What is Plane: Definition and 1000 Discussions

Homework Statement [/B] This problem is from David Morin's Introduction to Classical Mechanics, Chapter 3, Problem 7: A block is placed on a plane inclined at angle θ. The coefficient of friction between the block and the plane is μ = tan θ. The block is given a kick so that it initially moves...

Suppose a plane contains the origin and has normal $n$. Is it true that the projection of a vector $u$ on the plane along vector $v$ is $(v\times u)\times n$, where $\times$ denotes the cross product? I can see that the direction is right, but I am not sure about the length. Links to textbooks...

Homework Statement a. Find a point at where these lines intersect b. Find the equation of a plane that contains the two lines. Homework Equations r[/B] = <1,3,0> + t<3,-3,2> r = <4,0,2> + s<-3,3,0> The Attempt at a Solution I correctly found the point of intersection to be...

It has a straight cone and a plane that cuts it as shown in the image. What angle should the plane form with the base of the cone ?, so that the plane cuts the cone in 2 parts of equal volume.

After watching a video on YouTube, I recently became interested in the dynamics and physic's of why we aren't using electrical powered planes instead of burning thousands of fossil fuels every day. After doing a bit of my own research, I found the problem. When we increase the weight, we have to...

A question came up with some friends recently that googling hasn't turned up a satisfying answer to. Simply put: If the world was flat and infinite (ignoring all the stupidity of this) how far could you see from sea level before the atmosphere itself is preventing any light reaching you...

Homework Statement As part of an elaborate prank, a well-greased watermelon (m=4.72 kg) is placed on a ramp inclined with angle θ=27.4° with respect to the horizontal. Because of the grease, the coefficients of static and kinetic friction are µs= 0.560 and µk= 0.392 respectively. The...

Homework Statement Two blocks m1 and m2 are connected by a weightless rod are on a inclined plane of ∅=37° and μ =0.25 .What is the common acceleration and Tension of rod if m1 is 4 kg and m2 is 2 kg such that the 4kg block is the upper block. OPTIONS A =4m/2 T=0 B =2m/2 T=5N C =10m/2 T=10N D...

Homework Statement x = <0, 10, 0> v1 = <4, 3, 0> v2 = <0, 0, 1> Project x onto plane spanned by v1 and v2 Homework Equations Projection equation The Attempt at a Solution I took the cross product k = v1xv2 = <3, -4, 0> I projected x onto v1xv2 [(x*k)/(k*k)]*k = <-4.8, 6.4, 0 = p I finished...

Dear Everybody, I am wanting to check the solution to this question: Sketch the set of points determined by the given conditions: a.) $\left| z-1+i \right|=1$ b.)$\left| z+i \right|\le3$ c.)$\left| z-4i \right|\ge4$ work: I know (a.) is a circle with radius 1 and its center at (-1,1) on the...

Homework Statement See question number 1. Homework Equations Work Energy Theorem, work done by all the forces=change in K.E. The Attempt at a Solution I tried solving this question this way, please help me calculate the Work Done by spring here?? I will be thankful for any help!

Homework Statement The edges of a parallelopiped are given by the vectors (2î + 3j^+ 4k^), 4j^ and (5j^ + mk^). What should be the value of m inorder that the volume of the parallelopiped be 24? Homework EquationsThe Attempt at a Solution Volume of the parallelopiped is the scalar triple...

1. Vo Mass=m 2.So we tried two ways of doing this, one is by taking the y component of the i itial velocity and using that and the other by using the component of its weight parallel to the initial velocity.They give conflicting answers. For the left one it turns out to be t=Vosinθ/g But for...

We have a cube on an inclined plane. The tipping condition is the presence of an unbalanced torque relative to the center of mass (contributing forces are: the normal force and the force of friction). However, is this conditions equivalent to the previous one: The line of action of the force of...

Homework Statement Homework Equations [/B]The Attempt at a Solution I got -1, but the answer says "6". Could you help me, please?

What's the minimal angle of a ramp such that a cube with side 10 cm placed on it will tip over? The coefficient of friction between the cube and the ramp is 0.6. I have given it some thought and I have come to certain conclusions: I think that the cube will tip over once the force of gravity...

Homework Statement Prove that ## \sin(z_1+z_2) = \sin z_1\cos z_2+\sin z_2\cos z_1## such that ##z_1,z_2\in\mathbb{C}## Homework Equations ##\sin z = \sum\limits_{n=1, \mathrm{ odd}}^\infty (-1)^{(n-1)/2}\dfrac{z^n}{n!} = \sum\limits_{s=0}^\infty (-1)^s\dfrac{z^{2s+1}}{(2s+1)!}## ##\cos z =...

Homework Statement A speed of a body of mass 8 kg is 6 m/s in position A. By the time it gets to B, the speed is measured to be 12 m/s. What is the frictional force opposing the motion? The incline is 30 degrees, the height of the ramp is 12 meters. Position A is at the top of the ramp...

In these notes, https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016/lecture-notes/MIT8_04S16_LecNotes11.pdf, in the middle of page 5, it is mentioned: We will be interested in bound states namely, energy eigenstates that are normalizable. For this the energy E of the states...

I am doubting that any plane wave is generated from a spherical wave. At large distance the radii of curvature becomes so large that we can think it as plane. Like we se Earth surface as plane though it is spherical. Is it true? I have a mathematical proof for my argument!

How do you find the equation of a plane in determined by say three or four points in $\mathbb{R}^4$? In $\mathbb{R}^{3}$ we would use the cross product to find normal vector, but that doesn't apply in $\mathbb{R}^4$.

Hello, I believe that this is the correct forum for this post but please let me know if otherwise. I have the following data in R4, id x y z a B -0.0700177 0.382249 -0.289338 0.00349957 A 1.13388 1.77602 -0.679365...

hi everyone iam new here and i need help in general plane motion when we applied this eq aG=(angular acceleration)*r

Homework Statement Homework Equations maximum torsional shear stress = (Torque*radius)/polar moment of inertia The Attempt at a Solution I am lost on equation(4-14), I looked through the textbook but didn't find a derivation.

If I try to calculate the electric field in the x-y plane of a ring of charge resting at the origin on the x-y plane, I keep getting zero. I start with Coulomb's Law. $$ dE(r) = \frac{1}{4\pi\epsilon}\frac{dq}{r^2} = \frac{\lambda R}{4\pi\epsilon}\frac{d\theta}{r^2},$$ in which ##\vec R## is...

Hello! I am reading about image charges for an infinite plane and a charge above the plane. In the book I am reading (Griffiths) the author says (and uses this results several times) that the field below the plane is 0. How do we know this? The method of the mirror charges gives the V above the...

Homework Statement 15.1 The airspeed of the plane is 200m/s, directed north. If the wind speed is 30m/s in the direction shown, determine the ground speed and the course (angle θ) of the plane. Homework Equations The Attempt at a Solution Is it so far correct the above? More questions...

How do i apply the laws of refraction to plane and curved surfaces. I have absolutely no idea how to even start on this one, its got nothing to do with the course, i am going to study. i need to understand this to move on but i genuinely have absolutely no interest in optics. I really can not...

Homework Statement Problem: Please find an equation for the plane that contains the point <3, -2, 4> and that includes the line given by (x-3)/2 = (y+1)/-1, z=5 (in symmetric form). Simplify Homework Equations I'm really not sure where to start and what process to take to arrive to my answer...

Homework Statement A light rod ##AB## of length ##2a## has a particle ##P## of mass ##m## attached to ##B##. The rod is rotating in a vertical plane about a fixed smooth horizontal axis through ##A##. Given that the greatest tension in the rod is ##\frac {9mg}{8}##, find, to the nearest degree...

Homework Statement Identify the following figures in the plane, saying if they are circles, ellipses, hyperboles or parabolas and giving their centers, rays, foci, and guidelines as the case may be:Homework Equations x² + y² - 3x = 0 The Attempt at a Solution x² + y² - 3x = 0 x(x - 3) + y² = 0...

Hello guys, i`m currently making simulation of 2 dimension rolling disk on elastic sin/cosine plane. I`m just wondering if the theory applicable.

Homework Statement [IMG]http://[url=https://ibb.co/b3Emfo]https://preview.ibb.co/gLaEY8/20180527_055248.jpg[ A conducting bar slides down without friction on a pair of conducting rails separated by distance d. Connected to resistor R and there magnetic field B directed upward, perpendicular to...

Homework Statement for an assignment, we must investigate physics in context, my selected context is a log flume ride, focusing on the final slope. the height of the inclined plane is 13m, the hypotenuse is 17m and the horizontal length is 11m, calculated with a scale diagram and kinematics...

Homework Statement A block of mass 20kg is on rest on a rough plane inclined at 60 degrees to the horizontal. A force P is applied to the block to "maintain equilibrium". P is parallel to the line of greatest slope of the inclined plane. The maximum value of P is twice the minimum value of P...

Homework Statement {(x,y) ∈ ℝ^2 : (y-x)(y+x) = 0 } Homework EquationsThe Attempt at a Solution [/B] Is the reason the answer is the union of y = -x and y = x because if you divide (y-x)(y+x) = 0 by y-x you get y = -x and if you divide (y-x)(y+x) = 0 by y+x you get y = x? and if you...

Homework Statement Suppose that you want to take a mirror selfie, standing 3.05 m in front of a plane mirror. Calculate the distance that the camera will focus to, to get a clearly focused image of your beautiful self. Homework Equations d0 = diThe Attempt at a Solution Would I be correct in...

To whom it may concern, I am having issues with a given assignment in my quantum mechanics class. The instructions listed below are all I have to go on since the prof. is not available for discussion and I have searched through at least 15 articles regarding plane waves and a dozen textbooks...

Homework Statement Find the value of the parameter α for which the pencil of planes through the straight line AB has a common plane with the pencil of planes through the straight line CD, where A(1, 2α, α), B(3, 2, 1), C(−α, 0, α) and D(−1, 3, −3). Homework Equations Let Δ be a line given by...

Homework Statement Two spheres are placed side by side on an inclined plane and released at the same time. Both spheres roll down the inclined plane without slipping. (a) Using FBD, explain what force provides the torque allowing the sphere to roll down the inclined plane. (b) Which sphere...

Homework Statement A particle is thrown upward with speed 10√3 m/sec. It strikes an inclined surface. Collision between the particle and inclined plane is perfectly inelastic. What will be the maximum height attained by the particle from the ground. 2. Relevant information and equations In...

Would there be a way to take a uv map and compute the 2 dimensional position of a viewing plane or eye or camera, without the need to expand the parametric equation into three dimensions? In the above video the uv map in the background yellow is calculated first. Then only the bright portions...

Homework Statement Two block M1 and M2 rest upon each other on an inclined plane. Coefficient of friction between surfaces are shown. If the angle θ is slowly increased, and M1<M2 then Options : 1- Block A slips first. 2- Block B slips first. 3- Both slip simultaneously. 4- Both remain at...

I love this stuff! An amateur gets this one, though his result is refined by the pros. His paper on arXiv is here.

Homework Statement A plane starts its descent from height ##y =h## at ##x = -L## to land at ##(0,0)##. Choose ##a, b, c, d## so its landing path ##y =ax^3 + bx^2 + cx + d## is "smooth". With ##\frac{\mathrm {d}x}{\mathrm {d}t} = V =##constant, find ##\frac{\mathrm {d}y}{\mathrm {d}t}## and...

Homework Statement Not sure if the link is showing. But it's imgur.com/a/LEvd0 Homework Equations The steps I've taken so far as written in the attempt section below is correct. The solution provided then proceeds with letting ##z = x + iy## and setting ##\ddot z+i \omega \dot z = 0##. Then...

Hi. Are all transverse waves plane waves ? Are all plane waves transverse ? I'm confused about the difference. I know the difference between transverse and longitudinal waves but I'm not sure on how plane waves fit into the picture ? Thanks

I"m wondering, at the abstract level, why different mathematics is used to calculate the Normal Force in an inclined plane versus a banked turn (which a vehicle is driving around). For an inclined plane, the standard approach is take weight and resolved into parallel and perpendicular vectors...

1. Homework Statement picture Homework Equations f=ma The Attempt at a Solution Below is my attempt for part B, i am not sure what i am doing wrong here but my answer is off for acceleration

The question that I'm trying to answer states "Make a vector equation of a plane that is perpendicular to the z axis." How do i ensure its perpendicular? How do i start this equation? Another question similar to this that i am also struggling states "What is the vector equation of a 2D line...