced surface current density on the plane. b) Show that the above current density produces a vanishing magnetic force on the charge. Homework...

Homework Statement An infinite plane in z=0 is held in potential 0, except a square sheet -2a<x,y<2a which is held in potential V. Above it in z=d there is a grounded plane. Find: a) the potential in 0<z<d? b) the total induced charge on the z=0 plane. Homework Equations Green's function for a...

Homework Statement An infinite plane in z=0 is held in potential 0, except a square sheet -2a<x,y<2a which is held in potential V. Above it in z=d there is a grounded plane. Find: a) the potential in 0<z<d? b) the total induced charge on the z=0 plane. Homework Equations Green's function for a...

Homework Statement A wheel consists of a circular uniform disk with a circular hole in it. The disc is of radius R and mass per unit area ρ. The hole is of radius ro and an axle of radius ro passes through it. The centre of the hole is offset radially from the centre of the disk by ro. The...

Hello PF! I have a project/competition in freshman college Aerospace that calls for a plane that can stay in the air for as long a time as possible while going as far as possible. The requirements don't explicitly say we need rubber bands as a propulsion but pretty much prohibit everything but...

Homework Statement Does the line through the point P(1, 2, 3) with direction vector d = (1, 2, -3) lie in the plane 2x+y-z=3? Homework EquationsThe Attempt at a Solution From the 2x+y-z i can get the vector (2, 1, -3) and the direction vector, their dot product does not equal zero. So, no it...

Homework Statement A skateboarder in a death-defying stunt decides to launch herself from a ramp on a hill. The skateboarder leaves the ramp at a height of 1.4 m above the slope, traveling 15 m/s and at an angle of 40° to the horizontal. The slope is inclined at 45° to the horizontal. With what...

Could someone please help with me with part $(b)$? By "the other set of vectors" they mean $R$, and the linear combination is $(1,2,9) = -3(1,0,-1)+2(2,1,3)$. https://i.imgsafe.org/b80212f.png

In Zee "Einstei gravity in a nutshell" section I.6, page 83, the author says about the approxiamtion of the south pole of sphere How is the first equation approximated by the second? One page later he does this expansion again. Is this thecalculus Leibnitz rule? Or some clever trick...

I am trying to find an equation for a plane that passes through the point (2, 1, 5) however is also perpendicular to the line that passes through the points A(0, 1, 1) and B(1,-1,-1). I am unsure how to begin with this. I have started by finding the normal vector to A and B = (0,1,-1), to find...

For the following question I am given a plane: x + 2y + 3z = 12. I want to find the equation of a line normal to the plane and going through the point (4,6,8). I am trying to use the formula N . (r - r0) = 0 however seem to be getting the incorrect answer :(

If the vector $P = (1,2,-1)$ is parallel to the plane $7x+2y+kz = 5$, then what's the value of $k$?

Homework Statement When resolving forces on an inclined plane, can anyone explain to me why 1.2g in my pic is used as the hypotenuse? It looks intuitively like it should be the opposite or adjacent. Thanks for any help :) Homework EquationsThe Attempt at a Solution

Hello! (Wave) If we want to find the equation of the plane that is perpendicular to the line $l(t)=(-1,-2,3)t+(0,7,1)$ and passes through $(2,4,-1)$. If (x,y,z) is a point of the line then it is of the form (-t,-2t+7,3t+1). We get that $t=-x=\frac{7-y}{2}=\frac{z-1}{3} \Rightarrow...

Close look at the ATLASGAL image of the plane of the Milky Way, Video, available in ultra HD at, http://www.eso.org/public/videos/eso1606a/ Also, Comparison of the central part of the Milky Way at different wavelengths (annotated). Up to 228MB in size, here...

Homework Statement A block of mass m = 2.00 kg is released from rest at h = 0.300 m above the surface of a table, at the top of a θ = 50.0° incline as shown in the figure below. The frictionless incline is fixed on a table of height H = 2.00 m. a. Find a on the incline a=7.51 :) b. Find V(f)...

A particle has initial velocity 3i + 4j and acceleration of 0.4i + 0.3j. what is its speed after 10 seconds? I know the correct way to solve this question is by dealing with x and y components separately and it gets us to the answer 7√2. But what if we first find the magnitude of velocity and...

Homework Statement Show that the orthoprojection of a circle onto a plane is an ellipse Homework Equations Let's say the circle ##{\cal C}## of center ##O## and radius ##R## lies on plane ##P## and we want to orthoproject ##{\cal C}## onto ##P'## The Attempt at a Solution We can say that...

Function kind of cross between a helicoid and a complex plane wave? I would like to translate a mental picture into a mathematical expression if possible. The picture might be roughly thought of as a cross between a complex plane wave and a helicoid. A construction I think goes as follows, take...

Homework Statement Find the locally flat coordinates on the Poincaré half plane. Problem I.6.4 by A. Zee Homework Equations [/B] Poincaré Metric: ##ds^2 = \frac{dx^2 + dy^2}{y^2}## The Attempt at a Solution First, I'm having problems with the explanation in Zee's book. He said that we can...

Homework Statement You are traveling on an airplane. The velocity of the plane with respect to the air is 160 m/s due east. The velocity of the air with respect to the ground is 41 m/s at an angle of 30° west of due north. 1) What is the speed of the plane with respect to the ground? Homework...

Homework Statement A suitcase of mass 16 kg is placed on a ramp inclined at 15 ° to the horizontal. The coefficient of friction between the suitcase and the ramp is 0.4. Determine whether the suitcase rests in equilibrium on the ramp, and state the magnitude of the frictional force acting on...

Homework Statement Based on wave attenuation and reflection measurements conducted at 1MHz, it was determined that the intrinsic impedance of a certain medium is , and the skin depth is 2m. Determine: a) The conductivity of the medium b) The wavelength in the medium c) The phase velocity...

Homework Statement A 77.0 kg patient is suspended in a raised hospital bed as shown in the figure. The wire is attached to a brace on the patient's neck and pulls parallel to the bed, and the coefficients of kinetic and static friction between the patient and the bed are 0.500 and 0.800...

I've done a question similar to this, however this one has no complete equations i can solve for. Determine the equation of the plane that passes through (1,3,8) and is perpendicular to the line of intersection of the planes 3x−2z+1=0 and 4x+3y+7=0. I know to take the cross product of the two...

Homework Statement Provide an expression in Cartesian coordinates for a plane wave of amplitude 1 [V/m] and wavelength 700 nm propagating in u = cosθx + sinθy direction, where x and y are unit vectors along the x and y-axis and θ is the measured angle from the x axis. Homework Equations...

when deriving the electric field through using gauss's law, I do not completely understand why when calculating for the charge enclosed the answer key says "The surface charge distribution on is uniform. The area of the intersection of he non-conducting plane with the Gaussian cylinder is equal...

Consider two blocks connected by an ideal rope that passes through an ideal pulley fixed on the corner of the wedge as shown in the figure. The blocks have masses m1 and m2. The block of mass m1 is on the incline surface (which is frictionless) while the block of mass m2 hangs up in the air...

Homework Statement Say you push a sled of mass m up a hill that is angled upwards at a certain angle \theta at a constant velocity. The hill has snow on it offering a friction force that is equal to 30% of the sleds weight. If you pushed the sled down the hill with the same amount of force...

Homework Statement A 2000 kg plane is landing at an airfield with an initial speed of 50 m/s. The force of friction is 1/4 the weight of the plane. What is the acceleration of the plane? Homework Equations Fnet = ma Fnet = something - ff The Attempt at a Solution 2000a = thing I don't know...

I was wondering it the projection of the measurement axes onto a spinning vector modeled by a plane would produce correlations of entangled particles in line with what is found by experiment. Does anyone know of any discussions on this subject? Would this lead to stronger correlations than spin...

I'm not really sure where to post this. I saw that this Homework section exists even for technically non-homework (I'm designing a machine at work, but the problem is homework-esque and my fluid dynamics knowledge is rusty at best). I'm not sure if this introductory or advanced, and the template...

Hi, I'm doing an experiment to get my silver CREST award, in which I've created a mechanical paper plane thrower. I have thrown various types of plane, but all with the same design. The thrower uses a 9V battery, but is more like 6 now. The thrower has two motors, each which take 70mA. The...

I am reading David Poole's book: Linear Algebra: A Modern Introduction (Third Edition) ... I have a basic (and probably simple) question regarding Poole's introductory discussion of the vector or parametric form of the equation of a plane \mathscr{P} (page 38, Section 1.3 Lines and Planes) ...

So if I'm given a coordinate plane that graphs the position of a particle, how do you get the s(t), in respect to time if given a table of time intervals. Given: f(x) = -x^2 Needed: s(t)? v(t)? a(t)?

Homework Statement A motorised model plane is attached to a light string anchored to a ceiling. The plane follows a circular path of radius 0∙35 m as shown in Figure 2. The plane has a mass of 0∙20 kg and moves with a constant angular velocity of 6∙0 rad s−1 . (a) Calculate the central force...

Homework Statement How do we find the motion equation and more specifically the motion equation of something with a mass $m$ in the vertical plane along a cylindrical path of radius $R$, (Translation: A point of mass $m$ slides frictionless in the vertical plane along a cylindrical path of...