Plane Definition and 1000 Threads

Homework Statement A uniform right circular cone of height h, half angle α, and density ρ rolls on its side without slipping on a uniform horizontal plane in such a manner that it returns to its original position in a time \tau. Find expressions for the kinetic energy and the components of...

Homework Statement While you were looking at the reflection of your feet in a plane mirror, you saw a dark spot on the glass. Assuming your height is 1.50 m, and that the eyes are located 0.1 m below the top of the head (a) What is the distance between the spot and the floor? (b)...

Say I have a plane, and it intersects with a [edited]cylinder*. What kind of method should I use to go about solving this? I've tried setting up a ##\int \int dA## situation, but wasn't sure that was applicable because it's in 3-space (also my plane is in terms of x y and z). I know it's...

Ok, so I'm really hoping someone can help me logic my way through this. I have a function to the effect of: ##r(u,v)=f(u,v)\hat{i} + g(u,v)\hat{j} +h(u,v)\hat{k}## I need to find an equation of a tangent plane at a point ##(u_{0},v_{0})## and quite frankly I'm at a loss on how to do this. So...

Homework Statement Find the volume enclosed by the cone x^{2}+y^{2}=z^{2} and the plane 2z-y-2=0. Homework Equations \int\int\int dV The Attempt at a Solution In the image Cono=Cone and Plano=Plane

Homework Statement Homework Equations N/AThe Attempt at a Solution The problem is that I don't get the right answer which is: 2x + y + 7z = -3. Can you please help me find where I went wrong?

Homework Statement Given a transformation of the plane F(x,y) = (2x+y,x-2y), find F-1. Homework Equations Actually this exercise had an item (a) which I had to prove this is a transformation. So I proved this function is injective and surjective. I know F(x,y) = (u,v) IFF F-1(u,v) =...

Problem: a 1200-N go-cart is being pulled up a 25 degree incline by a rope that makes an angle of 35 degrees with the horizontal. Neglecting all frictional effects, determine the tension in the rope necessary to pull the cart up the incline at a constant speed Relevant equations: Sum of the...

The tension in the rope is actually being provided by a solid sphere with radius 23.5 cm that rolls down an incline as shown in the figure. The incline makes an angle of 32° with the vertical. The end of the rope is attached to a yoke that runs through the center of the sphere, parallel to the...

Hey guys, I'm really really confused on how we come about the plane z = x - y. I always have been and it's proving to hurt my progress, any help will be accepted.

Hello, I have a project whereby I am designing a toy that spins a horizontally positioned propeller, then releases it. After releasing it, the propeller gains height, but moves somewhat away from the operator of the toy. Is the direction of airflow through the propeller vertically? If...

Homework Statement A block with mass m = 5.00kg slides down a surface inclined 36.9 ∘ to the horizontal (the figure (Figure 1) ). The coefficient of kinetic friction is 0.27. A string attached to the block is wrapped around a flywheel on a fixed axis at O. The flywheel has mass 23.0kg and...

Homework Statement For the series x^n - x^(n-1) - x^(n-2) ... - x^(0) the roots seem to be x = 2 and the circle around the complex plane with radius i or 1 I'm not sure how you would say it as n approaches infinity. Here's an image of the roots where n = 15...

Hi Im busy creating an application to simulation a rocket in orbit. I am having trouble as the results I am getting are incorrect. Could someone please check if I am using the correct method as stated below. Everything works on a 2d plane, and has a x and y coordinate and a x and y...

Can someone tell me how a German plane Messerschmitt Me 163 lands? Because I found out that this plane lands without landing gears.

Given the transfer function G(s) = 1 / (s(s+1)(s^2 + 4s + 13)), how would I determine the range of the values of K>0 such that the closed-loop poles are in the left-hand plane? Picture of block diagram with transfer function: Not sure if this is right at all, but I know that a system is...

Homework Statement If a,b and c are the x-,y-, and z-intercepts of a plane, respectively, and d is the distance from the origin to the plane show that: 1/d2=1/a2+1/b2+1/c2 Homework Equations distance from a point to a plane: [tex] d=|Ax0 + By0 + Cz0 +D|/√a2+b2+c2 The Attempt...

Homework Statement using a rotation transform, show that the plane z = b - y can be transformed to the horizontal plane \widehat{z} = \frac {b} {\sqrt{b^2 + c^2}} Homework Equations ^ The Attempt at a Solution I just need some help understanding the question, if I could get a...

Homework Statement I've been stuck on this problem for hours now. I know it has to be somewhat simple, but I am not too great in physics, so I am asking for help on how to complete this problem. Two blocks are positioned on surfaces, each inclined at the same angle 50 degrees with respect...

Hello to everybody, the question seems trivial in my mind, yet, is it legal to say that there is not unique frame of 0 total momentum in the Minkowski spacetime plane? I am thinking of two non-accelerating equal masses on a horizontal plane, one is moving horizontally, the other...

Homework Statement A skier, mass m = 85 kg including skis, poles and clothes, skis directly down a slope with an angle Φ = 21° to the horizontal. His body is rigid, the poles are not touching the snow. He is traveling at a constant speed of 71 kph in a straight line. The coefficient of...

Alright, so I have tried my hand at this problem but keep hitting a wall. (NOTE: Every time I have tried to use ##\LaTeX## syntax in this post, it has not worked. As a result of this, and in the interest of making it easier for those who read this post to help me, I have attached a LaTex...

For a mass on an incline plane, is the downward force mg cos Θ or -mg cos Θ? I'm inclined to state there should be a negative but from my lectures, the negative does not appear to be stipulated. I was wondering if it's was a mistake by the lecturer. mg cos Θ + FN = 0 mg cos Θ = -FN the...

Homework Statement Show that arg[(z-1)/(z+1)] represents a circle. Find it's radius and centre. Homework Equations The Attempt at a Solution using z = (x+iy) i narrowed down to (z-1)/(z+1) = (iy)/(1+x) , assuming it was a circle. What next? Is this correct approach??

Homework Statement I attached the question. Homework Equations M = r x F M = F x d Resolving forces, Fx/Fy/Fz = F cos/sin theta (depending on which angle you take) The Attempt at a Solution I can easily find the moment of the 100 N and 120 forces, but I'm having trouble finding...

Homework Statement again there is no answer provided in the book! a +bt +ct^2 = z where t is a real parameter, and a, b, c are complex numbers with b/c real Homework Equations The Attempt at a Solution b/c real indicates that b and c are pure imaginary so when you split the...

Homework Statement find the locus in the complex plane that satisfies z -c = p (1+it/1-it) c is complex, p is real t is a real parameter Homework Equations The Attempt at a Solution there is no answer in the textbook so i wanted to check my answer. I got a unit circle...

Consider the configuration below shown in the attached picture! The wedge can slide on the inclined plane and the cube on the wedge.Their motion is described by x_1 and x_2 respectively. There is no friction and the inclined plane doesn't move. Here's the Lagrangian of the system...

Homework Statement To illustrate there is an incline plane (Mass=M) on a frictionless horizontal plane. It is being pushed by an F force on its non incline side. There is also an m mass on the incline. Mass m does not slide over M. Angle of the incline is Beta. sin B= 0.6, cos B= 0.8, M= 3...

Homework Statement 3a) Find the equation of the tangent plane to the function f(x,y) = sin(x)cos(y) at the point (∏/3,∏/2). The Attempt at a Solution There is quite clearly a z in the definition. What's going on?

Homework Statement A block of mass m=18kg is pushed horizontally with a force of Fp=150N up an inclined plane of angle θ=32° and coefficient of friction of μ=0.10, a distance of x=5m. a) What is the work done by Fp. b) Work done by the gravitational force. c) Work done by the normal force...

Homework Statement Find equation of plan H in R^4 that contains the point P= (2,-1,10,6) and is parallel to plain H2: 4a +4b + 5c-6d = 3 then answer the following questions: A. find normalized normal of plane H which has an angle theta with the normal n= (4,4,5,-6) of H2 such that cos(theta)...

Homework Statement An infinite, charged plane/plate has a uniform positive charge density of σ. Another positively charged particle is found at a distant of D from the plane. In point P, positioned between the two, the electric field equals 0. A. What is the distance between point P and...

two cylinder conected, by two roads, rolling down an inclined plane. Find equation of motion and tension of roads. I know that the lagrangian is: 0.5 m \dot{x}^2+0.5 I_1 \dot{\theta}^2++0.5 I_1 \dot{\theta}^2+mgx\sin \alpha + mg(x+l)\sin \alpha ¿ is good my lagrangian?, ¿how is present...

Homework Statement A conducting spherical shell of outer radius a and inner radius 3a/4 is cut in two pieces via a horizontal plane a distance a/2 above the center of the spherical shell, as shown in Figure 1. Let us label "A" the upper part of the shell and "B" the lower part of the shell...

My question and attempted solution are in the pics below...not sure if what I did was correct though :/ I was thinking that the work done would have been equal to PE+Change in KE + Energy Lost to friction...but not sure how to calculate the energy lost to friction as I'm not sure if it has to...

Given the stress tensor in a point, determine the zero normal stress plane. ...2 3 0 T= 3 2 0 ...0 0 5 ---------------------- Eigenvalues: σ1=σ2=5, σ3=-1 It must be simple, but I don't know how to determine the normal vector of that plane analytically. I know σ=0. t=Tn=σ+τ=τ If normal stress...

Hello, I have a certain diffusion problem I am trying to solve. Admittedly, I'm further behind on my math than I'd like, and have trouble setting it up properly, and no luck finding an exact analogue in the literature. I would like to solve for the time-dependent concentration profile...

so i joined this forum almost 2 weeks ago i was wandering in its vast halls till now and still feel a bit lost,as an student couldn't let myself to get into many things i couldn't understand but i enjoyed this huge amount of knowledge being shared here :) sorry if that was much off topic now...

Homework Statement A cyclinder of mass m and radius r is rotated about its axis by an angular velocity ω and then lowered gently on an inclined plane as shown in figure. Then: (a) It will start going upward. (b) It will first go up and then downward. (c) It will go downward just after it is...

Shortly after the Big Bang was there an extremely brief period of time when the universe consisted of an xy plane with z as time, the third dimension? In other words did a three dimensional universe predate a four dimensional universe?

Hello everyone, I'm trying to find the exact velocities of three balls in the plane after they collide elastically. I'm assuming arbitrary positive masses and arbitrary positive radii. Of course, three balls can collide in many ways: in an equilateral triangle: one coming from north, one...

I just have a quick question, and I'm guessing the answer is no but I wanted to make sure that this was sensible. In general whenever we consider flux we think of some kind of closed surface or a scenario where charge closes back on itself. If I were to cut a hole in an infinite plate of...

Before I start the problem, I would like to apologize for not using the formating. I am posting this from my high school's network and they have an absurd filtering algorithm that blocks css and other web scripts so I can't use the normal formatting since I can't remember the format tags for...

What is the relation between these two concepts?

Hey y'all, this is my first post. I am currently stuck on a multivariable question. Please let me know if you can help. Homework Statement The point, P = (1, 2, 2) lies on the surface z = x^2 + y^2 -3x. Find parametric equations for the tangent line to the surface through the point P parallel...

Hello fellow scientists, I'm working on describing the heat that's being stored in a sanitation pipe when hot water starts flowing through the pipe. I'm starting off with a simplified approach by assuming that the water in the pipe suddenly changes from 20°C to 60°C. I found a good start by...

Okay the question is, given a plane electromagnetic wave in a vacuum given by E=(Ex,Ey,Ez)exp^{(i(k_{x}x+k_{y}y+k_{z}z-wt)} and B=(Bx,By,Bz)exp^{(i(k_{x}x+k_{y}y+k_{z}z-wt)} , where k = (kx,ky,kz), to show that kXE=wB. So I'm mainly fine with the method. I can see the maxwell's equaion...

In a report I am writing I want to define the extended complex plane/Riemann Sphere and I would like to check if I grasp the concept properly: Consider the Euclidean space \mathbb{R}^3 where the x-y plane represents \mathbb{C}. Consider the sphere with south pole (0,0,0) and north pole...

I've looked at this topic for a while and I have yet to come to any sort of conclusive answer when it comes to calculating the basis of a surface's tangent vector. Do you have a concrete method or know where I can find one for doing this? Thank you