Angle Definition and 1000 Threads

The magnitude of each force is shown below: F1 = 10 N F2 = 20 N F3 = 40 N R = \sqrt {Rx^2 + Ry^2} R = \sqrt {-10^2 -15^2} = 18N θ = tan^{-1} \frac{Ry}{Rx} θ = tan^{-1} \frac{Ry}{Rx} = 56 To express the direction of R, we need to calculate the direction angle (i.e. the counterclockwise angle...

F1x = 120. Cos 300 = 103.92 ; F1y = 120.sin 300 = 60N F2x = 150.cos 110 = - 51.30, F2y = 150.sin 110 = 140.95 why taking angle 110 instead of 70 for finding the magnitude of F2 in X and Y components?

##AD## is diameter, thus ##\angle ACD = \angle ABD = 90^\circ##. Also ##HBDC## is a parallelogram because ##HC||BD, HB||CD##. It seems useless and I don't know how to continue. Thank you in advance!

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Hello, I was toying around with shapes and dies and wanted to calculate the load distribution in all spots so to get a rough idea of the maximum load I can use before breaking the die. The "problem" is as follows: I have a die shaped like a trapezium and I have to press an item (5-10mm thick)...

Hi, I was wondering whether I could get some help on this problem. I think my questions arise from a misunderstanding. I have attached an image of my working and an image of the solution copied out (that is all it says, doesn't have much explanation). I know the working I attached was for a...

Using the givens I found ωd=862 rad/s, and with some help I got tanϕ=-1 and Z=56.5685 ohms. But I can't figure out any of the other variables. I'm not even exactly sure what "driving frequency" is and I can't find an equation for it.

Hello. So I have a coil and a resistor in parallel connection. It is powered by alternating current. I have to calculate angle between voltage and current, what is the formula? I know the reactive resistance in coil, I know resistance of resistor, voltage across both of them and amps flowing...

I'm a physics student, and working on a class project that requires coming up with a method to control the exit angle (diffraction angle) of a monochromatic light source. For example, taking a laser (monochromatic, coherent light source), spreading the beam, and directing the light at a piece...

-I tried to draw the forces on the hoop when it is in the equilibrium state. I know there are friction and normal force on the contact point of the shaft and the hoop -I also put the weight force to the M object -But when i used the torque equilibrium, where the pivot is the contact point of the...

Used to play with gravitational attraction simulations ages ago. One thing I noticed it was difficult to get a small object to collide with a bigger spherical one vertically and far more likely to hit at an angle far from 0. Has the math of this been worked out for asteroids entering the Earth's...

Is it like using the sine rule to figure it out: 1.5/sin 68 = x/sin 17 = 0.47 which doesn't seem to be correct. I tried to determine the angle. I though the 5 degree slope means it could be 95 degrees cause the triangle looks like a right angle triangle.

With talk of the Earth's magnetic field slowly moving, (enough to cause navigational issues I've heard) does it effect how the sun's ray hit us? For example, the Northern Lights are solar partials interacts with the magnetic field (I think). If the poles moves, would it affect the effectiveness...

Im really stuck with this problem ! any help would be much appreciated

I am in Algebra 2 and the homework asks a question: "You and a friend arw driving golf balls at a driving range. If the angle of elevation is 30 degrees and the ball travels 625 feet horizontally, what is the initial velocity of the ball?"

I have a question in my text (Intro Mechanics by Kleppner) and a question is to find the cosine and sine between two vectors. It gives me the cosine piece: $$\cos(\vec A, \vec B) = \frac{\vec A ⋅\vec B}{|A||B|}$$ which I assume is just from the dot product, but it has no derivation of this, and...

Homework Statement [/B] Ball with a mass of 0.1 kg travels at a speed of 10 m /s to the boy. Boy kicks the ball with foot so that it bounces back at an angle of 30 degrees with respect to the horizontal floor. The ball falls back to the ground 20 meters from the boy. With what average force...

Hi all, I am a self learner (graduated very long ago and rusty at math) working through the Riley, Hobson and Bence text, chapter 1. 1. Homework Statement Use the fact that ##sin(\pi/6) = 1/2## to prove that ##tan(π/12) = 2 − \sqrt{3}.## Homework Equations ##tan(2x) = \frac { 2 tan(x)} {1...

So here's the problem: A sled slides down a long snow-covered slope that is at an angle θ to the horizontal. Kinetic friction acts on the sled as it slides where the kinetic coefficient of friction between the sled and snow is μk = 0.050. Ignore air-resistance when solving this problem. If we...

Homework Statement This is not a direct homework problem. Rather, I modified several that I saw that had different slopes but with the same initial velocity, and the same height answer: An icy, frictionless road slopes upward with angle Θ ° above the horizontal. A snowboarder of mass m...

Homework Statement The equation; 0.966= -0.354sin(φ+60) + 0.935cos(φ+60) and we're trying to find φ. Homework Equations 3. The Attempt at a Solution [/B] (edited) I tried doing ^2; 0.933= 0.125sin2(φ+60) -2*0.331sin(φ+60)cos(φ+60) + 0.874cos2(φ+60) x=φ+60 0.933= 0.125sin2x - 0.331sin(2x) +...

<< Mentor Note -- Two threads on the same question merged into one thread >> How does the maximum Power equation change if there's an angle to the way the wind falls into the wind turbine's blades? Example, when it falls vertically to the blades, it's Pmax= 8/27Sρu13 But if there's for...

I am simulating random angles from 0 to 2π with a uniform distribution. However, if I take the differences between random angles, I get a non-uniform (monotonically decreasing) distribution of angles. In math speek: Ai = uniform(0,2π) dA = Ai - Aj dA is not uniform. Here is a rough image of...

Hello, I have a question about this optics related problem. The distance between atomic planes in calcite is 0.30 nm. what is the smallest angle between these planes and an incident beam of 30pm x-rays at which diffracted x-rays can be detected? Thank you so much for the help guys!

Given the following vectors: how can i determine that Θ = Δp/p ? I can understand that p + Δp = p' but nothing arrives from this. Any help is welcome!

I was reading *Introduction to Nuclear Physics* by Krane and stumbled on the following (page 47): In Elastic scattering, the initial electron wave function is of the form ##e^{i k_i r}## (free particle of momentum ##p_i = \hbar k_i##). The scattered electron can also be regarded as a free...

Homework Statement A solid body begins to rotate around a fixed axis with angular acceleration ##\beta=\beta_0\cosφ##, where ##\beta_0## is a constant vector, ##φ##, is the angle of rotation of the body from initial position. Determine the angular velocity of this body as a function of the...

What's the difference between P = FSin Angle / A P = FCos Angle / A Why cannot we use F / A only in both forumlas? I am really confused When I should use each one of these forumlas ? I just need someone to explain each one of them ... Here's a pic to what I am referring to , why cannot we...

Homework Statement A frog jumps at t=0s and follows a projectile motion. The maximum height he reaches is 0.45m. The air resistance can be neglected. a) What is the initial speed of the frog in y-direction and how long is the total time until he lands on the ground? b) At which degree should...

Hello, I am trying to find an analytical expression to determine the solid angle subtended by a disk source onto the face of the cylinder. I will appreciate if someone can provide me directions. I am aware how to calculate solid angle by a point source to cylinder's face ( omega =...

Homework Statement What is the ideal speed to take a 70 m radius curve banked at a 30.0° angle? Homework Equations tan θ = v2/r g The Attempt at a Solution This has me stuck, when I attempted this I came to the equation v= √ g*r* tan Θ But when I substitute in the variables, I enter then into...

The formula for the angle required for you to launch a projectile with a given velocity, gravity, distance and height difference is, taking g as gravity, v as total velocity, x as total distance on the horizontal plane and y as how high the target is above you (Negative value means the target is...

Hi PF! Given a 2D plane, the following is a parameterization of a circular arc with contact angle ##\alpha## to the x-axis: $$\left\langle \frac{\sin s}{\sin\alpha},\frac{\cos s - \cos\alpha}{\sin\alpha} \right\rangle : s \in [-\alpha,\alpha]$$ However, I am trying to parameterize a circle...

A space vehicle enters the sensible atmosphere of the Earth (300,000 ft) with a velocity of 25,000 ft/sec at a flight-path angle of -60 degrees. What is its velocity and flight-path angle at an altitude of 100 nautical miles during descent? (Assuming no drag or perturbations, two body orbital...

Homework Statement For a physics experiment I need to find the uncertainties and I am using the angle of minimum derivation formula: The value of A=60° and one of the values of D is 29.7° which has a uncertainty of ±2 (I know it's a very high value) Homework Equations How do I calculate the...

Homework Statement I would like to understand why alpha particles experience large angle deflections and if this is the same thing as recoil of alpha particles? Do large angle deflections occur near the end of the alpha particle track or can they occur at any point along the trajectory...

I am looking for an optical piece that can act as a mirror when the angle of incidence is close to normal (90 degrees) but acts as a see-through glass when the angle of incidence is less than 60 degrees? Alternatively it can be a filter placed in front of a mirror that passes a lot of light at...

Homework Statement ABC is a triangle The angle A = 30 degrees AB = 7cm BC = 5 cm C is an acute angle. Find the size of angle C? Homework Equations I need to use the cosine rule here Cos C = (a^2 + b^2 - c^2) / 2ac The Attempt at a Solution The problem is I do not know the size of side b? So...

Homework Statement If the plane 3x+y+2z+6=0 is parallel to the line (3x-1)/2b = 3-y = (z-1)/a then 3a+3b is? Homework Equations angle between two lines=90 degree when l1l2+m1m2+n1n2=0 where l,m,n are direction ratios...(i) The Attempt at a Solution First I divided x/3 and 3-y by -1 to get the...

I seem to have come across a new problem I am trying to programm a sloping pipe system to match an array of vector points. I thought I had it all sorted out until I tested with a very high slope angle. With a normal slope of around 2% everything looks fine. If I increase the slope to 30% there...

I know how to find the cos(theta) between two vectors but I do not know how to find the sin(theta). vector w=i+3j vector v=<5, 2>

Triangle ABC has area 25*sqrt(3). if Angle BAC=30 degrees, find |AC|=|BC|=? the answer I got was 10*4th root(3) Is this correct? I am asking because someone other than my professor wrote the study guid for us for the final and I am not 100% sure what |AC|=|BC| means as my professor never...

Homework Statement [/B] Homework Equations Drawing a diagram for the forces is the easy part. I am not sure I am doing the equation of the sum of the torques well. The Attempt at a Solution This is my attempt for the forces[/B] And this for the torques:

How do I determine the degrees of an angle if I three X and Y coordinates? I honestly just need a formula to plug into some code. Thank you in advance.

Homework Statement Tarzan runs at 6 m/s and grabs a vertical vine (negligible mass) of length 4.1 m which is tied to a branch at the top. Tarzan then swings up. Determine the maximum height Tarzan will swing up and the maximum angle the vine will make with respect to vertical. Homework...

Tomorrow is my math test and I'm going over the study guide: I have vector U=<1, 3> and vector V=<5, 2> It says let theta be the missing angle between the two vectors. What is the cos(theta) and sin(theta)? I already know how to find the missing angle for cos(theta) but we never covered how...

Hello, I was struggling with solving a specific integral. I know that I can rewrite the exponential matrices and the range of the three Euler angles. However, I am not sure I should I write in terms those three Euler angles.

MY apologies that I don't think this is particularly advanced; my algebra and trigonometry is quite good, but all seems to fall apart once i move from 2D to 3D environments. Johnson Solid J2 is a pentagonal pyramid consisting of five equilateral triangles on a pentagonal pase, meeting at the...

Homework Statement We shot a projectile with mass ##m## and velocity ##v_0## with angle ##\phi## it collide with a box with mass ##M## at the maximum height of its path. Then, they both start to move with another speed. (We define ##t=0## at this time) (Completely Inelastic Collision). The box...