Normal Definition and 1000 Threads

Homework Statement An ice cube is placed on top of an overturned spherical bowl of radius r, as indicated in the figure. If the ice cube slides downward from rest at the top of the bowl, at what angle θdoes it separate from the bowl? In other words, at what angle does the normal force between...

Homework Statement An engineer is measuring a quantity q. It is assumed that there is a random error in each measurement, so the engineer will take n measurements and reports the average of the measurements as the estimated value of q. Specifically, if Yi is the value that is obtained in the...

Homework Statement Here's the problem. I was able to find the a_n and b_n values, my question is mainly on part (c), how do I find which modes are missing? The function is odd, so even modes should disappear, but cos(n*pi) doesn't disappear, it's either +1 or -1. I'd greatly appreciate any...

why does the normal on a mass have different values at pole and equator

Hi Folks, I got stuck towards the end where it ask to derive the unit normal (eqn 3.2.29 I don't know how they arrived at n_x. I have looked at trig identities...and I have assumed the following n_x=\frac{N_x}{|N_x|} I don't see the (r+p) term anywhere in neither the top nor bottom. PS: I...

It can be found in any advanced calculus textbook the proof that, for a "well-behaved" space curve, the acceleration vector can be decomposed into components along the tangent and normal unit vectors. The acceleration vector is always orthogonal to the binormal vector. The decomposition is...

Hi Folks, I got stuck towards the end where it ask to derive the unit normal. I don't know how they arrived at n_x. I have looked at trig identities... n_x=\frac{N_x}{|N_x|}= 1) I don't see the (r+p) term anywhere in neither the top nor bottom. 2) Is the bottom just based on simple trig...

Homework Statement [/B] Homework EquationsThe Attempt at a Solution I'm not really sure how to attempt this question tbh. In order for the lamps to have normal brightness I think the circuit must be parallel. I also think maybe for A there can only be one lamp per branch because there's...

Homework Statement I am supposed to find the tangent and normal unit vector to r(t)=<2sint,5t,cost>.Homework Equations . The Attempt at a Solution r1(t)=<2cost,5,-sint> which is a tangent vector to the curve, and then to make it a unit vector I would multiply by 1/(sqrt(4cos^2t+25+sin^2t)...

Not a textbook/homework problem so I'm not using the format (hopefully that's ok). Can someone offer an explanation of normal modes and how to calculate the degrees of freedom in a system of coupled oscillators? From what I've seen the degrees of freedom seems to be equal to the number of...

Homework Statement 11) The tangent at P on the ellipse \frac{x^2}{a^2}+ \frac{y^2}{b^2}=1 meets the x and y axes at A and B. Find, in terms of the eccentric angle of P, the ratio of the lengths AP and BP. 12) Repeat Question 11 using the normal at P. Homework Equations bx \cos \theta + ay...

Why do people say that RVs that have the normal distribution has a constant variance. What does that mean constant variance.

why do we consider normal line in expressing a plane,say in ##R^3## ,of the form ## ax + by + cz = d ##? What is the logic behind this normal line selection? Plz provide intuitive explanations.Thanks

Hello everyone, I am currently considering a set of random variables, \vec{x} = [x_1,x_2,...x_N] which are know to follow a multivariate normal distribution, P(\vec{x}) \propto \mathrm{exp}(-\frac{1}{2}(\vec{x}-\vec{\mu})^\mathrm{T}\Sigma^{-1}(\vec{x}-\vec{\mu})) The covariance matrix Σ and...

Homework Statement A cup is represented by the surface -(z-1)2 + x2 + y2 = 1 and it is on a table represented by the plane z=0 a) find the angle at which the cup intersects the table b) find the equation of the normal line to the cup at the point (0, √2 , 2) c) find the equation the tangent...

Is there a relatively simple algorithm to compute the area in percentage under the curve as represented by a sigma value? For example; 3 sigma = 99.7 2 sigma = 95 1 sigma = 68.3 Now suppose I wanted to know 2.5 sigma without a table.

My main difficulty is finding E(XY), where if we find it by integrating, we get ∫xy f(x,y) dy dx where f(x,y) is the bivariate normal density function. This integral is a nightmare... are there any tricks to evaluating this integral, or finding E(XY) for that matter?

How do you find a normal vector of a function at a point, such as f(x,y)= ax^y+yx^y^x+b at (X_o,Y_o) where a and b are just arbitrary constants, and the function is an arbitrary function. So I guess, what is the general steps you take to find the normal? I thought it had to do with the...

Homework Statement So, a string with length L and a mass of M is given tension T. Find the frequencies of the smallest three modes of transverse motion. Then compare with a massless string with the same tension and length, but there are 3 masses of M/3 equally spaced. So this is problem #1...

Homework Statement It is known that the IQ score of ten-year-old children in a particular population has a normal distribution with mean 100 and standard deviation 15. (a) What proportion of this population have an IQ score above 115? (b) Mary’s IQ is equal to the 80th percentile of this...

So, I know that there is a Normal force exerted on the book by the table, and, according to Newton's Third Law, the book exerts a force onto the table. However, I have two questions: if I were to push down on the book, would that Normal force increase? What "creates" the Normal force? Is it the...

Homework Statement...

Hey guys, I'm just wondering if it's normal to feel this way. "Depressed" isn't the right word (a bit overdramatic), but I keep seeing people around me with "senioritis" who can't wait to graduate and move on. My fellow students keep talking about how they want to fast-forward time until May...

Homework Statement Find vector normal to z = x^2 + y^2 - 3 at point r = (2, -1, 2) Homework EquationsThe Attempt at a Solution here is the markscheme. I understand how to find the gradient, but i don't understand how they calculated the magnitude. thanks

"A study of long distance phone calls made from the corporate offices of the Pepsi Bottling Group Inc. showed the calls follow the normal distribution. The mean length of time per call was 4.2 minutes and the standard deviation was 0.60 minutes. a.What is the probability the calls lasted...

Homework Statement let's say you have a regular bathroom scale, which we know measures the normal force that it exerts on a person aka. apparent weight. Now let's say that we didn't know that it measured the normal force when a object was on it. Obviously we still know that the only two forces...

Homework Statement Consider a unit sphere centered at the origin. In terms of the Cartesian unit vectors i, j and k, find the unit normal vector on the surface Homework Equations A dot B = AB cos(theta) A cross B = AB (normal vector) sin(theta) Unit sphere radius = 1 The Attempt at a...

Is there a relationship between QM probability and normal distribution ? I'm thinking about drawing probability densities as functions of phase. Thanks

Homework Statement A point moves along the curve y = x3 + x such that the vertical component of velocity is always 3. Find the tangential and normal components of acceleration at the point P(2,10). Homework Equations Tangential Acceleration - aT(t) = v(t) ⋅ a(t)/ magnitude of velocity vector...

Hi, I read somewhere the geodesic distance between an arbitrary point ##x## and the base point ##x_0## in normal coordinates is just the Euclidean distance. Why?! That's the part I don't understand. I know that one can write g_{\mu \nu} = \delta_{\mu \nu} - \frac{1}{6} (R_{\mu \rho \nu \sigma}...

The lengths of a certain species of worm follow a normal distribution. Thirty percent of the worms are at least 16cm long, and 15% of the worms are less than 10cm long. Find, to 2 decimal places, the standard deviation of the lengths of the worms.

Homework Statement How does P(-1<Z<1) equal to 1-2P(Z>1)? (So you can find the values on the Normal Distribution Table) Homework EquationsThe Attempt at a Solution I tried P(-1+1<Z+1<1+1) but ended up with P(1<Z+1<2).

Homework Statement Let ##G## be a group and ##\sim## and equivalence relation on ##G##. Prove that if ##\sim## respects multiplication, then ##\sim## is the equivalence relation associated to some normal subgroup ##N\trianglelefteq G##; i.e., prove there is a normal subgroup ##N## such that...

Hello, given the figure above, how do I get the tangential and normal components of a vector in any plane by integration?

Homework Statement Hi all! I have been blindly drawing normal forces till today and i stumbled on this question. Homework EquationsThe Attempt at a Solution I have drawn 3 normal forces, - Hand - Leg - Center of mass Is there a normal force at the center of mass and is it the sum of the...

I'm trying to get my head around the calculation for coefficient of friction: COF = Friction/Normal force. And what happens if you vary normal force. Am I right in saying: The COF is a constant - every pair of materials has a specific COF which is independent of how hard they are pressed...

Please help with below. is it correct? A 41 kg crate rests on a horizontal floor and a 67kg person is standing on the crate. a. determine the magnitude of the normal force the floor exerts on the crate b. determine the magnitude of the normal force that the crate exerts on the person...

How is the expected frequency column worked out for each interval of trains? 2) My attempt Take the first interval, 60 - 62, I thought about doing this: (62 - mean) / standard deviation (62 - 67.45) / 2.92 = - 1.866 using Z score < - 1.886, from the normal distribution table, I get: 1 -...

I'm having a very hard time understanding the concept of a "Normal Force." The only framework with which I've come to terms with is imagining the Normal Force as the force exerted when object A comes into contact with object B which keeps object B from losing its macroscopic structural...

Here's a few stacks of the milky way I took last week, using an 85mm lens and a static tripod- 3.2s exposures. Two from the region around Cygnus: And a panorama closer to the horizon (12 stacks): This is about 13k x 11k pixels. At 100% the nebulae are still clear: Unfortunately, I...

I'm so impressed with many modular phone concepts including GOOGLE ARA and some other main concepts like "Puzzle Phone"(http://www.puzzlephone.com/), "ZTE Eco Mobius"(http://www.theverge.com/2014/1/8/5289998/zte-shows-off-eco-mobius-modular-smartphone-concept) and "Phone...

Homework Statement A block of mass m is kept on a smooth wedge of angle α and mass M which is in turn kept on a smooth floor. When the system is released from rest, calculate the force exerted by block on the wedge. Homework Equations None. The Attempt at a Solution Let the block a have a...

Why is the normal reaction of an object circulating a planet, equals to the gravitational force minus the centripetal force? I thought both gravitational force and centripetal force are directed towards the centre of the circular path i.e. in the same direction, therefore having, normal reaction...

Homework Statement A 10 N horizontal force is applied to a 50 N block initially at rest on a rough horizontal surface. If the coefficient of static friction is 0.5 and the coefficient of kinetic friction is 0.4, then the frictional force on the block is A 10 N B 20 N C 0 N D...

WARNING. I'm not a physicist! If there was a universe that only had 10000 photons and we observed all of them then ran the double slit experiment would we get a normal pattern or an interference pattern? If we observe a particle is that it forever in the universe that we happen to be running...

Note: I only need help on the underlined portion of the problem, but I'm including all parts since they may provide relevant information. Thanks in advance. 1. Homework Statement Let S be a subset of a group G such that g−1Sg ⊂ S for any g∈G. Show that the subgroup ⟨S⟩ generated by S is...

Homework Statement The airplane traveling at a constant speed of 50m/s is executing a horizontal turn. If the plane is banked at ##\theta=15## when the pilot experiences only a normal force on the seat of the plane, determine the radius of curvature of the turn. Also what is the normal force of...

I am trying to use the Israel junction conditions for a null surface, but I am running into complications with defining a normal vector for a null surface. As I understand it the normal vector is defined to be perpendicular to the surfaces tangent vectors n\cdot e_i=0, as well as satisfying...

Homework Statement In a children's park, there is a slide which has a total length of 10 m and a height of 8.0 m . Vertical ladder are provided to reach the top. A boy weighing 200 N climbs up the ladder to the top of the slide and slides down to the ground. The average friction offered by the...

I need help understanding normal distribution. I am self studying statistics to help me in my role of teaching excel as a business tool. I understand taking a data set and creating a frequency distribution. I don't understand about normal distribution. Why should any data set regardless of...