Point Definition and 1000 Threads

The removed mass is ##\frac{1}{8}M## My idea is to find ##g## from large sphere then minus it with ##g## from small sphere (because of the removed mass): ##g## at A = $$\frac{GM}{R^3}\left(\frac{1}{2}R\right)-\frac{G\left(\frac{1}{8}M\right)}{R^2}$$ Is this correct? Thanks

Hi. I have this idea that might be useful for celestial navigation. If you were on a random place on the Earth, and you had a way of measuring the altitude of the sun above the horizon, at a precise moment, could you then predict the complete path, such that you could determine the altitude at...

So we are finding the L2 Lagrange point, specifically the distance from the earth, or d in this instance. I have used the equation above and I have come out with 1.5 * 10^9 meters as d, or L2's distance from the earth. Can anyone verify this, is the equation correct and is my final distance...

I tried solving the part (a), and got I =1.82 A for the current value using Kirchoff's law. Next, I want to use Ohm's law to calculate the voltage at point a. Va = IR In this equation, will resistance R correspond to 4.4Ω or 8.8Ω? How do you determine which resistance to use when solving this...

I don't get what is meant with the last part: that takes any one given point to any other given point. Thanks in advance

From the graph we see that at ##H=4 kA/m,\ B=1.5T##. We have that ##M=\frac{B}{\mu_0}-H=\frac{1.5T}{\mu_0}-4kA/m## and from Ampere's Law that ##i=\frac{HL}{N}=\frac{4kA/m\cdot 0.1 m}{100}## and the current (density on the surface is) ##\sigma_{m}=M##. Does this make sense? I am having...

I don't understand why my solution is wrong. Here is my solution. $$ r_{\theta} = R\cos{\theta} \vec{i} + R\sin{\theta} \vec{j} $$ $$ v_{\theta} = v\cos(\theta + \frac{\pi}{2}) \vec{i} + v\sin(\theta + \frac{\pi}{2}) \vec{j} $$ $$ p_{\theta} = mvR(-\sin{\theta}) \vec{i} +mvR(\cos{\theta}...

A set is nothing more than a collection. To determine whether or not an object belongs to the set , we test it against one or more conditions. If it satisfies these conditions then it belongs to the set, otherwise it doesn't. The geometric point of view of sets- a set can be viewed as being...

“Given any class of mutually exclusive classes, of which none is null, there is at least one class which has exactly one term in common with each of the given classes…” The reason this statement sounds like one of those theora is that I recall reading a Time-Life book on Mathematics, and there...

Hello guys, I am getting more and more confused each time I try to get a definitive answer on this doubt: what's the acceleration at the contact point between a surface and a wheel spinning on it(without slipping). Considering this standard FBD for the above-described situation, (the direction...

Wawawawawawa! This was a tough one...:biggrin: Find the question below; Find my approach below: We have the following equations; 1. ##v=30-0.5t## 2. ##v=30-1.5t## Now the car changes its acceleration at some point i.e from ##-\frac{1}{2}## ##m/s^2## to ##-\frac{3}{2}## ##m/s^2## ... I...

I have been experimenting in producing some strain to this object. However, after applying a prescribed displacement and setting it to a certain value, it does not exceed 2.18[um] no matter any extreme value for the prescribed displacement. I have also experimented with an applied force as well...

The action is the time integral of the Lagrangian - check. We take the variation of it, and set it to zero - check But how do we know it is a minimum and not a maximum? (Don't we formally have to deal with the second variation to be positive?) Or am I confused? Is it really just important to...

Question: My attempt: Could someone please confirm my answer?

Question: Here's my attempt with the relevant equations: The correct answer is F = -99.4 az μN. Could someone please figure out my mistake?

I'm confused about wrote a root of function when plotting here graph with pgf-tikz. Any help is welcome.

Let ##m_s = 0.05, m_{s_1} = 0.02, m_r = 0.12, L = 0.8.## be the masses of the two spheres, mass of the rod, and length of the rod. Then the work done by gravity when the rod reaches the vertical position is ##(m_s(L/2) - m_{s_2}(L/2))g## and the kinetic energy equals ##\frac{1}2 (\frac{1}{12}...

I am trying to determine if there is a set of formula to calculate if a cabinet will when subjected to a force on it's upper edge for an angular distance (not a duration) will gain enough momentum to continue over the balance point and fall over or whether the opposing moment due to mass and...

Hi, PF I left reading for a while, and now I must revisit a quote from Spanish 6th edition of "Calculus", by Robert A. Adams. The quote is " 4.2 Extreme values problems (...) As we've seen, the sign of ##f'## shows if ##f## is increasing or decreasing". Obvious, I shouldn't care and...

This is an offshoot of @Angela G 's thread. I don't want to hijack her thread so I decided to create a new one. Original thread https://www.physicsforums.com/threads/unstable-or-stable-electrostatic-equilibrium.1007881/ @kuruman @PeroK @bob012345 If you have the time I'd appreciate your input...

I need an equation to graph a sine wave that act like a unit circle but only positive numbers. so I need it to be 0 at 0, A at 90 , 0 at 180, A at 270, 0 at 360, and A at 450 and so on and so on... Now I know sin(0) is 0 in degrees and sin(90) 1 and I know if you Square a number is...

Hi everyone :)! I resolve this problem with components method and trigonometry method. My results with components method its okay, but i can´t obtain the correct VE velocity. Im sure that the problem its in the angles, but i don't know how to fix it. The correct answers: -Angular velocity...

Let the point P(2,8) be a point in xy-plane and line m: y = -0.75*x+3.25 be a line in the xy-plan. The distance from a point P to a point B is 7 unites. Where the x coordinate of B is negative. Find the acute angle between PB and m. To find B I then construct a circle of radius 7 with center...

Hi , I've been trying to manage a solution in my head and i think I'm on the right path , i just need some approval and maybe some tips. So it's obvious I can't solve this without integration because law's only apply to point charges , and i can't shrink this object to a point as i could do with...

I studied the basics of geometric quantization for a recent work in quantum-classical hybrid systems1. It was an easy application of the method of gometric quantization (prequantization + polarization in ##\mathbb{R}^{3}##). The whole topic seems interesting since I want to learn more of...

Hi all! In this assignment I have to formulate an equation for the shortest distance from a point on a circle perimeter to an arbitrary axis in a circle with angle theta. I included an image with the sketch. Anyone that can help?

I am currently reading David Morin book and found this statement : ##\,\,\,\,\,\,\,\,## "It is important to remember that you are free to choose your origin from the legal possibilities of fixed points or the CM" Is it really alright to choose the center of a...

I'm not sure of my answer but it is e(downwards). I arrive at this answer since gravity always exists so no matter what happens it always pulls an object downwards. But I am not sure. Thank you -sun1108

Hey all, I can't seem to find the answer anywhere, I'm not sure if I'm asking the right question though, if the name or label "Pivot" describes the rotational axis of an object is there a term or label used to describe the outer most point of the rotation?

Hi, I was looking at this problem and just having a go at it. Question: Let us randomly generate points ##(x,y)## on the circumference of a circle (two dimensions). (a) What is ##\text{Var}(x)##? (b) What if you randomly generate points on the surface of a sphere instead? Attempt: In terms of...

I have broken the ring into a top arc and a bottom arc. First, let's assume an imaginary charge of +1 C is placed at point P. We will determine the force on this unit charge from top and bottom arcs. The charges in the top arc will result in electric fields that will all cancel each other...

I have found the turning point. I want to ask how to check the nature of the turning point. My idea is to change the equation into cartesian form then find the second derivative and put the ##x## value of the turning point. If second derivative is positive, then it is minimum and if the second...

Nothing I do seems to matter anymore and it is becoming nearly impossible for me to take interest in the world around me.

If I connect a voltmeter with the positive terminal of a battery and leave the other wire hanging in the air, it won't measure anything since it's not a closed circuit. But if there was a way to measure the voltage between those two points, what would the voltage be? Or is this a meaningless...

I came across this 'problem' when I was trying to think about how a torsion spring would apply torque in something like a miniature catapult. I understand that in the context of something like turning a wrench, we can find the net torque on the wrench by treating the hand applying the force as...

Potential inside is given as in ,https://en.wikipedia.org/wiki/Method_of_image_charges, which is the sum of excitation and induced potential. When the charge is outside it is easy to argue potential is zero in the sphere. But when we have charge inside and image outside, what is potential...

Let's speak in the classical context (non quantum). We assume that point charges move in a conductor following Newtonian mechanics. How do point charges move along the boundary of the conductor and how do they stop (equilibrium) in the end?

So I have a ring(red) of uniform charge ##\lambda## per unit length, and I want to calculate the electric potential at the origin (actually on any point of the ring). It is clear that the ring is given by the equation $$r=2 R \sin \theta$$, in polar coordinates, where R is the radius of the...

I can calculate the fields generated by the cylinder and the wire but I don't know how to calculate their vector sum to evaluate it at point A. Cylinder field inside: ρR^2/2rε Cylinder field outside: ρr/2ε Field generated by the wire: λ/2πr I should break the fields into components but I don't...

Greetings according to the function we can see that there is a jump at x=e and I know that the value of the function at x=e should be the average between the value of f(x) at this points my problem is the following the limit of f(x) at x=e is -infinity and f(e)=1 how can we deal with such...

$\tiny{APC.2.1.06}$ The graph of $y=e^{\tan x}-2$ crosses the x-axis at one point in the interval [0,1] What is the slope of the graph at this point. a, 0.606 b. 2 c, 2.242 d.2.961 e.3.747 [d] $\begin{array}{rll} \textit{given} &e^{\tan \:x}-2 &(1)\\...

Hello all Trying to solve this one, faced a dilemma if i should trasfer the 5N vector from third to first quadrat becuase it head is on the 0 axis ass opposed to the two other vectors. If it remains in third quadrant its components eouls be both negative, if transferred to first quadrant both...

I wanted to calculate the focal length and focal point of the collimator. The collimator diameter is 3mm, and I wanted to focus on the 100-micrometre active area of the detector.

Hey! :giggle: We have the function $$f(x,y)=(x-3)^2+y^2+(x-y)^2$$ and I have shown that at $(2,1)$ we have a minimum and so $f(2,1)\leq f(x,y)$ for all $(x,y\in \mathbb{R}^2$. I did that in this way: I calculated the gradient and set this equal to zero and found that the only critical point...

answer is 78oCdelta G = delta H - T delta S -235,310- (-277,690) = -38.56e3- T (282.59-160.70) T = -664K I am not sure if my concept is correct. May anyone help a little bit on that please? thank you

I thought the equation listed should be used, with the 'charge density' determined by the point charge multiplied by the area of the plate, but not sure if that makes sense.

For car 1, the parametric equations are x = 1 + 0.8t and y=t. For car 2, the parametric equations are x=0.6s and y=2+s. (Let t and s represent time). Solving the system of equations, when the x values are equated are the y values are equated, I get s = -13 and t = -11. I assume that the 2 cars...

This proof has three steps and is very similar to (if not the same as) that other proof I posted here.(1) Prove the existence of a ball centered around ##a## with the property that ##f'## evaluated at any point in the ball is positive. (2) Prove that the right end-point of this ball is bounded...

Without giving possible options, as to not lead people in a wrong direction perhaps, I have a question I am struggling with. Mostly because I get different answers from different people 🤔 When an aircraft is coming into land and starts the landing flare, around which point does it rotate? It...