What is Plane: Definition and 1000 Discussions

I know the osculating plane is normal to the binormal vector ##B(t)=(a,b,c)##. And since the point on which I am supposed to find the osculating plane is not given, I'm trying to find the osculating plane at an arbitrary point ##P(x_0,y_0,z_0)##. So, if ##R(x,y,z)## is a point on the plane, the...

What is wrong with saying that since the speed of fuel goes from 0 to -313m/s (rel to ground) in 1s, then its acceleration is -313m/s^2. This leads to wrong answer according to author's solution but I don't see why.

Hi guys, Online I found this really cool experiment that uses a glucose solution(e.g. in a beaker) to rotate the plane of polarization of a polarized light beam passing through it, of an angle ##\theta## which depends on the frequency of the EM wave. Then, for example, watching white light...

I have calculated the force equation on the x-plane which is f - mgsin(30) - friction force = ma and from the equation vf = vi + at resulting a = v/10

$\tiny{whit.a.6.1}$ Show that the plane H defined by: $H=\left\{ \alpha_1\left[ \begin{array}{rrr}1\\1\\1\end{array} \right] +\alpha_2\left[\begin{array}{rrr}1\\-1\\0\end{array} \right] \textit{ Such that } \alpha_1,\ \alpha_1\in\mathbb{R}\right\} =\begin{bmatrix}a_1+a_2\\ a_1+a_2\\...

Summary:: Please see the picture below Let say: ##W_1## is weight of ##m_1## ##W_2## is weight of ##m_2## ##f_1## is friction on ##m_1## ##f_2## is friction on ##m_2## I want to find the acceleration of the system. Since I don't know in which direction they will move, I just assume ##m_1##...

6.2(9.8)=60.8 (incorrect) 46.2cos40.4= 35.2 (incorrect)

Hi, I'm missing something really stupid here... The problem is the usual one with a block sliding down (or moving up, it should be the same) a frictionless inclined plane,which itself is free to move on a orizontal frictionless surface. These problems are usually solved stating that only...

Summary:: Describe what the intersection of the following surfaces - one on one - would look like? Cone, sphere and plane. My answers : (1) A cone intersects a sphere forming a circle. (2) A sphere intersects a plane forming a circle. (3) A plane intersects a cone forming (a pair of?)...

I did part a and part b but stuck in part c. Could you help me? (Part a and b attached.)

This is a discussion on MathOverflow where a conjecture is discussed that the curve of ##\zeta(0.5+it)## is "dense" on the complex plane. https://mathoverflow.net/questions/73098/negative-values-of-riemann-zeta-function-on-the-critical-line From a couple of sources, e.g...

$\tiny{311.1.3.16}$ For what value(s) of h if y in the plane spanned by $v_1$ and $v_2$? $ v_1=\left[\begin{array}{rr} 1&\\0&\\-2 \end{array}\right], v_2=\left[\begin{array}{rr} 2&\\1&\\7 \end{array}\right],\textit{ and } y =\left[\begin{array}{rr} h&\\-3&\\-5 \end{array}\right]$ ok I...

Hello there, I have a question regarding this problem. I have no problem with part A. However, in part B, my solution manual states that the hollow cylinder will reach the bottom last. Why is it? I mean shouldn't the solid cylinder and the hollow one reach the bottom at the same time? you know...

Given the equation : ##|y| x = x##. Two conditions are possible : (1) ##\underline{y\geq 0}## : ##xy = x\Rightarrow \boxed{y = 1}\; (x \neq 0)##. We note that except for zero, ##-\infty<x<+\infty## for this case. (2) ##\underline{y < 0}## : ##-xy = x\Rightarrow \boxed{y = -1}\; (x \neq 0)##...

We can write the equation given as ##y+|y| = x+|x|## This has a few conditions. (1) If ##\underline{y\geq 0\; \text{and}\; x\geq 0}##, we obtain ##2y = 2x \Rightarrow \boxed{y = x}##. (2) If ##\underline{y\geq 0\; \text{and}\; x < 0}##, we obtain ##2y = 0 \Rightarrow \boxed{y = 0}##. (3) If...

Hello, Today I started to think about why graphs, of the same equation, look different on the Cartesian plane vs. the polar grid. I have this visualization where every point on the cartesian plane gets mapped to a point on the polar grid through a transformation of the grids themselves...

Hello, We know that most celestial objects in our solar system are in the equatorial plane of the sun. So too, does most of our spacecraft orbit in this plane as it explores our solar system. For a spacecraft already traveling away from the sun and towards the outer solar system, how hard...

Suppose there is a 3d plane z=a*x+b*y+c. Suppose there is a point in space near, but not on the plane. (xo, yo, zo). What is the coordinate (x1,y1,z1) on the plane that is nearest the original point? My attempt uses minimization but the result is blowing up into large answer. I wonder if...

Hello! I need some help with this problem. I've solved most of it, but I need some help with the Hamiltonian. I will run through the problem as I've solved it, but it's the Hamiltonian at the end that gives me trouble. To find the Lagrangian, start by finding the x- and y-positions of the...

Let's assume a plane wave going in the x-direction. Going by Huygens' principle, each point on the wavefront should act like a source. If that's the case, wouldn't plane wavefront become spherical like shown below? I am so confused

Hey Everyone, my physics teacher has assigned us a task which involves predicting the range of a ball falling down an inclined plane into a free-fall, the equation for the final velocity of the ball down the ramp, accounting for rotational velocity has been provided, this is the initial velocity...

Hello! So my main and first problem about this question is, I do not know what the problem is about. What I mean by that is, in class we talked about pendulums and are given formulas and assignments regarding pendulums. But this problem here does not seem like it has anything to do with...

Hello! So the way I have tried to solve this problem is the following;Since it is an inclined plane and the cofficient of static friction is known, getting to the angle at which the box starts sliding is the following ##μH = \frac {sin (\alpha)} {cos(\alpha)} = μH = tan(\alpha) ## ## \alpha =...

I have no idea how to solve this problem. The solution says that the component parallel to the plane of separation is conserved, i am not sure why. Seems to me that in the problem was assumed a special field, but not a generic field.

Pendulum plane, which suspension executes a horizontal harmonic motion $$x = acos(\gamma t)$$ Position P, orientation x to right and y points below, phi is the pendulum's angle wrt y. $$P = (acos(\gamma t) + lsin(\phi(t)), lcos(\phi(t)) )$$ So executing all that is necessary, i found it...

So after trying to calculate the horizontal forces to solve it: f + Wx(gravity force component of x) - Fy ( the Force that is supposedly giving the the acceleration) = 0 It got to me that the question said "plane has the acceleration" is that even possible? Unless the plane is another object...

A block of mass 0.2 kg which slides without friction on a θ = 30° incline is connected to the top of the incline by a mass-less spring of relaxed length of 23.75 cm and spring constant 80 N/m as shown in the following figure. (a) How far from the top of the incline does the block stop? (b) If...

At first I take the uniformly distributed charge and then divide it by the area of the carpet to get the surface charge density σ -10E-6 C / 8m^2 = σ = -1.25E-6C/m^2 Then I divide the surface charge density by 2e0 to get the electric field strength caused by the infinite plane...

I have problems to even start with this exercise.

I solved for T on m1 and arrived at 6.72. I plugged that value into the ΣFx equation as shown above (pardon my handwriting) and got a mass of 0.88 kg. The online program indicated that I needed to check my expression for tension, noting that the two tensions are heading in opposite directions...

Why is the divergence of an amplitude of an electric field of a monochromatic plane wave zero?

I understand how the diagram below determined the ##x## and ##y## axis for the velocity vectors but I don't understand the gravity vectors. What I don't understand about the gravity vectors is why is ##-mg## in the ##y-##axis equal to ##-mg\cos\theta## and the ##x-##axis is equal to...

When drawing a diagram of the forces acting on the block, I have the following forces: $$\sum F_x =mg\sin\theta = ma$$ $$g\sin\theta = a$$ however the solution has $$F_x = ax = (g \sin\theta) \cos \theta$$ but I am not sure how they got that? I know the normal force is $$N=mg\cos\theta$$ but the...

Find point d on the line of r(t)=(0,0,0)+(−1,1,1)t which make the triangular pyramid abcd has the volume of 4 unit cube when a(0,0,0),b(1,0,1),c(0,1,0) are the points on the plane of −x+z=0.

I've tried a few ways of solving this, both directly and by using Stokes' Theorem. I may be messing up what the surface is in the first place F= r x (i + j+ k) = (y-z, z-x, x-y) Idea 1: Solve directly. So ∇ x F = (-2,-2,-2). I was unsure on which surface I could use for the normal vector...

This problem was from the chapter on Work and Energy so, I thought of using the principle of conservation of mechanical energy. Clearly, the potential energy of the block decreases by mgh (assuming the block has mass m). This energy should have been converted to kinetic energy, but it clearly...

AB, AB, AD are Ld, that is, the three vectors lie on the same plane, so, "yes, the points lie on the same plane" However, AB CB and AD are Li, that is, the three vectors span the space R3, and don't lie in the same plane, so, how can four points that lie on the same plane, that can generate only...

Hey guys! I´m having a lot of trouble , even on starting this problem. Can someone give me a help?? [Moderator's note: Moved from a technical forum and thus no template.]

2d sin q = nl d = nl / (2 sin q) d = (1 x 0.16) / (2 sin 30o) = 0.16 nm But 0.16 is not in the option. And how to find other value of d? Thanks

A hollow rod closed at the ends A and B, has mass M and length R. The rod is free to rotate on a horizontal frictionless plane around the z axis passing through A and coming out of the sheet. A body can slide without friction inside the cavity point mass m. Initially the rod is stationary and...

first, i calculated the kinetic friction: 0.77 x (weight of the 2 boxes x 9.8)= 55.16N then i calculated the angle of the triangle: tan^-1(2.5/4.75)=27.758 then i drew this then i used sine to find out force 3 which is 33.3556 so the final force needed is 33.3556 + kinetic friction=...

i tried to solve the problem with the above way then i calculated Fg= mass x 9.8 = 242.06 N FgII= Fg x sin50 =185.4287N so the force required is 185. is this correct?

Assuming we have an infinite plane capacitor,where the upper plate is charged positively and the bottom layer is charged negatively. Now we know the field outside the capacitor is zero so we can't tell if the positive charge is on the upper plate or the lower plate. But, if we place it inside...

I was always a little confused about the rolling down of a body, let's say, a sphere. It's know that to body rotate, from the rest, in a referential frame on the ground [inertial], is necessary a friction, that will just act like a medium that transforms kinetic energy of translation into...

The slope of the v^2 vs h graph is g

I tried solving this by assuming the acceleration of the truck and block to be the same so the block would stay on the incline. Also, I would assume truck ma = static friction, block ma = mgsintheta... then I solved for a to plug into 1st equation to get 12990 N. Is this correct? I wasn't sure...

Hello everybody, I have to find the amplitudes of a wave that goes through 4 different mediums in terms of ##E_0##, suffering reflection in the first three but not the last one. I calculated the corresponding reflection indexes of the three mediums (all of them real). Following calculations, I...

I can imagine a frame within a blimp/hybrid airship so when the hydrogen inside the blimp is recaptured the skin retracts to form a wing. As the blimp travels faster it shrinks, the buoyancy giving way to the lift from its wing shape to a point in which it is no longer a blimp, but a plane. What...

While all orientable 2 dimensional compact smooth manifolds are boundaries e.g. the sphere is the boundary of a solid sphere, the torus is the boundary of a cream filled doughnut - not all unorientable surfaces are boundaries. For instance, The Projective Plane is not the boundary of any 3...