A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is the portion with which other materials first interact. The surface of an object is more than "a mere geometric solid", but is "filled with, spread over by, or suffused with perceivable qualities such as color and warmth".The concept of surface has been abstracted and formalized in mathematics, specifically in geometry. Depending on the properties on which the emphasis is given, there are several non equivalent such formalizations, that are all called surface, sometimes with some qualifier, such as algebraic surface, smooth surface or fractal surface.
The concept of surface and its mathematical abstraction are both widely used in physics, engineering, computer graphics, and many other disciplines, primarily in representing the surfaces of physical objects. For example, in analyzing the aerodynamic properties of an airplane, the central consideration is the flow of air along its surface. The concept also raises certain philosophical questions—for example, how thick is the layer of atoms or molecules that can be considered part of the surface of an object (i.e., where does the "surface" end and the "interior" begin), and do objects really have a surface at all if, at the subatomic level, they never actually come in contact with other objects.
Homework Statement
A man of mass 70[kg] pules a box at an angle 100. the static coefficient of friction between his legs and the floor is 0.6 and the kinetic coefficient between the box and the floor is 0.3
What's the maximum's box's mass
Homework Equations
Friction: f=μN
The Attempt at a...
Homework Statement
For a 0.90km radius cylinder, find the time for one revolution if "gravity" at the surface is to be 9.8 m/s2.
Homework Equations
rω^2=a
The Attempt at a Solution
i tried solving for omega but i couldn't find a solution that i only had 1 variable in it.
- You are driving car with 100 mile/hour
- You are pressing brake pedal.
- The speed of car is suddenly gone down. Decelerated.
- However, Wheel is rolling on road without sliding and car stopped smoothly finally.In this case,
- the tangent force acting on road surface is related with...
Homework Statement
The drawing shows an edge-on view of two planar surfaces that intersect and are mutually perpendicular. Surface (1) has an area of 2.20 m², while surface (2) has an area of 3.90 m². The electric field in the drawing is uniform and has a magnitude of 200 N/C. Find the...
Homework Statement
I am not asking you to help me solve this, so i won't put in any usefull relevant equations or attempts at a solution. The nature of my problem is more of an understanding this collision - it is more of a thinking thing to process here.
The problem goes like this.
Ball is...
I have also posted this question here: Relationship between surface area of electrode and reaction rate of hydrogen in fuel cells, but I really need an answer before tomorrow morning so I hope you don't mind me posting it here as well!
I am looking at the effects of increasing the surface area...
Hi!
Here is my task:
Calculate surface area of sphere $$x^{2}+y^{2}+z^{2}=16$$ between $$z=2$$ and $$z=-2\sqrt{3}$$.
Here are 3D graphs of our surfaces:
Surface area of interest is P3. It would be P-(P1+P2), where P is surface area of whole sphere. Is it correct?
Here is how I calculated...
When I learned Integrals in Calc III, the formula looked like this
∫∫ F(r(s,t))⋅(rs x rt)*dA
but in physics for Gauss's law it is
∫∫E⋅nhat dA
How are these the same basic formula? I know that nhat is a unit vector, so it is n/|n|, but in the actual equation, it is a dot between the cross...
Homework Statement
I have a coordinate system, (x,y,z). There is a uniform-magnetic-field of 2.0 T that exists along
the direction of the y-axis. There is a rectangular plane bounded by the points
(3,0,0),(0,1,0),(0,1,1),(3,0,1).
Calculate how much flux is traveling through the rectangular...
Homework Statement
find the values of the integral
\int_{S} \vec A\cdot\ d\vec a
where,
\vec A\ = (x^2+y^2+z^2)(x\hat e_{1}+y\hat e_{2}+z\hat e_{3})
and the surface S is defined by the sphere R^2=x^2+y^2+z^2
Homework Equations
first i must evaluate the integral directly, so i don't...
Let us suppose that a cylindrical bottle is on the surface of the water (filled with air for simplicity). A little spin is given to the bottle makes it rotating around the symmetry axis of the cylinder. After a while the bottle stops rotating. How to calculate the time duration of spinning?
Homework Statement
Homework Equations
The sphere is positively charged and appears to have its charge concentrated at its centre.
Potential V is calculate to be 285V
The Attempt at a Solution
The charge induced on inside of box is negative.
THe potential is less. It is said that it's being...
Homework Statement
A small ball of m=1kg at height hp = 8m at point p, is given an initial horizontal speed vp = 10 m/s. It slides over an uneven frictionless surface. What is speed vq of the ball at height hq = 3m at point q?
Homework Equations
Ui + KEi = Uf + KEf
The Attempt at a Solution...
I am trying to understand in more detail the answer to:
http://math.stackexchange.com/questions/673187/universal-cover-of-a-surface-with-boundary
It is mentioned that the universal cover of a hyperbolic surface ##S## with geodesic boundary is a closed disk ##D^2## with a Cantor set removed from...
I'm going through Kerr metric, and following the 'Relativist's toolkit' derivation of the surface gravity, I've come to a part that I don't understand.
Firstly, the metric is given by...
we say the surface element of x(u,v),y(u,v),z(u,v) is absolute value of the cross product
or
i don't understand why this is. i know that the absolute value of the cross product is the area of a parallelogram formed by a,b,a+b, but i get lost after that
im guessing something happens where dudv...
So i am working on a program that models the movement of a rocket through different planets. and i sm starting to get teach my self fluid dynamics. As i was reading a presentation by NASA about the forces that act on a rocket they got into shape effects on drag, i noticed from their equation Cd...
Hello every one .
What is the Surface Area vector form in exterior algebra ,I mean by that the Surface Area vector as an exterior form in 3D , just like the volume form .THANKS
So I have a physics midterm tomorrow that will have a five part, 10 point question about the following
"an object pushed across a horizontal surface. You should be able to calculate net force, frictional forces from the coefficient of friction, acceleration, velocity, momentum, impulse, and...
Stephen hawking came to know of a study that stated that surface area of an event horizon increases. So he said that since area has increased Entropy also had increased.
But why does surface area of an Event Horizon increase?
A block is at rest at the top of a frictionless hemisphere of radius r. It is slightly disturbed at starts sliding down. I already know where it will leave the surface (height = 2r/3). My question is, WHEN will it leave the surface?
Homework Statement
http://ocw.mit.edu/courses/mechanical-engineering/2-06-fluid-dynamics-spring-2013/assignments/MIT2_06S13_ps2.pdf
Problem 7[/B]Homework Equations
##F=2*V/(a^2)*\sigma*cos(180-\theta)##
The Attempt at a Solution
With the problem statement given, it seems like the component of...
Homework Statement
A uniform rod of mass M and length L can rotate around point P which is at position x from one end of the rod as shown in the figure. The rod is gently placed on a rough horizontal surface that has a friction coefficient μ. and at t=0 starts rotating with angular velocity...
The event horizon is a null surface in spacetime separating events that are causally connected to an observer from those that are not. Does anyone have a good, simple argument on why it must be a null surface?
Im having trouble convincing myself that a charge located anywhere inside a conducting sphere will create an induced charge on the surface of the sphere with an electric field that is completely uniform. This doesn't make much sense to me.
Also same with how the electric field inside solid...
Homework Statement
The problem and its solution are attached in TheProblemAndSolution.jpg.
Homework Equations
Stoke's theorem: ∮_C F ⋅ dr = ∮_C (F ⋅ T^) dS = ∫∫_S (curl F) ⋅ n^ dS
The Attempt at a Solution
In the solution attached in the TheProblemAndSolution.jpg file, I don't understand...
If I have a U-shape wire frame and it contains a straight sliding wire and I dip this in soap, a film forms between the sliding wire and the boundary of U shape frame. Why is the force due to surface tension F = 2Tl where l is length of sliding wire?
They say there are 2 layers in contact...
Homework Statement
What exactly does it mean for a surface to span a contour/curve? For example, which surface(s) span the contour/curve defined by the equations x^2 + y^2 = 1 and z = y^2?
Homework Equations
N/A
The Attempt at a Solution
I'm not sure if I'm saying something nonsensical, but...
I had this problem in my exam. It required me to calculate relative permittivity of a dielectric slab which acquires a surface charge density of 800micro Coulomb/m^2 when subjected to an electric field of 10^8 V/m. Applying E=sigma/(2epsilon), I got relative permittivity as 0.45 which is less...
Homework Statement
A spherical air bubble in a lake expands as it rises slowly to the surface. At the point it starts to rise, the pressure is 2.00 atm, the temperature of the water is 10.0 ∘C, and the radius of the bubble is 5.00 × 10^−3 m. At the surface, the pressure is 1.00 atm and the...
Hi, I have a simple problem.
A Lambertian emitter has the shape of a square planar surface, with area Ae=4mm2,
total power P=1mW, and is located in yz plane.
Another square planar surface, with area Ad=6mm2, is located in the
xy plane, at a distance d=10cm to the Ae, and is tilted 20 Degrees...
For the following three-dimensional surface, z = -4.53 + 2.67x + 2.78y - 1.09xy, I would like to calculate the area for each of three subsections of this surface: (1) for which z is in between the corresponding x and y values (i.e., x < z < y OR y < z < x); (2) for which x is in between the...
What's the difference between surface tension and capillary force?
Surface tension, a tensor, is the force per unit length. Again surface energy is the energy required to increase the surface area by one unit. Is the surface tension a capillary force?
I am writing a simulation in MATLAB of particles that perfectly reflect off of a surface. However, my question is physics based, not code based.
So here is my issue. A particle is traveling towards a flat plane in space at z=1 with a velocity vector of [0,0,1]. The normal vector of the...
If the magnetization vector is in the z direction, is the bound surface current of a cube always 0, since z cross z is 0, and x and -x cancels and y and -y cancels out?
Hi
How is circular surface area values square rooted ??. I am using this formula r2Xπ=mm2 to calculate the surface area of a circle but i want to know if there is a formula to get back to the diameter or the radius of the circle ?.
example i have a circular surface area of 5.26mm2 and i want...
Homework Statement
Homework Equations
∫∫D F((r(u,v))⋅(ru x rv) dA
The Attempt at a Solution
[/B]
I got stuck after finding the above, at where the double integrals are. :(
May I know how do I find the limits of this? (I always have trouble finding the limits to sub into the integrals...
I have been investigating the damping of an oscillating mass on a spring by a piece of card of varying surface area, in order to work out the damping constant λ for the equation y = A₀ e-λt sin(ωt). I took the natural log of the amplitude of each successive oscillation and plotting that against...
I have a problem with some question I had to answer for the Surface Brightness \Sigma \propto \frac{Flux}{Angular~area}= \frac{F}{\Omega}.
I was able to show that \Sigma \propto (1+z)^{-4}
Then the question asks whether knowing its value for known candles or yardsticks, is a good way to...
Homework Statement
A) Suppose you are on Earth's equator and observe a satellite passing directly overhead and moving from west to east in the sky. Exactly 12.0 hours later, you again observe this satellite to be directly overhead. How far above the Earth's surface is the satellite's orbit...
Is the air pressure acting on the top of the head of a person standing in a room equal to the air pressure acting on a same area on the floor of the same room?
Since F = pA , it seems as if the air pressure is independent of the height of the surface on which it is acting. But that doesn't seem...
My first idea is this will result in a elliptic torus. The horizontal semi-axis a=R and the vertical semi-axis b=R*cos(beta). assuming the titled or inclined angle is beta. The distance away from the z-axisis c and it is a constant. But it looks not when I plot the surface in 3D using the...
Homework Statement
A block of mass m=2kg and one of mass M=8kg have initial velocity zero.
The friction coeffecient between m and M blocks is 0.3
Between block M and the surfasse there is no friction.
L=3 metres
F is a force constant and horizontal with magnitude 10 N, applied on block m and so...
Hi,
I'm trying to solve this problem and I'm stuck.
What I want to do is determine the kind of surface from this equation:
x2-2y2-3z2-4xy-2xz-6yz = 11
Matrix representation:
1 -2 -1
-2 -2 -3
-1 -3 -3
I want to find the eigenvalues so I write the characteristic equation like...
After watching these videos about Computational photography:
and lensless image sensors:
was wondering if it is at least theoretically possible to calculate the light of the surroundings of a white surface just from the light information on that surface.
For instance taking a picture of a...
Homework Statement
The problem is given in the attached file.
Homework Equations
Divergence theorem, flux / surface integral
The Attempt at a Solution
[/B]
As you can see I got the question correct using Divergence theorem. But I wanted to make sure that I could arrive at the same answer...
why surface area increases with foldings ,invaginations,roughness and powdered form?please someone explain concept of surface area.
what is difference between perimeter or (circumference in case of circle)and surface area?
Mentor Note: Two posts have been merged.
Homework Statement
Evaluate ∫∫ F⋅dS, where F = yi+x2j+z2k and S is the portion of the plane 3x+2y+z = 6
in the first octant.
The orientation of S is given by the upward normal vector.
Homework Equations
∫∫S F⋅dS = ∫∫D F(r(u,v))⋅||ru x rv|| dA, dA=dudv
The Attempt at a Solution
[/B]
Since...