Angle Definition and 1000 Threads

Homework Statement If the firing angle is set to ##\alpha = \frac{\pi}{3}## estimate the power dissipated in the bulb if it is rated at ##100w## and the voltage source is ##230V## @ ##50Hz## Homework Equations [/B] ##Vpeak = \frac{230}{0.707}## = 325V ##Vload = 325\sqrt\frac{\left(2\pi...

Homework Statement Homework Equations Gamma factor: $$\gamma = \frac{1}{\sqrt{1-\beta^2}} $$ Lorentz contraction $$l'=\frac{l}{\gamma}$$ Trig: $$ cos\theta = \frac{adjacent}{hypotenuse}$$ The Attempt at a Solution I have all the quantities but the algebra doesn't seem to work out...

Hello, everyone! Now I'm trying to develop 2 wheels robot, which travels along the line simulator. The robot can turn only by increasing velocities of each wheel. The conditions are below: - I know velocities of 2 wheels - I know radius between wheels The task is next: How to find new location...

Andy Resnick submitted a new PF Insights post New High Performance Ultra-wide Angle Lenses Continue reading the Original PF Insights Post.

Hi. I was wondering if anyone could help me with the following problem. I am doing a independent lab at the moment. I am using video footage to measure displacement of a ball. I have cameras set up on the x and y-axis where a ball is in line with the centre of both cameras. I have 1cm grids on...

Hi all! I was studying the datasheet of a CMOS sensor when I bumped into a graph which defined the CRA (Chief Ray Angle) of a lens as function of the FoV (Field of View). cdn.sparkfun.com/datasheets/Dev/RaspberryPi/ov5647_full.pdf page 134 I've understood what is the CRA, and I've got the...

Homework Statement Two m = 4.0 g point charges on 1.0-m-long threads repel each other after being charged to q = 80 nC , as shown in the figure. What is the angle θ? You can assume that θ is a small angle. Homework Equations Fe=kq2/r2 F=ma Fg=mg The Attempt at a Solution Equation 1:[/B] r =...

1. The problem statement, all variables, and given/known data Attached is a diagram of what I am trying to solve. I need to calculate the X and Y components for both F1 and F2. The results will then be used in a later problem that I've already solved but I am coming up with an error and I was...

Homework Statement I need to find how to find the optimum angle for take off on the ski flying hill using projectile motion. and why? Homework Equations The Attempt at a Solution [/B] I'm just confused, because would I just use all the formulas above to solve the problem? or do I have to...

The average angle made by a curve ##f(x)## between ##x=a## and ##x=b## is: $$\alpha=\frac{\int_a^b\tan^{-1}{(f'(x))}}{b-a}$$ I don't think there should be any questions on that. Since ##f'(x)## is the value of ##\tan{\theta}## at every point, so ##tan^{-1}{(f'(x))}##, should be the angle made by...

The Weinberg angle ##\Theta_{W}## is commonly expressed as $$\cos\Theta_{W} = M_{W}/M_{Z}.$$ Can the Weinberg angle ##\Theta_{W}## be expressed in terms of the Higgs mass and the mass of the W boson as $$\sin^{2}\Theta_{W}= m_{H}/M_{W}?$$

Homework Statement A 100 kg block is pushed across a level frictionless surface at a 60 degree angle, with a force of 20 Newtons. How many seconds does it take to go 100 meters? m = 100kg Mu = 0Homework Equations F = MA The Attempt at a Solution I sketched out the problem on my paper here...

Ive been reading about reflections and transmission at Air water surface. I get the idea that at the Brewster's angle dipoles aligned at the surface can not emit p-oscillations in the reflected direction as the dipole is aligned parallel to this direction. What I don't get is that if the...

Homework Statement The uniform 5 m-long round wooden rod (ρ = 800 kg/m3 ) is tied to the bottom by a string with length 1 m. Determine the inclination angle θ if the water level is 3.5 m. What if the water level is 7m? Homework Equations Fb = ρgV The Attempt at a Solution So I'm really...

Homework Statement A football punter can punt a maximum range of 40.8 m. If he instead wants to punt only 34.6 m, but maximize the time the ball is in the air, at what angle from the horizontal should he kick the ball, and how long will it stay in the air if he hits it perfectly? (neglect air...

Homework Statement The electric potential at points in an xy plane is given by V = (1.5 V/m2)x2 -(2.9 V/m2)y2. What are (a) the magnitude of the electric field at the point (3.9 m, 2.9 m) and (b) the angle that the field there makes with the positive x direction. Homework EquationsThe Attempt...

Homework Statement Problem: A 12.0-kg block is pushed to the left across a rough horizontal surface by a force that is angled 30.0◦ below the horizontal. The magnitude of the force is 75.0 N and the acceleration of the block as it is pushed is 3.20 m/s^2 . What angle does the force exerted on...

The angle between two ℝ2 or ℝ3 vectors makes sense. I have a vector like [0 0.707 1 0.707 0 -.707 -1 -.707]T (Actually my vector is A/D conversions of a sine wave from the wall power outlet. The sample rate is 4800 so there are 80 samples, separated by 1/Fs for a 60Hz sine wave. If I...

The question is about a box with no movement standing on a hill. The hill has an angle of 25 degrees. The box has a mass of 40 kg. 1. Calculte the gravity This I still get: F= M x A = 40 x 9,81 = 3,9 x 10^2 The next question tough: 2. Calculate the component Fgravity,x off the gravity...

Homework Statement My problem is: For the logarithmic spiral R(t) = (e^t cost, e^t sint), show that the angle between R(t) and the tangent vector at R(t) is independent of t. Homework Equations N/A The Attempt at a Solution The tangent vector is just the vector that you get when you take the...

How to find the length of an angle bisector ($$BK$$) in a triangle $$A(1;4), B(7;8), C(9;2)$$. I calc $$BK$$: \frac{x-7}{\frac{1+\frac{\sqrt{13}}{\sqrt{10}} \cdot 9}{1+\frac{\sqrt{13}}{\sqrt{10}}} - 7} - \frac{y-8}{\frac{4+\frac{\sqrt{13}}{\sqrt{10}} \cdot 2}{1+\frac{\sqrt{13}}{\sqrt{10}}} -...

$\tiny{231.12.3.19}$ $\textsf{Given $v=-7i-j$ and $w=-i-7j$}\\$ $\textsf{find the angle between v and w}\\$ $\displaystyle \frac{\left(-7, -1, 0\right)\cdot\left(-1, -7, 0\right)} {\sqrt{50}\cdot \sqrt{50}} =\frac{14}{50}\approx 0.28$ $\arccos(0.28)\approx 73.74^o$ $\textit{not sure if this is...

Hi everyone, this is a real world problem following the sinking of a narrowboat in 2014. The boat caught on the side of the lock as the water level dropped, and the resultant combination of pitch and heel resulted in the boat taking on water at the stern and sinking - luckily with no loss of...

Homework Statement In the first photo , i was told that the fixed end moment is zero when the far end is pinned or roller supported . Why in the example in the second and third photo( both end are fixed) , the angle is zero ? Homework EquationsThe Attempt at a Solution I think it's wrong ...

My book had these two solved examples that gave contradictory replies. The power output of an alternator is 100 kW. Now if the tangent of pf angle is 0.8 lagging, the KVAR rating must be -80KVAR. I drew phasor and got this. I took it that since tangent is negative. Now tangent is opposite...

$\tiny{s4.854.13.5.47}$ $\textsf{a. Find symmeteric equations for the line of intersection of planes}\\$ $\textsf{b. Find the angle between the planes}\\$ \begin{align}\displaystyle j+y-z&=2 \\ 3x-4y+5z &=6 \end{align} \begin{align}\displaystyle n_1&=\langle 1,1,-1\rangle\\ n_2&=\langle...

Homework Statement Calculate the reciprocal lattice vectors for LiF. Given the lattice parameter ##a = 0.402 nm## calculate the magnitude of the ##\textbf{G_{220}}## reciprocal lattice vector for LiF and thus deduce the Bragg angle for the (2,2,0) Bragg peak for incoming wavelength of ##0.9...

Homework Statement why we need to consider 2 moment caused by the 85Nm in this question ? The question ask for the determine the angle of twist of gear A relative to D . Homework EquationsThe Attempt at a Solution Why shouldn't the angle of twist = (85)(0.4) / ( (0.5pi)( 0.015^4-...

Homework Statement https://imgur.com/zEoCpc0 I am trying to figure put the angle and my attempt is tanx=sy/sx (I have calculated a value for the distances) But my book is saying: tanx =vy/vx I don't understand why my way of solving it is wrong... I don't get the same answer for x :/

Homework Statement why the mean area enclosed within the boundary of the centerline of tube thickness is (0.035)(0.057) ? Is it wrong ? Second question , why for the ds it's 2(57) and 2(35) respctively ? what is ds actually ? Homework EquationsThe Attempt at a Solution for the first...

Homework Statement what is the angle the force should apply in order to be box number 1 in static position and box number 2 move Homework Equations F=ma The Attempt at a Solution

Workings $\triangle ADE \cong \triangle CFE \left(AAS\right)$ $\angle AED = \angle CEF $( vertically opposite angles ) $\angle CFE= \angle EDA $( alternate angles ) $AE=EC $( E midpoint ) $ii.$ADCF is a parallelogram because diagonals bisect each other. Where is help needed How should...

I have a high pressure volume coupled with a low pressure volume by a pipe and valve . If the pipe was straight I would expect the isobars of the pressure gradient to be parallel to the pressure differences and perpendicular to the pipe , I would expect a reaction force (red arrow) on the wall...

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...

How do I use the double angle identity in order to derive this expression: cos6(u)?

$\tiny{s6.12.3.17}\\$ $\textsf{ Find the angle between the vectors $a$ and $b$}\\$ \begin{align} \displaystyle a&=\langle 3,-1,5\rangle &b&=\langle -2,4,3\rangle\\ \\ \cos\left({\theta}\right)&=\frac{(3\cdot -2)+(-1\cdot4)+(5\cdot3)} {|\sqrt{35}|\cdot|\sqrt{29}|}\\ &\approx 0.1569 \\...

Homework Statement I'm having problem with the angle of $$theta_s1$$ . My ans is +35 (as in my working) , but the ans provided is $$theta_s1$$ = -55[/B] Homework EquationsThe Attempt at a Solution As in the picture posted

Homework Statement Why can't i use the equation to determine the normal stress and shear stress ? Is my concept wrong ? I use the method in the link to do this question. The question said the stress on a plane making angle 30 degree anticlockwise from plane AD . Homework EquationsThe Attempt...

Hello! Let's consider a plane wave represented by a ray, propagating in a 2D dielectric slab. It has a medium with refractive index n_1 as its core and a medium with refractive index n_2, n_2 < n_1, as its cladding. In order for this ray to represent a mode, it must satisfy two conditions: -...

Homework Statement A particle flies along in the positive +x direction. It has a constant force F applied 30º clockwise to the x-axis. It is moving at .6 c. What is the angle of acceleration? Homework Equations a = F/(mγ3) The Attempt at a Solution [/B] I'm pretty sure I know how to do...

1. Homework Statement I am looking at problem 2.2 pictured above. I have solved all portions of the question except the last part, which asks for the angle between the normal vector to the surface and the z-axis. I am aware that the normal vector is simply equal to the gradient of the surface...

Hi, could someone please tell me what theorem I need to be looking at to work out the angle at $\gamma$ please? I've worked out the rest but can't find a theorem for this one. Thanks

Imagine a point with n vectors (all with equal magnitude) coming out from that point that equally cancel each other out in magnitude. How would you calculate the equal angle between n vectors? For example: 2 vectors (equal magnitudes) coming from one point that cancel each others magnitude...

How can we find the angle at which the curve of equation : r=b + acosθ hits the x-axis. I want a fast way or method since I only need it to plot the graph well. I'm only asked to plot the curve well and pay attention to the angle at which the curve hits the x-axis and not to calculate and...

Homework Statement It looks as if 50 degrees is an external angle of the triangle.So it should be greater than the two opposite interior angles (i.e x and the other one). But book tells a different answer. Somebody please guide me.Zulfi. Homework Equations No eq. Rule: Exterior angle of a...

As most know and rest can find out, radians are a dimensionless unit. Actually, it's even worse: angle in general is a dimensionless quantity. That stems from it being defined as a ratio of the arc versus the radius. I now present my opinion of disagreement to this concept. In the strict...

Homework Statement Simplify cos^2 8x - sin^2x Homework EquationsThe Attempt at a Solution I thought it would be in the format of cos2x But I can't seem to figure it out I tried cos (4 * 2x) And I tried to change the sin^2x into 1-cos^2x and I could get any farther. Not sure how else to...

I am looking for free solved exercises about: right angle projections, (cross) section views Here are some pictures of my book so you can understand what I am looking for http://1.1m.yt/3cNNDl-.jpg http://1.1m.yt/FekMn6x.jpg http://1.1m.yt/1t3KEer.jpg http://1.1m.yt/urA5V2_.jpg...

Homework Statement A solid sphere rolls down a hemisphere from rest. Find the angle at which the sphere loses contact with the surface. R = radius of hemisphere a = radius of sphere Homework Equations ΣFr = Macm,r N-mgcosθ = -mVcm2/(R+a) N = mgcosθ - mvcm2/(R+a) eq. (1) Conservation in...

Hi everyone, I am a new student who is studying on collecting data from TV signal. I hope everyone can help me for ideas. I am having spectrum analyzer which can define a TV station around me, so I chose 4 stations WHUT-TV [584MHz 590MHz], WPXN-TV [590MHz 596MHz], WTTG [60 MHz 608MHz], and WNVC...