Initial Definition and 1000 Threads

I am reading Paolo Aluffi's book, Algebra: Chapter 0. I am currently focused on Chapter I, Section 5: Universal Properties. I need some help Example 5.3 and Exercise 5.2 in this section. QUESTION 1Example 5.3 reads as follows: Can someone clearly explain why $$\emptyset$$ is initial ... We...

I am reading Paolo Aluffi's book, Algebra: Chapter 0. I have a question related to Aluffi's description of initial objects in the category ring ... ... In Chapter III, Section 2. on the category ring, we read the following: QUESTION 1 In the above text, we read the following: " ... ... This...

Good evening all, I am looking for a little guidance with relation to trying to find the initial and impact velocity of a section of a steel casting if it shears. Given the results of stress analysis, the mass of the sheared section would be 200kg maximum. The input force at that would be...

I have three questions regarding Newton's method. https://en.m.wikipedia.org/wiki/Newton-Raphson#Failure_of_the_method_to_converge_to_the_root According to this wikipedia article, "if the first derivative is not well behaved in the neighborhood of a particular root, the method may overshoot, and...

Homework Statement The angle of a pendulum is θ(t)=(0.270rad)cos(4.00t+1.00π), where t is in seconds. Determine the initial angular velocity. Homework Equations ω=2πf The Attempt at a Solution [/B] I solved for the frequency, which was 6.37E-1 Hz and subbed it into the formula above and...

Homework Statement An initially pure 3.4 g sample of Ga-67, an isotope with a half life of 78 hr. What is its initial decay rate? Note: Molar Mass values given in tables for chemical elements are for natural mix isotopic ratios. (i.e. the relative percentages of each isotope normally present...

Homework Statement Find a power series representation for the function below & determine the radius of convergence. f (x)=(1+x)/(1-x)2 2.Relevant equation Shown in attached image below which is the solution the problem. 3.The attempt at a solution I'm trying to fathom the solution here...

Hey! :o We have the following initial value problem: $$x' = \frac{1}{2}(45 − x) + \frac{1}{4}(y − x) \\ y' = \frac{1}{4}(x − y) + \frac{1}{2}(35 − y) + \frac{1}{2}(z − y) + 20 \\ z' = \frac{1}{2}(y − z) + \frac{1}{2}(35 − z)$$ This can be written as follows: $$\begin{pmatrix} x\\ y\\...

Let M = {x1, x2, x3, ...} U {p} be a perfect metric space. Let f be continuous, taking M to M with f(xn) = xn+1 and f(p) = p. I would like to know if this dynamical system is necessarily sensitive to initial conditions.

Homework Statement Hello, usually when solving basic velocity problems, if the object starts from rest, then its initial velocity would be 0. But why is it that, if a cat were to leap from rest, its initial velocity wouldn't be 0, but something else? My friend told me about muscle...

Hi! I'm working on a problem for class and am having trouble figuring out how to calculate the initial velocity, which I need in order to calculate acceleration and from there the value of an unknown force. I thought I was on the right track, but my professor reminded me that I need to use the...

Homework Statement A girl of the mass 30kg and a boy of the mass 45kg sit on a frictionless floor holding two ends of a rope. The boy pulls on the rope. The girl moves towards the boy with an initial acceleration of 3ms^-2. The boy A. Moves towards the girl with an initial greater acceleration...

Homework Statement A locust jumps at an angle of 43.8 degrees and lands 1.0 m from where it jumped. If it jumps with the same initial speed at an angle of 62.4 degrees, how far would it jump then? X-component knowns: Initial velocity = v(cos(43.8)) displacement = 1m angle = 43.8 degrees...

1. Homework Statement A 75.0 kg person runs at 3.00 m/s and jumps onto a sled of mass 10.0 kg already moving in the same direction as the person at 2.00 m/s. a) What is the initial momentum of the sled-person system? b) What will the final momentum of the sled and the person be? c) What is the...

Suppose we have an RC series dc circuit with two capacitors C1 and C2 and resistance R. If the switch is closed at t=0, all the voltage appears across R initially. Fine.. But how does it reach across R through two insulation barriers (breaks) in the circuit? I can understand the mechanism for...

Homework Statement [/B] A 2.4 kg piece of wood slides on the surface shown in the figure . The curved sides are perfectly smooth, but the rough horizontal bottom is 31m long and has a kinetic friction coefficient of 0.27 with the wood. The piece of wood starts from rest 4.0m above the rough...

If the switch in an RL dc circuit is closed at t=0, the current i in the inductor rises exponentially. But at t=0, i=0 because the inductor generates a back emf equal to the applied voltage at t=0. So in absence of any current,how does the inductor come to know that the switch has been closed...

Homework Statement A block of mass m = 0.1 kg is connected to a spring of unknown spring constant k. It is compressed to a distance x from its equilibrium position and released from rest. After approaching half the distance (x/2) from equilibrium position, it hits another block and comes to...

Homework Statement :block slides on smooth triangular wedge kept on smooth floor.Find velocity of wedge when block reaches bottom. (image is attached) Homework Equations :Let the velocity of the triangular wedge be V.And v be the velocity of block m. [/B] applying conservation of linear...

People say that if you could break a function down into these three functions (constant, successor, projection or sometimes called initial/basic functions) using some operators, then it is primitive recursive. What makes these three functions so special?

Homework Statement How to calculate initial tension or pretension in a system of two parallel springs. F=5.33213N K1+K2=53.0597 x=0.095 Individual springs have initial tension of 0.25N so I would expect an answer of 0.5N but I can't get there. Homework Equations F=(k1+k2)x The Attempt at a...

Homework Statement For the equation y=-4e^t -4/3-2t+Ce^(3t/2), find the initial value y(0)=y_0 that separates solutions that grow positively as t -> infinity from those that grow negatively. Homework Equations (All are given in the problem statement.) The Attempt at a Solution I have half...

Homework Statement A mass-spring system with a natural frequency of 3.6 Hz is started in motion with an initial displacement from equilibrium of 6.1 cm and an initial velocity of 0.7 m/s. What is the value of ϕ? (Question aside: Finding the amplitude of the resulting function?) Homework...

An object fired at an angle of 30° above the horizontal takes 2.5 s to travel the last 12 m of its vertical distance and the last 10 m of its horizontal distance. With what speed was the object launched? (Note: This problem does not stipulate that the initial and final elevation of the object...

I have created an initial state code with perodic boundary conditions and normal distribution of velocities. I not know where is the problem, when I compile the computer detect the 112 error. Could anyone help me please? Thanks! the code is...

I just want to start by saying that I have found many questions very similar to this one using the search bar, but I still don't understand exactly what happens initially in a simple voltaic cell with a salt bridge (Daniel cell). For example, I am trying to figure out what initially happens in...

While reading some articles on Wikipedia I came upon one interesting statement that essential says (I've rephrased for clarity; correct me if I'm wrong): "The Time-asymmetry of the second law of thermodynamics is due to the initial conditions of our universe" Can someone elaborate on what...

Homework Statement A football is kicked at an angle of 60 degrees to the horizontal and travels a distance "R" before hitting the ground A.) find the initial speed of the football Homework EquationsThe Attempt at a Solution : [/B] I would presume I would need to find initial velocity of X...

I am considering the following question and I want you to agree (but perhaps you don’t):Rutherford wrote a letter to Bohr, as an answer to a previous letter from Bohr containing one of the first of Bohr’s descriptions of the atomic model, saying that he understood the atom model Bohr advocated...

Hi, I am trying to use NDSolve in Mathematica to solve a set of differential-algebraic equations: NDSolve[{-6250 f[t] + 0.025 p[t]^2 f[t] + 0.1 f[t]^3 + 3 q[t] f'[t] + f''[t] == 0, 1.5230870989335428*^-35 p[t]^4 + q'[t] == 0, -4.32*^36 q[t]^2 + 10/3 \[Pi]^2 p[t]^4 + 0.0125 p[t]^2...

Question: A car of mass 1500kg collides head-on with a truck of mass 9000kg. After the collision, the wreckage is at rest. The speed of the car just before the collision was 30m/s. What was the speed of the truck just before the collision? Relevant Equation(s): m1v1+m2v2 = m1v1'+m2v2' (?) My...

Homework Statement In the Fig. What should be the initial velocity (magnitude and direction) of the arrow? Also calculate the time of flight. Homework EquationsThe Attempt at a Solution I have formulated 2 equations: v*cos(theta) * t = 20 and 3 = (v * Sin(theta) * t) + (9.81 * t^2)/2 when...

y''-10y'+25=0 Solve the ODE with initial condition: y(0) = 0, y' (1) = 12e^5 . I keep getting y=12/5e^5x when c1=0 and c2=12/5 ... but Answer key says y=2xe^5x what am I doing wrong?

Homework Statement A ball is thrown upward at an angle of 30degrees to the horizontal and lands on the top edge of a building that is 20m away. The top edge is 5.0m above the throwing point. How fast was the ball thrown? Homework Equations x=v0t+(1/2)at2 vf2=V02+2ax vx=v0cosθ vy=v0sinθ The...

Hi everybody, I'm writing an exploration on the mathematics of simple harmonic motion and I stumbled across something I fail to understand in one of my resources (http://tutorial.math.lamar.edu/Classes/DE/Vibrations.aspx). In the example the author uses toward the end of the resource, the...

Homework Statement A 5000-kg freight car rolls along rails with negligible friction. The car is brought to rest by a combination of two coiled springs as illustrated in the figure below. Both springs are described by Hooke's law and have spring constants with k1 = 1700 N/m and k2 = 3000 N/m...

Hi, Quick Qustion : If an object is propelled through the air (e.g. a ball is thrown), once the ball has left the throwers hand it will immediatly start to have negative acceleration (at least in the x plane). If the negative acceleration is measured at the same point in time after the ball...

Homework Statement A stone is dropped from a bridge that is 65 m high. A second stone is thrown downwards 2 seconds later. Both the stones are heard hitting the water at the same time. The speed of sound is a constant 343 m/s. What is the initial velocity of the second stone. Homework...

Hello, I am taking an introductory class on non relativistic classical field theory and right now we are doing the more mathematical aspect of things right now. The types of differential equations in the function ##f(\vec{r},t)## that are considered in this course are linear in the following...

Homework Statement a projectile is launched at an angle of 26.5 above the horizontal at a height of 1.11m. the range is 2.331m. find the initial velocity and time given that acceleration due to gravity is 9.8m/s^2. The Attempt at a Solution first, I split the velocity into its components...

Hello, All! The following problem wasn't assigned to me, it was used for last semesters physics class at my college. However, I feel it is interesting enough and I can't seem to find the correct answer. A ball is launched from the top of a 28-m high vertical cliff at an angle of 31° . Ignoring...

Homework Statement A helicopter is ascending vertically with a speed of 5.30m/s . At a height of 100m above the Earth, a package is dropped from a window. How much time does it take for the package to reach the ground? [Hint: v0 for the package equals the speed of the helicopter.] Homework...

Homework Statement Given the following circuit: [/B] Where R=C=L=1, with Vs(t) = sin(wt) and complete response Vo(t)=A*sin(wt + π/4). Homework Equations Determine the init. cond. of the capacitor voltage Vc and Inductor current Ic at t = 0. Also, find A and w.[/B]The Attempt at a Solution...

Homework Statement Two charged, parallel, flat conducting surfaces are spaced d = 1.3 cm apart and produce a potential difference ΔV = 625 V between them. An electron is projected from one surface directly toward the second. What is the initial speed of the electron if its comes to rest just at...

Hello guys, actually I'am working on a model to describe the creep-behaviour of a concrete specimen. This model is based on a 'generalized maxwell-chain'. I attached a picture, where you can see it: The acting load is the tension \sigma, while E_0 and E_1 are the stiffnesses of the...

Homework Statement A truck is initially moving at velocity v. The driver presses the brake in order to slow the truck to a stop. The brake applies a constant force F to the truck. The truck rolls a distance x before coming to a stop, and the time it takes to stop is t. 8. Which of the following...

Hello! (Smile) I want to find the exact solution of the recurrence relation: $T(n)=2T(\sqrt{n})+1$.$$m=\lg n \Rightarrow 2^m=n \\ \ \ \ \ \ \ \ \ 2^{\frac{m}{2}}=\sqrt{n}$$ So we have: $T(2^m)=2T(2^{\frac{m}{2}})+1$ We set $T(2^m)=S(m)$, so we get: $S(m)=2S \left( \frac{m}{2}\right)+1$...

Homework Statement Equation for the time of a free fall with an initial velocity? Homework Equations √ (2 ⋅ h / a ) The Attempt at a Solution Is it √ (2 ⋅ h / via )Thanks for the help :)

How to find the Initial guess for Newton method with high accuracy ?? Is there a way rather than using mean value theorem [which is used to test whether there is a solution on a closed interval to the equation] ?

Homework Statement A UPS delivery man pushes a 5kg box (A) along a smooth surface where the coefficient of kinetic friction, [µ][/k], is equal to 0.20. The box slides for 1.5m before colliding with a 3kg box (B). The boxes then move together as one unit on a rough surface with [µ][/k]= 0.9 for...