Doubt Definition and 591 Threads

i'm copying from the book... Hookes Law - F = -kx W = Fdcos∅ since ∅ is 180°, W = -Fd = -Fx W = ∫(-Fxdx) now the book says, from Hookes Law equation "the force magnitude F is kx. Thus, substitution leads to W = ∫(-kxdx)" why are they saying to substitute the magnitude of the force and not the...

Speaking of variable mass systems... it seems to me that there is a flaw in Halliday's reasoning when he talks about this subject. But the formula he derives seems to work to me! He starts with a system of points of total mass \ M and cm velocity \ v. Due to the action of external forces after...

Two substances are known to be miscible when the intermolecular interactions formed between the molecules of one substance are equal to those formed between the molecules of the other substance. That said, why is benzoic acid, which is predominantly apolar, so it mainly forms London...

Let ##P(x,y)## be a multivariable polynomial equation given by $$P(x,y)=52+50x^{2}-20x(1+12y)+8y(31+61y)+(1+2y)(-120+124+488y)=0,$$ which is zero at ##q=\left(-1, -\frac{1}{2}\right)##. That is to say, $$ P(q)=P\left(-1, -\frac{1}{2}\right)=0.$$ My doubts relie on the multiplicity of this point...

Well people i'm looking electric Motorcycles. And the same seller it's selling a 72V50Ah battery and a 72V60Ah battery, both IN THE SAME WEIGHT, every battery in the shop occurs the same. So or we have a factory mistake, scam, witchery .....or...graphene in the lithium. I have been reading that...

The doubt is about this question. Which the answer is They say that all the forces are pulling forces? How is this the case? How would this setup even work? I don't think block 2 could pull the rod.

I have a doubt about the notation and alternative ways to represent the terms involved in sums. Suppose that we have the following multivariable function, $$f(x,y)=\sum^{m}_{j=0}y^{j}\sum^{j-m}_{i=0}x^{i+j}$$. Now, let ##\psi_{j}(x)=\sum^{j-m}_{i=0}x^{i+j}##. In the light of the foregoing, is...

In classical physics we know photon emits when electron move from higher to lower state but in nuclear fusion photon emits when neutron turn into proton. Is both correct?

We're given the series ##\sum_{n=1}^{\infty} [ \sqrt{n+1} - \sqrt{n} ]##. ##s_n = \sqrt{n+1} - 1## ##s_n## is, of course, an increasing sequence, and unbounded, given any ##M \gt 0##, we have ##N = M^2 +2M## such that ##n \gt N \implies s_n \gt M##. Thus, the series must be divergent. But...

In the solution, the term Lcm and Icm is used. Explain the meaning of these terms? I think cm stands for centre of mass. why that is used in the subscript?does the term angular momentum from the centre of mass of the sphere makes sense? Is the term Lcm and Icm stand for angular momentum of the...

I have a little doubt about Morse potential used for vibration levels of diatomic molecules. With regard to the image below, if the diatomic molecule is in the vibrational ground state, when the oscillation reaches the maximum amplitude for that state the velocity of the molecule must be zero so...

I am new to the operating system and I want to know, Is it right Banker's Algorithm is mainly used to prevent deadlock? I picked this question from https://www.interviewbit.com/operating-system-mcq/ and I think it is also used for Solving deadlock, Can anyone know, Is this right?

Say you want to find the following Integrals $$\int \frac{1}{(x-1)(x+2)} (dx)$$ $$\int \frac{1}{(x-1)(x^2 + 2)} (dx)$$ The easiest way to solve them will be by using partial fraction decomposition on both the given functions. Decomposing the first function, $$\frac{1}{(x-1)(x+2)} =...

McIntyre, quantum mechanics,pg360 Suppose states ##\left|2^{(0)}\right\rangle## and ##\left|3^{(0)}\right\rangle## are degenerate eigenstates of unperturbed Hamiltonian ##H## Author writes: "The first-order perturbation equation we want to solve is ##...

In Chapter 3 of Thomas’s Calculus, they give the following proof of the Chain Rule. After the proof, the text says that this proof doesn’t apply when the function g(x) oscillates rapidly near the origin and therefore leads delta u to be 0 even when delta x is not equal to 0. Doesn’t this proof...

We've two operators ##\hat{a}##,##\hat{b}##. I know their position representation ##\langle r|\hat{b} \mid \psi\rangle=b## ##\langle r|\hat{a}| \psi\rangle=a ## Is it generally true that the position representation of the combined operator ##\hat{a}\hat{b}## is ##a b## where ##a, b## are the...

I have a doubt regarding the basic function of vectors and scalars in physics- What is the guarantee that every quantity(measured) in physics can be classified as either a vector or a scalar, and that while performing operations on said quantities, they will obey the already established rules...

Hello! This is a problem from Halliday Resnick Krane (Chapter 4: Problem #15). “A puck is moving in a circle of radius r0 with a constant speed v0 on a level frictionless table. A string is attached to the puck, which holds it in the circle; the string passes through a frictionless hole and is...

Hello! In Chapter 4 of Halliday Resnick Krane on Pg. 73, they write “the descending motion is much steeper than the ascending motion” when discussing how the trajectory of a projectile changes when we consider drag force. Why is this statement true?

Goldstein 2nd ed. In its Appendix is given the derivation of Bertrands Theorem.Here ##x=u-u_0## is the deviation from circularity and ##J(u)=-\frac{m}{l^{2}} \frac{d}{d u} V\left(\frac{1}{u}\right)=-\frac{m}{l^{2} u^{2}} f\left(\frac{1}{u}\right)## If the R.H.S of A-10 was zero, the solution...

In the latest issue of American Scientist there is an article by Tony Rothman questioning ##E=mc^2##. Are the assertions made in the article valid? Are there comments by other physicists available?

(excuse me for my english, but I'm studying physics and I am not a native English speaker) One observer OE, is on the ground, we take him as the fixed frame of reference. The other OT is on the train that is moving relatively to the OE at a costant velocity ( they are both inertial frame of...

Image above is the question. Below image depicts solution. if F1 is removed then the acceleration of that mass must be sum of accelerations of remaining forces. Right?? But answer says that acceleration of that mass is equal to acceleration of F1. I don't understand it. Can someone explain it??

I would like to know what is the utility or purpose for which the elements below were defined in the Tensor Calculus. They are things that I think I understand how they work, but whose purpose I do not see clearly, so I would appreciate if someone could give me some clue about it. Tensors. As...

What does ##S=\partial V## and ##C=\partial S## signify, usually I have only seen books writing ##C## when evaluating a line integral over a curve ##C## and ##S## when evaluating a surface integral over a surface ##S##. Could someone clarify what ##\partial S## and ##\partial V## mean?

Suppose I am sliding a block very slowly on a rough surface. If the block has traveled ##d## distance then work done by me is ##W_1=\mu mg d## and that by friction is ##W_2=-\mu mg d##. Now the energy transferred from me to block is ##\mu mgd## and that taken by friction from block is ##\mu mgd...

I'm having a problem solving this, My approach is solving $x_1$ as a variable and rest as constants first and then going on further. But it is getting too lengthy. Is there any short method?

how does the partial pressure of oxygen (O2) that is raised to the (1/2) power "magically" combines to give PSO3? , i know that at constant Temperature you can pretty much express pressures between reactants and products using conversion but still you won't be able to factorize because they are...

I have some doubts with respect on how the functional derivative for the kinetic energy in density functional theory is obtained. I have been looking at this article in wikipedia: https://en.wikipedia.org/wiki/Functional_derivative In particular, I'm interested in how to get the...

Hi. I'm not sure about something related to the equilibrium points (or fixed points) of a non linear ode system solution. As far as I know, to check if an equilibrium point exists, I need to put the function of my ode system equal to zero. Then once the point is found, I can use it to evaluate...

Tangent is drawn at any point ( $x_1$ , $y_1$ ) other than vertex on the parabola $y^2$ = 4ax . If tangents are drawn from any point on this tangent to the circle $x^2$ + $y^2$ = $a^2$ such that all chords of contact pass through a fixed point ( $x_2$ , $y_2$ ) then (A) $x_1$ , a , $x_2$ are in...

Summary:: Doubt in a spring exercise Text of the exercise "a mass of ##m = 0.4 \ \text{kg} ## is attached to a spring and it oscillates horizontally with period ##T = 1.57 \text{s}##; the amplitude of the oscillation is ##d = 0.4 \text{m}##. Determine the spring constant, the total energy of...

I got this function in a function analysis and got confused on how to solve its positivity; I rewrote it as: $$\sqrt{x^{2}-2x}>x-1 \rightarrow x^2-2x>x^2-2x+1$$ And therefore concluded it must've been impossible... but I'm certainly missing something stupid, since plotting the graphs of the two...

If we have a cylinder rolling on the ground ##\tau = I\alpha## can only be applied about the point in contact with the surface(Instantaneous axis of rotation) and its CoM I don't see why this should be the case. why can the equation ##\tau = I\alpha## only be applied about the axis passing...

(I hope my English is understood). Hello, I have a question regarding the relativity of simultaneity. The mean temperature of the cosmic microwave background tells us how big the universe is with respect to the recombination epoch. If I now measure that the mean temperature of the cosmic...

While introducing tensile stress, we're shown a bar fixed at a support being subjected to a force in the axial direction at the opposite end. Then, since the bar is in translational equilibrium, we say that internal forces must balance it out, and this internal resistance per unit area is known...

fig equations that I used: Δz = 0 = and I got the following result (which is the same in the book's solution book): but in my test I can only choose one of these: I would like to know if there is a mistake by my teacher or if it is possible to obtain one of these multiple choice...

Drago rule states that if – the central atom has at least one lone pair of electron on it the central atom belongs to group 13,14,15 or 16 and is from the 3rd to 7th period. if electronegativity of the central element is 2.5 or less no. of sigma bonds+ lone pair=4 then, there is no need to...

this method of derivation is approximating the function using a polyhedron. concentrating on one of the surfaces(say the L'th surface which has an area ##\Delta S_l## and let ##(x_l,y_l,z_l)## be the coordinate of the point at which the face is tangent to the surface and let ##\hat n## be the...

(this problem is slightly modified from the original problem.) There is a contact force(friction and normal force) between the wedge and the walls of the container and there is a fluid thrust acting on the side of the wedge in contact with the fluid( this force is normal to the slanted surface...

how to plot these points in the same graph and find the foward biasand reverse bias dynamic resistance for the SILICONE DIODE IN4001 FORWARD BIAS REVERSE BIAS

In question 1. since there is no external force on the system of particles(and since it was initially at rest) shouldn't the ##V_{cm}## be zero? But the correct answer applies the above stated formula for ##V_{cm}## and gets ##V_{cm} = v/2## and in question 2 again as there is no external force...

I have not tried to make any calculation. It's nonsense, because I don't understand the statement. The first vector points to the west. Given a two dimensional coordinate system, the first vector is pointing to the left. I imagine geographical coordinates, north (+y), south (-y), west (-x), and...

Is said that, the superposition of two MHS X1 = A*cos(c/T1*t) X2 = A*cos(c/T2*t) The superposition will be a function which the period will be T in such way that satisfy: T = n1*T1 = n2*T2 But, if we add X1 and X2 we obtain: X = 2A*cos(((c/T1) - (c/T2))/2)*cos(((c/T1) + (c/T2))/2) Why those...

Let's say we have any two covariant derivative operators ##\nabla## and ##\nabla'##. Then there exists a tensor ##C^{\alpha}_{\mu\nu}## such that for all covariant vectors ##\omega_{\nu}##,$$\nabla_{\mu}\omega_{\nu}=\nabla'_{\mu}\omega_{\nu}-C^{\alpha}_{\mu\nu}\omega_{\alpha}$$ Now I'm quoting...

Say... A ball is moving to the right, and we want to say that it doesn't slip. My doubt is, in which case we put Vrot = - Vcm = - α*r or Vrot = Vcm = α * r

I was thinking to myself, if it were ask to me why is the orbit of planets elliptic, how to justify?: The bould phrases i just know to justify with collected dates. IS this a reasonable justification?