Plane Definition and 1000 Threads

Homework Statement Let's suppose we have a [cuboid](http://en.wikipedia.org/wiki/Cuboid) of dimensions ##a \times b \times c##. We put it on an inclined plane of an angle ##\alpha## so that only one edge of length ##c ## touches the plane. In time ##t = 0 ## the cuboid doesn't rotate. Let the...

Homework Statement A crate of mass 9.2 kg is pulled up a rough incline with an initial speed of 1.52 m/s. The pulling force is 110 N parallel to the incline, which makes an angle of 20.6° with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 4.94 m. (e)...

Hey! :o We want to show that if $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ are on the same plane, then there are $A, B, C$ not all $0$ such that $A \vec a+B \vec b+C \vec c=\vec 0$. The solution is the following: If $\overrightarrow{a}, \overrightarrow{b}...

I have a doubt in my mind regarding moment of inertia.in my textbook a question is somewhat like this The center of a disc of mass 'M' and radius 'R' is at a distance 'd' (here 'd' >'R') from a certain point 'O'.what is the moment of inertia of the disc about an axis perpendicular to the plane...

Almost always in xy plane we take that origin is ##(0,0)##. Is it possible to take that origin is in the point ##(1,1)##, or some other point?

Something strange regarding the 1904 plane (Flyer No 2) built by the Wright Brothers I am looking for an as simple as possible mathematical model that can explain how it really worked. In 1904, the Wright Brothers started to test a new plane, Flyer II, somewhere near Dayton, Ohio where they...

Hello, After collecting data for the classic physics experiment - motion down an inclined plane, I assembled my graph, and found something startling; in my graph, acceleration is proportional to mass (use the attached file for reference). Theoretically, my graph should resemble the inverse...

Hi! I need to figure out the Lagrange Equation for a rod or nail swinging from a horizontal plane. The thing is, that while it is swinging back and forth, the while nail is moving along the X axis as well. I was thinking to use 1/2mv^2+(1/2)Iø^2 . Any help would be appreciated! Thanks.

Homework Statement A solid uniform hemisphere rests in equilibrium with its curved surface in contact with a rough inclined plane which is elavated by an angle α where sin(α) = 3/16. Find the angle between the symmetry axis of the hemisphere and the vertical.[/B]Homework Equations Sine rule...

Homework Statement Homework Equations Fs = μ FN The Attempt at a Solution Ok, so I drew a free body diagram and tilted it 90 degrees so that Fg of the small box points right and Fstatic points left. Fg = 4.7 kg x 9.8m/s2 = 46 N we want Fs to equal 46 N , correct? so we use the formula Fs...

The question word for word : "Write the equation satisfied by all of the points P(x, y, z) that are at the same distance from the point F(0, 0, 4) and the plane z = 0." I figured I could maybe start by finding the distance between point F and the plane z = 0 but I can't figure out how to...

Suppose we have a block on an inclined plane. If we choose the x-y axis to be parallel and perpendicular to the inclined plane, then we have Fy = N - mgcos30 = 0 But if we choose our trivial x-y coordinate system, where y is parallel to the force of gravity, then we get: Fy = Ncos30 - mg =...

Homework Statement I'm doing project using xsens MTi-G. Data file example: I must plot motion in plane (decart coordinate system), without z component. Measurment is taken after 0.01 s. To do the task, I should use acceleration and velosity data. Homework Equations The Attempt at a...

Homework Statement Find the equation of the plane tangent to ##x^2+3y^2+6z^2=67## at the point ##(1, 2,3)## Homework Equations ##w-w_0 = F_x(x-x_0) + F_y(y-y_0) + F_z(z-z_0) ## The Attempt at a Solution Using the above formula, I get ##w-67 = 2x(x-1) + 6y(y-2) + 12z (z-3)## = ##w-67 = 2(x-1)...

Homework Statement A crate is pulled by a force (parallel to the incline) up a rough incline. The crate has an initial speed shown in the figure below. The crate is pulled a distance of 9.33 m on the incline by a 150 N force. The acceleration of gravity is 9.8 m/s 2 . What is the change in...

Homework Statement [/B] Charge is distributed uniformly over a large square plane of side l, as shown in the figure. The charge per unit area (C/m^2) is \sigma . Determine the electric field at a point P a distance z above the center of the plane, in the limit l \to \infty. [Hint: Divide the...

Homework Statement My textbook says that the state of plane stress at a point is uniquely represented by two normal stress components and one shear stress component acting on an element that has a specific orientation at the point. Also, the complementary property of shear says that all four...

Homework Statement What is the difference between the two given equations below? When would you use one or the either? Homework Equations ## z - z_1 = \frac{∂z}{∂x}(x_1, y_1, z_1)(x - x_1) + \frac{∂z}{∂y}(x_1, y_1, z_1)(y - y_1) ## ## \frac{∂f}{∂x}(x_0, y_0, z_0)(x - x_0) +...

Hey! :o Find an equation for the plane that passes through $(3, 2, -1)$ and $(1, -1, 2)$ and that is parallel to the line $\overrightarrow{v}=(1, -1, 0)+t(3, 2, -2)$. The general formula of the equation on the plane is $$Ax+By+Cz+D=0$$ where $(A, B, C)$ is a perpendicular. Since the plane...

Hello! :o When a plane contains the line $\overrightarrow{v}_1=\overrightarrow{a}+t\overrightarrow{u}$, does this mean that the vector $\overrightarrow{u}$ is parallel to the plane?? (Wondering)

Homework Statement What's the difference between the two equations for a plane? This question is somewhat related to my other, overarching question here: https://www.physicsforums.com/threads/i-am-confused-about-how-multivariable-calc-works.798798/ Homework Equations ## a(x - x_0) + b(y -...

Hello! :o I found the following in my notes: The plane that is constructed by two non-parallel vectors $\overrightarrow{v}$ and $\overrightarrow{w}$ consists of all the points of the form $a \overrightarrow{v}+b\overrightarrow{w}$, $a, b \in \mathbb{R}$. The plane that is defined by...

Homework Statement Find the equation for the plane containing the lines: x-y+2z=4 2x+y+3z=6 and the point: (1,-2,4) Homework Equations A(x-xi)+B(y-yi)+C(z-zi)=0 The Attempt at a Solution First I wrote down the vectors from the line equations, V1=<1,-1,2> V2=<2,1,3> After this I did the cross...

Homework Statement So the equipotential surface of a point charge is sphere with the charge in the center, and the equipotential surface of a infinite line is a cylinder with the line of charge as the axis. I was wondering what is the shape of the equipotential surface of a infinite plane...

Let say a plane flights at 1km/s, shoots a 2kg projectile at 1km/s, so to the Earth, the projectile flights at 2km/s with 2*2*2/2 = 4MJ. The same gun when fixed on Earth, shoots the same 2kg projectile at 1km/s, achieves 2*1*1/2 = 1MJ Assume that the energy comes from burning propellant or...

Let f: \mathbb R^2 \to \mathbb R^2 given by f=(sin(x-y),cos(x+y)) : find the equation of the tangent plane to the graph of the function in \mathbb R^4 at (\frac{\pi}{4}, \frac{\pi}{4}, 0 ,0 ) and then find a parametric representation of the equation of the tangent plane What I did: the...

I want to know the maximum shear stress acting on the y-z face(plane). I already know all 6 stress components: Sxx, Syy, Szz, Sxy, Syz, Sxz. The shear components on the y-z face are Sxy and Sxz, which are orthogonal to each other. Is the maximum shear on this plane simply the greater of the two...

Homework Statement Find the equation of the plane that goes through points P, Q and R. P = (3, -1, 2), Q = (8, 2, 4) and R = (-1, -2, -3) Homework Equations Eq of plane 0 = a(x - x0) + b(y - y0) + c(z - z0) The Attempt at a Solution In order to find vector normal to the plane, my teacher...

Homework Statement All charges in space are distributed on the xy-plane. The potential above the plane is known as \phi = \phi_0 exp(-kz) cos(kx) What's the charge distribution on xy-plane? Homework Equations \vec E =- grad(\phi) The Attempt at a Solution Applying the relationship between...

Homework Statement Find the acceleration of both blocks Homework Equations Dynamics The Attempt at a Solution Everything in black is given in the problem. The red/blue is my work. First I want to relate the acceleration of block A to block B by finding the constraint equations: Lrope = 2L1...

Would on a exoplanet with dense atmosphere zeppelin/blimp better idea than a plane? If I get it right there would be: -much higher buyancy (argument for zeppelin) -higher drag (argument against plane) -higher lift (argument for plane) (but I'm not good enough to know what would matter)...

Homework Statement http://www.sumoware.com/images/temp/xzafcttptkeoehmo.png An inclined plane is put on a smooth floor. The inclined plane is hit (collided) by an elastic ball moving horizontally before the collision. The ball bounce from the inclined plane and land again right at the point...

Homework Statement A block of mass m1= 3.70 kg on a frictionless plane inclined at angle θ=30.0° is connected by a cord over a massless, frictionless pulley to a second block of mass m2=2.30 kg. What are (a) the magnitude of the acceleration of each block, (b) the direction of the acceleration...

Homework Statement http://www.sumoware.com/images/temp/xzdmdjtlksnfhiqc.png A solid ball rolls perfectly with initial velocity v0 in horizontal axis ( y-axis ) on an inclined plane with elevation angle Θ as the picture above shown. This ball moves turning due to the gravitational acceleration...

I'm doing a problem where we have plane monochromatic waves incident on finite double slits (each of width a, separation d), and the transmitted light is observed in the focal plane of a lens of focal length f. The position of the lens isn't specified. So I have worked out that the intensity...

Do you just cube a variable? How does it work? Has this been figured out yet? Any thoughts if it hasn't? Any applications if it has?

Consider the Lines Below: r = <2, 3, 0> + t<3, -3, 1> r = <5, 0, 1> + s<-3, 3, 0> A.) Find the point at which the given lines intersect. B.) Find an equation of the plane that contains these lines.Homework Equations [/B] The vector equation of a line is given by r = r0 - tv The equation of...

Homework Statement How much of a wall 3m behind you can be observed in a 5 cm square mirror which is held centrally at a distance of 10 cm from your eye? Homework Equations None that I can think of. I think this is straight geometry. The Attempt at a Solution I know I have to use similar...

Find in rectangular coordinates a unit vector which is: A. in the direction of E at P(2,3,-4)if $\overline{E}=(x^2+y^2+z^2)\left(\frac{xa_{x}}{\sqrt{y^2+z^3}}+\frac{ya_{y}}{\sqrt{x^2+z^2}}+\frac{za_{z}}{\sqrt{x^2+y^2}}\right)$; B. Perpendicular to the plane passing through M(1,-5,5), N(-2,4,0)...

for example when you climb up an inclined plane why is there no work in the horizontal direction yet there is work in the vertical direction? I do not want examples I want a direct answer.

Hi, I have a problem with the following explanation of velocity in plane polar coordinates. I don't understand why the magnitude of Δer is approximately equal to Δθ. Thanks

Homework Statement "You are lowing two boxes, one on top of the other, down a ramp. Both boxes move together at a constant speed. The coefficient of kinetic friction between the ramp and the lower box is 0.430, and the coefficient of static friction between the two boxes is 0.779. The lower box...

Homework Statement A 2 kg object is placed on a plane inclined at an angle of 30 degrees. If the coefficient of static friction is 1, and the coefficient of kinetic friction is 0.1, what is the net force on the block? Homework Equations F = ma The Attempt at a Solution I made a FBD with a...

A person asked this question of me recently and it generated some discussion amongst the people in the room (many of whom had a limited background in physics). The original question went something like this: suppose that a ball is initially at rest in a wagon and the wagon is given a horizontal...

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >[/color] So the problem that I have been assigned has formulas of rotational energy, momentum, trajectories, inertia, and inclined planes. A solid sphere is rolling down an inclined plane (that is...

$\textbf{Problem}$ Let $\textbf{u}$ and $\textbf{v}$ be linearly independent vectors in $\mathbb{R}^3$, and let $P$ be the plane through $\textbf{u}, \textbf{v}$ and $\textbf{0}.$ The parametric equation of $P$ is $\textbf{x} = s\textbf{u} + \textbf{v}$ (with $s$, $t$ in $\mathbb{R}$). Show that...

Homework Statement f(x,y) = x^2 + xy + y^2 and z=2x+y intersect, find a parameterization of the curve where they intersect. Homework EquationsThe Attempt at a Solution I am lost. I know that z is the partial derivative of the original function, if that's of any use. I can visualize it but not...

A 1.54 kg green toy car accelerates at 1.70 m/s² down a ramp 3.38 m long. If the force of friction acting on the toy car is 1.31 N, how much work is done on the toy car to get it to the bottom of the ramp? Formulas: Ep=mgh W=fd F=ma a=gh/d Fr=u*Fn I know the acceleration, mass, and distance...

Homework Statement Describe the set of points determined by the given condition in the complex plane: |z - 1 + i| = 1 Homework Equations |z| = sqrt(x2 + y2) z = x + iy The Attempt at a Solution Tried to put absolute values on every thing by the Triangle inequality |z| - |1| + |i| = |1|...

Homework Statement Find a set of parametric equations for the line of intersection of the planes. 6x-3y+z=5 and -x+y+5z=5[/B]Homework Equations The cross product formula The formula for the parametric equations of a line in three dimensional space: x=x1+at, y=y1+bt, z=z1+ct Knowing the fact...