Angle Definition and 1000 Threads

Assume a flat one square foot vertical plate attached 6 feet up, outside on a wall. Dozens of yards away are various solar reflectors angled to reflect sunlight onto that plate. Problem is, the plate requires to be only struck straight on at a 0 degree angle of incidence. And, all the...

Hi all, I'm slowly working through "Mathematical Methods in the Physical Sciences" by Mary Boas, which I highly recommend, and I'm stumped on one of the questions. The problem is to prove the double angle formulas sin (2Θ)=2sinΘcosΘ and cos(2Θ)=cos2Θ-sin2Θ by using Euler's formula (raised to...

Hi, Can anybody tell me that is the formula to calculate the octahedral rotation angle in Perovskite. for example in SrTiO3, the TiO6 Octahedral angle. When SrTiO3 goes from Cubic to Tetragonal, this TiO6 Octahedral tilt. I have to find this angle. Thanks

Homework Statement This problem asks for the angle on an inclined plane-- I have attached the problem below. Homework Equations fnet=ma The Attempt at a Solution I honestly have no idea what to do. I found the vector components for gravity and made a FBD for the box, but I can't really figure...

I have been on the hunt looking for a precise equation that gives you the angle that a ship is displaced along its x-axis (roll). There is a somewhat simple equation:Roll angle (Θ) : Θ = Acos( ωt+ φ)------where A is the amplitude of the wave, ω is the frequency and φ is the phase chage. So...

Homework Statement A light ray falls from the air (##n_a=1##) into the center of the upper surface of a long cilindrical glass tube with an index of refraction ##n_t=3/2##. The tube is submerged into water all the way to the upper edge and the waters index of refraction is ##n_w=4/3##. What is...

Hi everybody, I would like to know what would be the best angle (or best geometry) to put the detector relative to the light source in order to observe the emission radiation from the fluorescent materials? As I know the most common geometry used for fluorescence is right angle observation...

The forces acting on the glider are the gravitational force, the lift force and the drag (air friction). The drag () and lift force () are a function of the angle that the wings have with the gliding direction. =122 with: =0.1+3∙10−32 =122 with: =0.2+0.1− 3∙10−32 In the above equations, is in...

Homework Statement You have been stranded on a deserted island. Fortunately, you managed to bring a flare gun. You can see a ship 300. m off shore. Unfortunately, because of the daylight the ship cannot see your flare unless it is within 100. m of the ship. A.) If you fire the flare gun from...

Homework Statement You come to a river and you see a vine you will use to swing across. Your mass is 75.0 kg, the vine is 18.0 m long, and the vine breaks when under 655 N of tension. a) at what angle from the vertical will the vine break? b) what should be the maximum tension supported by the...

What is the equation for how a light beam is bent by a mass? Say a mass M way out in space, and a light beam is aimed from VERY far away such that it should pass at a radius R from the mass.

Homework Statement A projectile was launched from the top of a 100m tower upward at an angle theta to the horizontal with an initial velocity of 36m/s. The time of flight of the projectile was 8 seconds. Determine: i) The angle of projection ii) The maximum height reached by the projectile...

Homework Statement Homework EquationsThe Attempt at a Solution Here is what i have done so far: Fx = cos 45 T - Ff =ma Fy=sin 45 T -mg+ Fn =ma I found ff= uk * Fn = 0.5 *sin 45 +mg fn = sin 45 +mg Isolated for T in the x and y: Tx = ma + Ff / cos 45 = 13.404 Ty = ma +mg - Fn / sin 45 =...

Homework Statement Two vectors of magnitude 5 units and 3 units are added such that the angle between the resultant and the vector of magnitude 5units is maximum. Find this angle. Homework EquationsThe Attempt at a Solution Knowing that the resultant vector makes a smaller angle with a...

A body in an absolute vacuum is suspended from an axle having no friction at the body or at the suspension points. A power source is affixed to the body which rotates the axle. At rest the body is horizontal. The body weighs 4000 lbs. The center of gravity of the body is vertically 4 ft. below...

This is the problem I am looking to solve: given two objects of different mass, find the angle of deflection after an elastic collision for each object. For both objects we know: m : Mass in Kilograms θi : Initial Angle in Degrees si : Initial Speed in Units per Second sf : Final Speed in...

Well, i have a cantilever beam where i have the displacement of the tip of the beam (y axis) data from a vibration of this beam. In the tip of the beam is a steel wire attached, pulling up the beam with an angle (30º for example). I want to know if exists a form to obtain the strain of the wire...

Homework Statement Question 2.b. from this paper - http://www.sqa.org.uk/files_ccc/PhysicsEQPAH.pdf Homework Equations let theta = x Tcosx = mg Tsinx = 2.5 (2.5 is the centripetal force) The Attempt at a Solution I rearranged the above equations and got 52 degrees as my answer. The...

Homework Statement Fresnel losses occur between two different media that have different refractive indices. To reduce these losses we can change the angle of incidence to brewster's angle. At this angle, the amount of reflective loss is minimized for p-polarized light. Do we assume that laser...

Homework Statement A ray of light falls on the surface AC of a prism with a straight angle and with two sides equal. For which incidence angle the ray won't come out of the surface AB. The index of refraction for the prism is n=2. Homework Equations sina/sinb=n2/n1 The Attempt at a Solution...

Homework Statement When the incidence angle is equal to the angle of refraction? Homework Equations sina/sinb=n2/n1The Attempt at a Solution I think as a=b => sina=sinb => n1=n2. We should have the same environment? But is that refraction?

Hello friends, I have a situation where I am looking to pull a load and would like to better understand the forces involved. In the first scenario I am pulling a load in a straight line, the load cell reads 10kN. In the second scenario I would like to pull the same load at an angle of 150o...

Homework Statement A spherical fruit has a radius of 1 inch. A slice has surface area of its peel equal to pi/8 . Determine the angle of cut for the slice. Homework Equations I'm sure there is a relevant equation here but I don't know it :-( The Attempt at a Solution So the radius is 1 inch...

This isn't for any particular project or assignment, but I've tried solving this in the past and haven't figured it out. Say you have an RC seaplane, like the one pictured, with the engine mounted well above and aft the CG. You're going to need to angle it down a little to counteract the...

Homework Statement I need to find how a ray of light will travel from the snail towards Andrews eye. I need to find the angle of incidence and angle of refraction. I know the index of refraction of both materials Air: 1 Water 1.33 Homework Equations Snells law 1.33 *sin(X) = sin(y) x is...

Should not angle between vector P and Q be 180-θ rather than θ? According to my book it is θ.

Hi all, I am very confused by this concept. As I searched online, all respondents say that friction decreases as angle increases because normal force decreases. BUT, they don't explain this phenomenon: A block on a ramp is static at certain angle, and after the ramp is raised by a certain...

Dear All, Hello, I'm studying electronics engineering and I'm new in vehicle dynamics, Recently, I make an autonomous vehicle for my final project. In order to control steering angle of vehicle, I have difficulty to measure the steering angle based on curvature road and vehicle velocity. Anybody...

Hello PF users hope all is well! I need a reminder of the formulas needed in order to get "Sine of angle of incidence" "Sine of angle of refraction" And "Index of refraction". The only information I have available now is "Angle of incidence" And "Angle of refraction" I'm guessing...

Homework Statement A thin rod of length l and mass M rotates about a vertical axis through its center with angular velocity ω. The rod makes an angle φ with the rotation axis. Determine the magnitude and direction of L (angular momentum). So we're given: mass - M, length - l, angular velocity...

Can someone help me in solving this question ? my attemp is sin42/sin 90 to get the refractive index then n =sin i/sin r to get c and for b n=1/sinc

Homework Statement A student stands 2.7 m in front of a floor-to-ceiling mirror. Her eyes are 1.64 m above the floor and she holds a flashlight at a distance 0.85 m above he floor. Calculate the angle θ, in degrees, that the flashlight makes with respect to the floor if the light is reflected...

Homework Statement Two ice skaters crash into each other. Before they collide, one of them (50 kg) is skating in a straight line at 5 m/s, the other (40 kg) is skating at 4 m/s in a straight line at 90 degrees to the 50 kg skater’s direction. After the collision, the 50 kg skater is moving at 4...

Homework Statement A uniform beam of mass m is inclined at an angle θ to the horizontal. Its upper end (point P) produces a 90° bend in a very rough rope tied to a wall, and its lower end rests on a rough floor (see figure below). Let μs represent the coefficient of static friction between...

In a triangle whose sides are 3,4 and root 38 metres respectively, prove that the largest angle is greater than 120° My answer: Here angle C > B...(1) and C > A ...(2) adding (1) and (2) we get 2c > A+B, taking sine both side , sin2C = sin(A+B) = sin(C), therefore cosc > (1/2) therefore...

Homework Statement A 0.7MeV (E°) photon scatters off a free electron such that the scattering angle of the photon is twice the scattering angle of the electron (θ=2φ). Determine the scattering angle for the electron. Homework Equations λ' - λ° = h/(mec)(1-cosθ) E = hc/λ ρelectron = mev /...

Consider the problem of projectile motion where the angle to hit a target ##(x,y)## is asked, once given the initial velocity magnitude ##v_0##. The projectile is fired from the point ##(0,0)##. Here is the final formula for theta, solving the equations of motion...

Hello! I have two quaternions with norm equal to 1. Both are represented in the angle-phase form, i.e, I have q=exp(i*\phi)exp(k*\psi)exp(j*\theta) and p=exp(i*\phi')exp(k*\psi')exp(j*\theta'). Let \alpha be the angle between q and p. I need to write \alpha in function of \phi-\phi', \psi-\psi'...

Homework Statement What is the angle of twist at gear A relative to the motor? (Round to the closest 6th decimal) Homework Equations I know to find the angle its θ = ∑ (TL/JG) but it can also be θ = Lτ/Gr The Attempt at a Solution So i used both these equations, and I got...

Homework Statement I'm trying to understand these two a bit better in terms of lasers. Fresnel Loss - The loss that occurs when there is a change in refractive index. Some light will be transmitted, while other light will be reflected back into the medium. This is bad for lasers because it...

Homework Statement This isn't so much of a problem itself but I found it interesting that on the All About Circuits website, two of the questions give a phase angle for impedance as opposite the angle of current. I understand the current is 90 degrees out of phase with voltage in both RL and RC...

Given a cube, choose a vertice and draw 2 of the three possible diagonals. What is the measure of the angel between those two diagonals? Proposed answer: We can say that both diagonals touch vertice A, to give it a name. We can also call the endpoints of both diagonals B and C. If we imagine...

Homework Statement Three receivers, with complex impedance \underline{Z_1}=(125+j375)\Omega,\underline{Z_2}=(700+j100)\Omega,\underline{Z_3}=(500-j500)\Omega, and two sinusoidal current generators of effective values I_{g2}=40mA and unknown I_{g1} are connected. When the switch is open...

Homework Statement I know the answer to this problem is IBNpir^2sin(90-theta). What I don't get, is why the angle is 90-theta. Homework EquationsThe Attempt at a Solution

Homework Statement Dispersion in a window pane. In Figure (a) below , a beam of white light is incident at angle θ1 = 67o on a common window pane (shown in cross section). For the pane's type of glass, the index of refraction for visible light ranges from 1.535 at the blue end of the spectrum...

Can someone help me relearn finding the angle between two forces when solving for work of each forces (gravity, tension, fF, normal)? I remember that cos(90°-α) = sin(α) but what I don't understand is when the angle in between is "90°-α" or when it's just "α". I tried doing this on my own and...

Homework Statement In the diagram , a block rests on a smooth horizontal surface . It is then pushed with a force of 45 N at an angle of Θ(theta) to the horizontal . 50 J of work has been done to push the block through a distance of 1.60 m Its speed is 2.50 m s^-1. Homework EquationsThe...

Homework Statement A box is dragged a distance d across the floor by a force F which makes an angle theta with the horizontal. If the magnitude of the force is held constant but the angle theta is increased, does the work remain the same, increase, decrease, or first increase and then decrease...

Hello everyone, i stumbled upon a trisection solution that was unknown to me and looked incredibly great (i am not an expert at all) http://andreasaronsson.com/guides/perspective-drawing/divide-into-equal-parts/ could someone please validate it and explain why it works and why it is not...

Homework Statement a) Find the acute angle between the line ## r = i+3j+5k+t (2i+4j+k) ## and the plane x-y+z=0 b)Two planes are defined by the equations ## x+2y+z=4## and ## 2x-3y=6 ## i. find the acute angle between them. ii. find a vector equation of their line of...