What is Plane: Definition and 1000 Discussions

When we take the x-axis parallel to incline surface its clear that the horizontal component of weight is causing the block to come down but when we take the standard orientation its not so clear to me. Is horizontal component of ##F_N## causing the block to come down? <Moderator's note: Use of...

If on a flat ground, we exert a force F to move forward, then we go to an incline plane of theta degrees. Why wouldn't the force F2 to move up the incline plane with respect to ground be F2*cos(theta) = F --> F2 = F/cos(theta) disregarding the effects of gravity?

$$\phi_E=\dfrac{Q_{\textrm{enclosed}}}{\varepsilon_0}\Rightarrow Q_{\textrm{enclosed}}=9,6\cdot 10^{-7}\, \textrm{C}$$ $$Q_{\textrm{enclosed}}=\sigma S=\sigma \pi R^2\Rightarrow \sigma =\dfrac{Q_{\textrm{enclosed}}}{\pi (0,1^2)}=3,04\cdot 10^{-5}\, \textrm{C}/\textrm{m}^2$$ I have a lot of...

A plane is flying 80km/h in horizontal direction and it has to drop a bomb into 30m wide and 30m deep hollow. What is the smallest possible height for the plane to fly above hollow if the bomb successfully hits the bottom? I made a mistake somewhere but not sure where... the correct result is...

For lower half ,$$Fnet=-\mu F_N+mg\sin \phi$$ For upper half, $$v^2=u^2+2as$$ (s is half of the total slant distance) $$v^2=0+2\frac{mg\sin \phi}ms$$ $$v=\sqrt{2g\sin \phi s}$$ again for lower half, $$v^2=u^2+2as$$ $$0=2g\sin \phi s+2\frac{-\mu F_N+mg\sin \phi}ms$$ $$\mu=\frac{2gm\sin...

Hi, When you have a one-dimensional plane, such as x-axis plane, when you move, you coordinates will change along all given axes. Actually, there is only one dimension available in this case so it doesn't make much sense here. When you have two-dimensional plane, such as x-y plane, when you...

1) By the Work-Energy Theorem, ##W=K_f-K_i=\frac{1}{2}I_{0}\omega^2=\frac{L^2}{2I_0}.## 2) By assuming that the initial length of the spring is ##0##, calling its final length ##S## and ##T## the tension in the rope connecting the pulley and mass ##m_p## I have: ##\begin{cases}(kS-T)r=0\\ m_p...

1. ##-f_k\cos\theta-T\cos\theta+F_n\cos\alpha=m_2a_x## 2. ##f_k\sin\theta+T\sin\theta+F_n\sin\alpha-m_2g=-m_2a_y## 3. ##T-m_1g=m_1a_y## I am unable to get anywhere. There are accelerations in x , y directions. I need the value of acceleration. Then I can simply use ##s=ut+\frac12at^2##

Hello, i wasn't in enginnering drawing class since 2 weeks because i was sick and my high school teacher told me to do this homework. This is what I've done so far I did not build the triangle 'cause i am not sure. Please, i just want that someone accompanies me with steps by steps explanation...

Let ##S## be a set of n geometric objects in the plane. The intersection graph of ##S## is a graph on ##n## vertices that correspond to the objects in ##S##. Two vertices are connected by an edge if and only if the corresponding objects intersect. Show that the number of intersection graphs of...

Hi all, a bit confused with regards to the whole term aspect angle. Most examples that I searched online involved either a 2D plane or a stationary object. In this case: Let's say the man is facing the ball. In this case, the ball is being thrown from the right to the left. Since the man is...

Hello all! As seen in the summary, I'm not sure if anyone can understand, but I will try to make this as clear as possible. Working in the 3D Plane: Given that there is a trajectory motion in the 3D Plane, and I have the coordinates of the motion at every 1s interval. This means at t=1s, the...

I came across the following problem and wondering how to solve it. There is a plane n1x + n2y + n3z + n4 = 0 where n1, n2, n3, n4 are known. The triangle is in this plane. We already know the two vertices P1(x1, y1, z1), P2(x2, y2, z2) of the triangle. Now we have to find the third vertex P(x...

The question I have is that if the aero plane is traveling in the same direction as the wind, would it not increase its velocity, as in with boats and streams? So, if by chance, ##w = v##, then the velocity of the aero plane would double. It feels weird as going by the same logic, if the speed...

Question: My attempt: Could someone please confirm my answer?

I hope this is okay to ask here. I'm working on a sci-fi short story, and for the purposes of the story I want to have a small ship that maintains its position over a specific location on the Earth's surface. Originally, I thought this would be easy. After all, that's what geostationary...

a. I solved a but I don't fully understand how it works. $$z = f_x'(1, -1)(x -1) + f_y'(1, -1)(y+1) = 2(x-1) + 3(y+1)$$ Eitherway it's b that's my issue. I can find the gradient of both plane and surface, but trying to do "dot-product of both normals = 1" will give an equation involving two...

Using Gauss's Law By using a symmetry argument, we expect the magnitude of the electric field to be constant on planes parallel to the non-conducting plane. We need to choose a Gaussian surface. A straightforward one is a cylinder, ie a "Gaussian pillbox". The charge enclosed is...

I don't know how solve this.. [User has been reminded by the Mentors to show their work on schoolwork problems]

So before I start I technically do now that the group I am dealing with is just a representation of the Klein bottle but I am not supposed to use that as a fact because the goal of the problem is to derive that information. Problem: Let G be a group of with two generators a and b such that aba...

I have attempted but I don’t get anywhere.

Body A rests on a inclined plane of body B . the angle of slope is α , the coefficient of friction between the two bodies is μ . Body A does not slip on body B because we accelerate body B with a. What is the minimum and maximum acceleration required for body A not to slip? What will be the...

It's the body. So there's friction on that plane and there's tension also. $$L=\frac{1}{2}m_1\dot{x}^2+\frac{1}{2}m_2\dot{x}^2-m_2g(l-x)-m_1gx\sin\theta$$ $$f=\mu N=-\mu m_1 g\dot{x}\cos\theta$$ I had found the frictional force's equation from [the...

The acceleration and velocity of a body rolling down without slipping on a frictionless inclined plane are given by $$ a=\dfrac{mg\sin \theta }{m+\dfrac{I}{r^{2}}}=\dfrac{g\sin \theta }{1+\dfrac{K^{2}}{r^{2}}} \cdots(1) $$ $$...

I tried to find the components of the vectors. ##a_y =2.60 sin 63.0 = 2.32## and assuming the z axis would behave the same as an x-axis ##a_z =2.60 cos 63.0 = 1.18## ##b_z =1.30 sin 51.0 = 1.01## making the same assumption ##b_x =1.3 cos 51.0 = 0.82## I now think I should have switched these...

I have a quick question. If a Vector is contained inside a plane, would the normal of the plane be orthogonal to said vector? Thank you!

So I've kind of made the assumption that there will be an odd number of plane waves and the same amount above and below the z-axis. Then, using the diagram below, I determined the angle the nth plane wave makes with respect to the z-axis to be the angle it makes with respect to the n =1 plane...

(I drew motion in the opposite direction so the object would rotate trigonometrically but it should be the same thing) I have just finished the Kinetic Energy and Work chapter in my course and this is the last problem from the problem set. I have not worked many problems with the Work-Kinetic...

I am trying to do exercise 8.5 from Misner Thorne and Wheeler and am a bit stuck on part (d). There seem to be some typos and I would rewrite the first part of question (d) as follows Verify that the noncoordinate basis ##{e}_{\hat{r}}\equiv{e}_r=\frac{\partial\mathcal{P}}{\partial r},\...

Find a vector that is perpendicular to the plane passing through the points P (1, 2, 3), Q (2, 3, 1), and R (3, 1, 2).

I’m pretty sure that the force on the sphere by the wall and plane has to equal mg so the sum of the normal force is steered by the wall and plane has to equal mg. I’m not sure where to go after this. Is mg the answer or is there something I’m missing?Here is Fig: 4-31:

Since z=0, the only variable that counts is x. So the solution would be: $$\frac {f \left(a + \Delta\ x, b \right) - f(a,b)} {\left( \Delta\ x\right)}$$

I have an extremely fast (f/1.05) night vision optic that I scavenged from a old night vision unit which is faster than current production lenses (f/1.23). However due to the design of newer night vision tubes, the lens will not focus to infinity on the night vision tube. This is because the old...

Yikes, this was a lot harder ditch/landing than I initially thought from the first reports. I thought they came in for the ditch with landing lights on so the pilot could judge the touchdown, but apparently with both engines off they had no lights (the APU can't power the landing lights?). No...

A wavefront is defined as a surface in space where the argument of the cosine has a constant value. So I set the argument of the cosine to an arbitrary constant s. ## k(\hat{u} \cdot r - c t) + \phi = s ## The positional information is is in r, so I rearrange the equation to be ## \hat{u}...

I apologize if this is the wrong area to post this in, I've never posted on thisforum before. I'm trying to form a FBD of a mechanism that uses linear motion to actuate a pin in a transverse direction. I've attached the general idea in a picture where the pin is free to move up and down. In...

In my textbook, it is stated that "if an object elastically hit an frictionless inclined surface with angle between the vector of initial velocity and an imaginary line that is perpendicular to the surface ##\alpha##,then the angle between the line and final velocity vector will also be...

The answer given states that: The entire x-y plane is obviously at the same potential since all the fields are strictly perpendicular to it (draw a diagram if youre confused). Since we choose the sphere to be at potential zero, the point on the sphere which cuts the x-y plane is also at zero...

Solution: u = [-2,3,1] Po = (6,0,0) & P = (4,2,3) PoP = v = [-2,2,3] Therefore, the answer is [6,0,0] + r[-2,3,1] + q[-2,2,3]; r, q are real numbers I don't understand why (6,0,0) is used as the point in the vector equation, since it only lies on the [-2,2,3] vector, not the u = [-2,3,1]...

Literally, don't know how to start.

Will translation parallel to x-axis work ? Else please suggest the symmetry? And does symmetry here refer to the symmetry of the sheet which causes the symmetry of the field or something else? Please be kind to help.

Here's what I did: ∮ B * dl ＝μ0 ＊ I ∮ AR * 2π*R ＝μ0 ＊ I ∮ 2π*AR^2 / μ0 = I ∮ 2π*AR^3 / 3μ0 = I Where did I do wrong?

ma = mg * sinα - fmg * cosα a = g (sinα-f * cosα) v = g*t(sinα - f * cosα) 14.7 = 10 * 2 (sin60 - f * cos60) f = 0.26 Can someone please check if my solution is correct? I'd really appreciate that.

Below is the measured values for the Debye rings I obtained. I have to multiply the ratio (which is (sin^2(theta_n))/(sin^2(theta_min))) by a multiplicand until I get an integer. However for the multiplicand and the values I measured I get 1, 3, 13, ??, 4, 8, ??. These should either correspond...

This question is from the David Morin ( Classical Mechanics ) - problem 3.7. I spent some time trying to figure it out the solution by myself, but since I couldn't, I looked into the solution in the book, but I got even more lost. So I searched for an online solution that could help me at least...

This image was provided, I've completed the first part of the question and got a = 4.8m/s^2 as well as T1= 24.5N and T2=34.3N. not sure about my answers though. also I don't understand the mass in static equilibrium part, can anyone explain how to solve that? Thanks.

Under plane stress (z direction perpendicular to the plane), there shouldn’t be any z stress component. Then if one end of the 2D model is fixed, does that mean the displacement on that fixed boundary is completely zero (u=v=w=0), but that will generally violate the stress component along z being 0.

a) When the system is in motion for the first time, the force causing ##M## to move is contact force with ##m## so: $$\Sigma F=M.a$$ $$N \sin \alpha=M.a$$ $$mg \cos \alpha \sin \alpha =M.a$$ $$a=\frac{mg \cos \alpha \sin \alpha}{M}$$ Is that correct? b) Is acceleration of ##m## the same as...

Confused how to approach problem after making a free body diagram and finding the length of the inclined plane