Sign Definition and 596 Threads

Homework Statement Cartesian sign convetion for microscope,compound microscope and telescope. Homework Equations distances in the direction of incident ray are negative and thsoe along it are positive. all distances are measured from pole of lens or mirror. The Attempt at a Solution 1.FOR...

In Schutz's A First Course in General Relativity (second edition, page 45, in the context of special relativity) he gives the scalar product of four basis vectors in a frame as follows: $$\vec{e}_{0}\cdot\vec{e}_{0}=-1,$$...

Homework Statement I don't understand why the fixed end moment at AE is 10KNm ( clockwise) . Homework EquationsThe Attempt at a Solution Forger about the sign convention here , i have the resultant moment = 10KNm , which ic clockwise , why in the 2nd picture ( SFD and BMD part) , the moment...

Homework Statement Two long fixed parallel wires, A and B, are 10 cm apart in air and carry 40 A and 20 A, respectively, in opposite directions. Determine the resultant field (a) on a line midway between the wires and parallel to them and (b) on a line 8.0 cm from wire A and 18 cm from wire B...

Homework Statement This was a problem on my fluids final and I'm trying to figure out if my rationale was correct here. The problem was an open air tank filled with water and at the bottom was a pipe pointing straight down. You had to find the exit velocity at the bottom of the pipe and account...

Hi, Our lecturer explained us the Reynold Transport theorem, its derivation , but I don't get where the - sign in control surface 1 comes from? He said that the Area goes in opposite direction compared with this system. I can't visualise this on our picture. Can you please help me understand...

it seems it is not reasonable Sorry it said that delta S>=0 in an isolated system. i know why they put " = " sign, but i don't know why it is still possible that dS>0 in an isolated systembecause in an isolated system,it is said that dQ=0 (because no heat transfer between the system and the...

Hey guys, so I stumbled across this, and I'm kinda confused on how do they get the sign convention of the value. I've attached the figure and also the soil pressure for better reference. Take for example at C, how do they get the minus and positive sign convention? Thanks a bunch. P/S : Please...

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown > Hi, I couldn't figure out from the equation that relate the current source IS to IA and IB. If both IA and IB is coming from the same direction and the positive terminal has been predicted...

Homework Statement A 45 deg wedge is pushed along a table with a constant accelaration A. A block of mass m slides without friction on the wedge. Find its accelaration. Homework EquationsThe Attempt at a Solution ##(x_b - x_w)\tan \theta = h -y_b## ##\ddot x_b + \ddot y_b = A## Now...

We say that, for gravity, F=mg, where g≈-9.8 m/s2. Then, we have U=mgh. But, it seems like that equation would only work if g were positive 9.8 m/s2. That is, because ##F=-\frac{dU}{dr}##, and ##\frac{dU}{dr}## is essentially ##\frac{dU}{dh}##, we should get F=-mg. So, for the two equations to...

Homework Statement In this question , we can see that in teh second picture , the 12.86kNm is in clockwise direction at the right of span BC . Homework EquationsThe Attempt at a Solution In meachnic of materials , i learned that when the beam curve upwards ( U shape) , then it has positive...

Consider the scattering process ##W^{+}W^{-} \to W^{+}W^{-}##. This process is mediated in the Standard Model by 1. a four-##W## scattering, 2. ##Z##-boson exchange, 3. Higgs exchange...

Hello I just want to ask that in problem 1.54 why the sign of area element da is negative how do we predict signs in spherical coordinates unit vectors can anybody tell me the rule I have only trouble in sign like in left face it is negative what rule do we use for this negative sign

$$\left \int \frac{dy}{y^{1/3}} \right.$$ Doesn't work. There also was an examples page in your site, i don't find it

Homework Statement [/B] Calculate the work done by a force, against an electric field, to bring a charged particle (2 coulomb) from the point (2,0,0) to (0,0,0). Also calculate the work from (0,0,0) to (0,2,0). Finally calculate the work done going directly from (2,0,0) to (0,2,0) and...

Homework Statement Let γ: I → ℝ2 be a smooth regular curve and let λ = γ ο φ with φ: Iλ → I be a reparameterisation of γ. Show, by using the general formula for curvature of a regular curve that κλ = ±κ ο Φ where the ± depends on whether φ is orientation preserving (+) or reversing (-)...

Oiy. It is my 6th year teaching physics and early on, I diverged from the textbook (Holt Modern Physics) regarding how they handled "g". To me, it made more sense that "g" was -9.81m/s2 , while the text handled it as "g" = 9.81 m/s2, and negatives are assigned directionally. Overall, my...

Homework Statement Consider the function ##f(x) = x^4 \sin(\frac 1 x)## for ##x \ne 0## and ##f(x) = 0## for ##x =0##. I have to prove that ##x=0## is the critical number of this function and its derivative changes the sign indefinitely. Homework Equations Definition of the critical number...

Homework Statement Can someone explain why the M is assigned to be anticlockwise here ? Homework EquationsThe Attempt at a Solution When i assign it as clockwise , i will get -P(δ -v) , which is different from the author ... Can i do so ? Why ?

Homework Statement In this question , how could the $$\theta_p$$ and $$\theta_s$$ has the same sign ? For $$\theta_p$$ , it is to be rotated clockwise to horizontal axis , right ? For $$\theta_s$$ , it is to be rotated anticlockwise to vertical axis , right ? They are in different...

Homework Statement In my book , i was told that when the shear stress turn a plane of element clockwise , then the shear stress is positive , In this question , we can notice the shear stress of 40 will turn the plane clockwise , why the author plot the stress at A = (80,-40) ? Shouldn't it be...

I'm having quite a deal of trouble trying to figure this out. Say, for example, you wanted to have a statically stable aircraft. How do you determine what the signs (positive or negative) of the control derivates need to be for this condition to be satisfied ( CXα, CZα, Cmα, Cmq, CZδe, etc) ?

I am reading GEOMETRY, TOPOLOGY AND PHYSICS written by MIKIO NAKAHARA (second edition). I have a problem on page 400. I wonder why the sign is minus in Eq. (10.85). And the same problem appears on page 405 in Eq.(10.108). I think it should be minus one half.

My question is : what is the meaning of the geodesic curvature sign for a coordinate patch? for a surface? Thank you.

Homework Statement Above is my attempt of the answer and the problem q. The correct answer is -2V. In the solutions given to us, it has this line: I understand that V- is 0V due to the characterisitcs of an op-amp. But I don't understand where is the - V0 coming from. Any ideas...

Homework Statement The Force applied to an object is equal its mass times its acceleration Assume that the ball has a mass of 40g. What is the force due to gravity acting on the ball? Homework Equations F=ma The Attempt at a Solution F=(.04)(-9.81) I get a negative answer, does that mean...

When we use the conservation of momentum with, for example, collisions do we include the sign with the velocities or are the signs inherent in the quantity? For examples, would we write ##m_1v_1 = m_1v_1 + m_2v_2## or ##m_1v_1 = -m_1v_1 + m_2v_2## for a collision where a moving object hits a...

I have a triangular sign, each face is 9000mm long horizontal, 2616mm high vertically, the "turntable /bearing "diameter is 3450 mm, the longest length from the sign edge is 5100mm from the centre shaft, the deadweight of the structure is 3200kg, i want to turn at 0,6 RPM, what torque shoul my...

Homework Statement I was trying to fit experimental data which are theoretically modeled by an exponential function. They are shown in the first graph below. For the first set (red line), the data does not appear to be exponential. My lecturer once said that I need to flip the signs of the...

My native language is not English. I try to read textbooks in English. I wonder how should I pronounce "=" in some special sentences: "equals", "is", "was equal", "being", "being equal" or somehow else. How to pronounce the "=" sign in the following sentences: 1) It moves from x1=5m to x2=9m...

Homework Statement Particle A has a mass of 1kg and velocity 2x10^8m/s to the right and collides with a stationary particle B that has a mass of 4kg. after the collision, particle A moves to the left with a velocity(v) and particle B moves to the right with a velocity of 1x10^7 m/s. calcuate...

Hello all, Well I work for a company that typically gives a sign on bonus for new hires. However, I'm (hopefully) switching positions internally to a new department. Do you think I should expect a sign on bonus in this scenario? Thanks!

I have the function $$\frac{5(1-x)}{3x^{1/3}}$$ for which I need to find a sign chart. I know that for $x = 0$ and $x = 1$ are the inflection points, since those are the points for which the numerator and denominator will equal zero. So, is the function positive or negative when $x < 0$, $x >...

Does the value of the potential energy of a system of objects depend on the reference point or the nature of force existing between them (attractive or repulsive)?

Imagine that I am pushing on a wall. Then my textbook says that by Newton's third law, ##F_{AB} = F_{BA}##, where I am B and the wall is A. Isn't this wrong? Shouldn't it be that ##F_{AB} = -F_{BA}##?

Homework Statement A = 20 cm Given the graph, what is the phase constant(in degrees)? (I have already solved for amplitude and frequency) Homework Equations x(t) = A cos (wt + ϕ) The Attempt at a Solution x(t) = A cos (wt + ϕ) Taking from t = 0, we find: 10 = 20cos(w*0 + ϕ) 10 = 20cos(ϕ) 1/2...

Given that ##\cos x = -0.4927##, ##\sin x = \pm \sqrt{1 - (\cos x)^2} = \pm \sqrt{1 - (-0.4927)^2} = \pm 0.8704##. How do I know which sign to choose for the correct sign?

Homework Statement In the in the first image , it's shown that the shear stresses has positive sign, whereas in the second image e (circled blue part) has different sign convention,which is positive and negative, which is correct? Homework EquationsThe Attempt at a Solution IMO, the second...

Homework Statement A 20gram bullet it shot out of a 10kg gun at a speed of 300 m/s What is the recoil speed of the gun (I am putting this in maths rather than physics because I understand the physics part it is just basic maths of using an equation that I am stuck with) Homework Equations G=...

Homework Statement I doubt that is the following notes (in the first picture), correct or not? Because i couldn't find any proof in the other book... Homework EquationsThe Attempt at a Solution Can I say that consider σ positive to right and τ positive downward, orientation (θ) clockwise as...

I am creating a website and wish to include a new integral sign that has an infinity sign over it but aligned with the same tilt angle as the integral. I'm using Mathjax to render the math code. I can code this in Latex outside an HTML file and it works perfectly but does require the graphicx...

I've seen in many equations of physics that whenever we demonstrate an attraction force we tend to use a negative sign before it,why is that? In case of coulomb force it makes sense because when the charged particles are of opposite signs a negative sign is sure to be appeared.But why do we...

I'm unsure about the sign of the circular polarization. Assume the magnetic field is pointed toward the observer. In the Zeeman effect spectrum, is the CCW polarized emission at higher or lower wavelength than the CW polarized emission. I think the CCW polarized emission is higher, and this is...

Homework Statement I don't understand why the sign of moment of beam at left (clockwise) and moment at the right of beam (anticlockwise) are considered as positive... Why we can't assume the clockwise moment as positive and anticlockwise moment as negative? Homework EquationsThe Attempt at a...

Homework Statement in this notes, the shear force is negative because at LHS, shear force cause the beam to turn counterclockwise , am i right? at RHS, the shear force cause the beam to turn anticlockwise, so that the shear force is also negative? Homework EquationsThe Attempt at a Solution...

Homework Statement http://nptel.ac.in/courses/112107146/22[/B] in the notes, the author define upward shear force as positive (LHS) , he take downward shear force as positive as positive (RHS)? Homework EquationsThe Attempt at a Solution why the author didnt fix downward shear force as...

A simple doubt came to my mind while browsing through logarithmic functions and natural logarithms we define $$\log_b(xy) = \log_b(x) + \log_b(y)$$ Here why is the condition imposed that b>1 and b is not equal to zero and that x and y are positive numbers? Is it something to do with the...

Homework Statement You drop a tennis ball on a hard floor, and it bounces upward. If the x-axis is directed upward, what is the sign of the acceleration while the ball is in contact with the floor? Homework Equations a=v/t The Attempt at a Solution I thought that the acceleration when the...

Homework Statement The signum function is defined by$$sgn(t)=\left\{\begin{matrix}-1, \ t<0\\0, \ t=0 \\ 1, \ t>0 \end{matrix}\right.$$It has derivative$$\frac{d}{dt} sign(t) = 2 \delta(t)$$Use this result to show that ##j2\pi \nu S(\nu)=2,## and give an argument why ##S(0)=0.## Where...