Maximum Definition and 1000 Threads

This is the problem, This is the textbook solution ; i think the textbook solution is not correct! My thought, ##S_{max}## will be given by $$\frac {dy}{dS}=0$$ $$\frac {dy}{dS}=\frac {-1}{400}S+\frac {1}{5}=0$$ $$S=80$$ It is maximum economy because ##y{''}<0##, i.e by use of the second...

Paper has a grain direction – the direction of the long fibres. For several reasons, publishers always print hardcover books with the grain of the paper in the same direction as the fold. I'm working on a book that will be 2:1 wire bound (two holes to the inch). I was wondering what the grain...

Hello! I had a random question while playing around with a garbage can that I hoped y'all could help me walk through: Let's say that I have a hinge on a table, rotating with gravity acting perpendicular to it. Energy is provided into the hinge, let's say by a spring, like so: I want to know the...

Hello brilliant engineers. How to calculate the bending stress of a lattice boom crane design? It’s clear how to calculate a single chord in a lattice box, at least as a cantilevered tube. However, when placed in a box lattice what is the proper approach? I’m constructing this crane in...

The following image represents the system under analysis: Using a reference point 1 on the surface of the lower reservoir, point 2 at the discharge of the middle reservoir, and point 3 at the discharge of the upper reservoir, and assuming the pressure is equal to atmospheric pressure at all of...

the mass will drop 1 m before it comes in contact with the spring. I’m stuck afterward. Please help. The total energy of 1 m is mgh= 1kgx9.8m/ss x 1m = 9.8J 9.8J = .5 x 20N/m x x^2 ---> x = .99 m the spring is compressed by .99 m ?

To find the initial potential energy of the system we can assume the disc to be placed inside a hollow sphere of the same radius and ##\sigma##, the potential energy inside a charged hollow shell is: $$V = \frac{\sigma(4\pi R^2)}{4\pi \epsilon_0 R} = \frac{\sigma R}{\epsilon_0}$$ the potential...

Why does f attain its local maximum at r' in (p,q). Is it because we have f(x)<= f(r') for all x in (p,p+delta)?

First, I am trying to find the external reactions in A and B, but I have only one equation relating ##V_A## and ##V_B##, what other relation could I use ? Once I find the reactions, I can find the external moment as well. Then, I may draw the diagram of moments in each cross section and then...

I read this - https://www.sciencedaily.com/releases/2018/01/180116093650.htm And I see this - "However, there are indications that a neutron star with a maximum mass would collapse to a black hole if even just a single neutron were added." And I think the maximum mass of a neutron star is...

Hi, I have to calculate the maximum flame temperature of the reaction above. The answer is 4805K but I didn't manage to obtain that answer. Please help me find my error, thank you so much! The values of C are below the solution attempt.

Through an intriguing fictitious dialog between Sadi Carnot and Robert Sterling, Prof. Israel Urieli of the Ohio University shows that it is not required to invoke entropy, the second law of thermodynamics, and the Carnot cycle with the [ideal] adiabatic processes in order to find out the...

Hi, I have been using Python for a while now, but so far for Least-squares fits using curve_fit from Scipy. I would like to start using Likelihood method to fit binned and unbinned data. I found some documentation in Scipy of how to implement unbinned likelihood fit, but I have not managed to...

When a heavier mass (or nucleus say) collides with a lighter one, it deflects through a certain angle which has a theoretical maximum. There are numerous derivations for this maximum angle of deflection ##(\sin\theta_{d_{max}}=m/M)## where m is the small mass and M the larger but none seem to...

This problem is from David Morin's classical mechanics textbook: I am having trouble with Part b. Here is the textbook's answer: I do not understand why large particle energies lead to capture. I would think that smaller energies would lead to capture because the particle wouldn't have enough...

I tried using Newton's first law as the net force in both the x and y directions should be zero in this case. In the free body diagram you need to consider weight, friction, normal force, and the horizontal force. I got a result that said that the horizontal force F you apply is at most W(mu_s +...

$$F =|\langle\psi|\phi \rangle|^2$$ $$|\psi\rangle=|\alpha\rangle|0\rangle$$ $$|\phi\rangle= |\cos(t)\alpha\rangle|i\alpha\sin(t)\rangle$$ $$F=|(|\langle\alpha|\langle 0|)(|\cos(t)\alpha\rangle|i\alpha\sin(t)\rangle)|^2$$ Now simplifying $$\langle\alpha|\cos(t)\alpha\rangle$$...

Summary:: What is the maximum safe mass of an asteroid in geostationary orbit before it causes problems? Hello everyone, If there was an asteroid in geostationary orbit around the Earth, over the Pacific Ocean, what would be the highest mass it could have before it would start having...

I would like to estimate the maximum acceleration (or deceleration) of an alpha particle that is backscattered by a heavy atom, like in Rutherford backscattering. I am interested in the order of magnitude, not in a precise value. I am assuming the collision is elastic. The kinetic energy of the...

If the maximum separation between two points on an infinite line is finite, then what is its value? So the maximum separation is infinite. Does this mean two points on an infinite line can be separated by an infinite distance? Why, why not?

I have a empty bottle and immersed it into the water, where the pressure inside the bottle is equal to air pressure. If I want to make a hole on the bottle, how big is the hole to prevent the water leak into the bottle at different depth? what kind of parameter is involve in this phenomena? can...

how to find a maximum load on a steel square tube that has one fixed end to the wall and another end is hanging free. suppose the beam is 2230 mm long and the load is applied on the beam on the free end w= 1040 mm. but there also a steel square tube that welded to the middle of the beam and...

I was discussing stepper motors with a friend. We touched upon different aspects. I showed how the coils in the motor have a limit to how fast they can be fully saturated with current, and how this time can be calculated by the aid of Kirchhoff's and Lentz's law. The theoretical speed calculated...

When we talk about systems at constant temperature and pressure, maximum amount of non-PV work can be extracted if process is carried reversibly and in that case it is equal to change in Gibbs energy of the system (decrease in Gibbs energy if system does non - PV work, A.K.A work is extracted...

How would you go about finding maximum value for this function without Calculus? You can draw in it a CAS tool like Geogebra, NSpire or Maple. And use the maximise ability. But is possible to do it by hand? Pre-Calculus?

I used a couple ways to do this question, but I got neither correct. Can someone help, please? Thank you. 1. E= V/r = 700 / (60*10^-3) = 11667 (very far from the given answer) 2. E = (-kQ/r)⋅ dr = kQ/r^2 = kQ/ [( 1/20/ 10^-3)^2 - (1/80/10^-3)^2] (For this method, I stuck...

I think it reaches its maximum efficiency when it is two continuous Carnot process. Its efficiency then will be H= 1-(W1+W2)/(Q1+Q2), with W1/Q1>=T2/T1 and W2/Q2>=T3/T2 therefore H<= 1- (Q1.T2/T1+Q2.T3/T2)/(Q1+Q2), that is as far as i can go, have not got a result yet

Basically, I want to determine how many microchannels I can have in parallel to drive a fluid (for now assume water),without the syringe pump stalling. Let's say a syringe pump have a maximum linear force of 50 lbf. and I want to drive the fluid at 60 ml/hr. So if I have 4 parallel channels...

Hello! I am having trouble solving the right part of the inequality. For left part of the inequality $n-k \le m$, here’s how I did it Let $ n = v_{1} + v_{2} + v_{3}...+v_{k}$, the sum of vertices of each component in G least number of edges = $(v_{1}-1) + (v_{2}-1) + (v_{3}-1)...+(v_{k}-1)$...

I want to calculate maximum gradient ability of my car in 1st gear to reach an estimation number. The specification of the car is as follows: Max torque = 155 nm @ 4250 RPM Curb weight = 1200 kg 1st gear ratio = 3.454 Final Drive ratio = 4.52941 Tire radius = 0.298 (meter) Acceleration force...

A Construction is stiffened by a bottemplate with welded ribs. A flange welded to the inletpipe is bolted at the botomplate. I want to simulate the current situation. Therfore I need a handcalculation of the stresses in the ribs of the constuction. The forces and moments are working in the worst...

I found the ratio between the weight exerted by the 70kg man to the weight exerted by the 20kg load, and equated it to the ratio of maximum extension by the 70kg man to the extension by the load Is this a right step to use, because the book didn’t give any answer nor solution which can help me...

I sketch a diagram for the problem and show it to the right. My approach is going to be along the following lines : (1) Use the equation of motion in the ##x## direction to express the total time of flight ##T## as a function of the range and initial angle ##T = T(R, \theta_0)##. (2) Plug this...

The experiment consists of a large field coil (connected to a current source) surrounding a coplanar and coaxial small detector coil in the center of the field coil connected to the oscilloscope. 1. Matching Current v. Time Graphs to Oscilloscope Graphs Example of one pair of graphs (I'll...

Hey! :giggle: An aeroplane flies over a tower of height $h> 0$ at height $H> h$. At what distance $x$ is the angle $\alpha$ at which the tower is seen from the aeroplane, maximum? (You can use elementary geometry and that $\arctan'(x)=\frac{1}{1+x^2}$.) From Pythagorean Theorem for the...

Hello! So what I've tried to tackle this problem is derive the equation,set it equal to zero,find a value for v and than put it in the second derivation.So when I derive this I get $$ \frac{v^2+9-v *(2v)}{v^4+8v^2+16)} $$ Now if i set that equal 0 and try to find a value for v I get this. ##...

Using Newton's second law, $$ cos\left( \frac{\pi}{6} \right) m(a+g) = 150 \Leftrightarrow a = \frac{\frac{2\times 150 }{\sqrt{3}}-mg}{m} =4.633. $$ Unfortunately, the possible answers are A. 1.025, B. 0.625, C. 3.75, D. 2.75, E. 1.75, F. 0. What am I getting wrong? Isn't the force exerted on...

What is best theoretical shape of undertray for maximum downforce , maybe wing shape or venturi shape? classic "venturi shape" with diffuser "wing shape"

First thank you for taking your time to take a look at this simple question. And sorry for the informal math language and equations, I hope you guys can understand it. So, depending on the case, I have 2 or 8 simple quadratic functions f(a), f(b), f(c),… f(z). Each a,b,c,…,z have a different...

Find the maximum area of a pentagon $ABCDE$ inscribed in a unit circle such that the diagonal $AC$ is perpendicular to the diagonal $BD$.

Hi, Here is the question. Answer given is d. But i don't understand how is that computed? I am working on this question. Meanwhile any member knowing the correct answer may help me in finding out correct answer.

Summary:: Maximum distance plane can cover A General Aviation plane of 3,994 kg flies at its best lift/drag ratio with constant speed at an altitude of 3,817 m. The engine provides a thrust of 1,493 N to overcome drag. Suddenly the engine fails. What is the maximum distance the plane can...

Hey! 😊 We consider the inner product $$\langle f,g\rangle:=\int_{-1}^1(1-x^2)f(x)g(x)\, dx$$ Calculate an orthonormal basis for the poynomials of degree maximum $2$. I have applied the Gram-Schmidt algorithm as follows: \begin{align*}\tilde{q}_1:=&1 \\...

In the attachment I am supposed to calculate the maximum frictional force of a block on a 35 degree angle incline (that is the point at which the force acting opposite frictional force is highest) I make it out to be sin(35)*120N = 69N but the book says 675N and it gives it as...

I'm not sure how to get this first derivative (mainly where does the 4 come from?) I know x̄ is the sample mean (which I think is 1/2?) Can someone suggest where to start with finding the log-likelihood? I know the mass function of a binomial distribution is: Thanks!

I would like to ask a question about the induced voltage of an AC generator. So, according to a graph I found on Google, the maximum induced voltage is reached when the loop is parallel to the loop. (The graph shown below.) Then I was wondering, what if the loop is initially (when it is at 0...

At first, I started with the result from an earlier problem regarding the capacitance of a cylindrical capacitor: $$C=\frac{Q}{V}=\frac{2\pi \varepsilon _0\varepsilon _rl}{ln(R_1/R_2)}$$ $$\Rightarrow V=\frac{Qln(R_2/R_1)}{2\pi \varepsilon _0\varepsilon _rl }$$ Then I used the equation...

My result for this problem is correct, but I would like to submit to you the method I used since it doesn't convince me. The problem asks for the maximum tension on the cable from the transition to 0 to 90 degrees; I firstly concluded just by thinking, not using formulas or particularly formal...