Uniform Definition and 1000 Threads

Homework Statement For a scene in a movie, a stunt driver drives a 1.20✕ 103 kg pickup truck with a length of 4.65 m around a circular curve with a radius of curvature of 0.333 km (Fig. 7.29). The truck is to curve off the road, jump across a gully 10.0 m wide, and land on the other side 2.96 m...

Hi everyone, 1. Homework Statement Homework Equations 1) centripetal acceleration = v^2 / R 2) centripetal acceleration = 4 pi^2 R / T^2 3) average velocity = displacement / time[/B]The Attempt at a Solution For #1a I first found the displacement of A to B. And then divided that by...

A solid cylinder of uniform density of 0.85 g/cm3 floats in a glass of water tinted light blue by food coloring...

Hey guys! What would be the gravitational effect of Earth on it's surface, if somehow the density of mass was uniform and equal to 2/5 of the real value? Assuming that the size e shape os the planet doesn't change.

We have never discussed about constant mechanical power transfer for the linear case, as against rotational well documented gear transmission. The energy acquired by linear motion, if varies linearly, then 0.5mv^2 must have constant differential. Trying it, if u=0, v=at...

Homework Statement Picture- https://flic.kr/p/zi1ays The rubber stopper will be spun at a constant speed in a horizontal circle. The hanging mass is only in contact with the string.[/B] A) For the rubber stopper, state the forces and what they are exerted by and on B) Does the net force have...

Homework Statement Marlene rides her bicycle to her friend Jon's house and returns home by the same route. Marlene rides her bike at constant speeds of 6 mph on level ground, 4 mph when going uphill, and 12 mph when going downhill. If her total time riding was 1 hour, how far is it to Jon’s...

Homework Statement Find an example of a sequence ##\{ f_n \}## in ##L^2(0,\infty)## such that ##f_n\to 0 ## uniformly but ##f_n \nrightarrow 0## in norm. Homework Equations As I understand it we have norm convergence if ##||f_n-f|| \to 0## as ##n\to \infty## and uniform convergence if there...

A manufacturer has designed a process to produce pipes that are 10 feet long. The distribution of the pipe length, however, is actually Uniform on the interval 10 feet to 10.57 feet. Assume that the lengths of individual pipes produced by the process are independent. Let X and Y represent the...

Hello! (Wave)Consider the boundary value problem $\left\{\begin{matrix} - \epsilon u''+u'=1 &, x \in [0,1] \\ u(0)=u(1)=0 & \end{matrix}\right.$ where $\epsilon$ is a positive given constant. I have to express a finite difference method for its numerical solution. How can we know whether it...

Homework Statement A manufacturer has designed a process to produce pipes that are 10 feet long. The distribution of the pipe length, however, is actually Uniform on the interval 10 feet to 10.57 feet. Assume that the lengths of individual pipes produced by the process are independent. Let X...

Homework Statement This example is from 3rd edition of Griffiths' textbook. Ex. 5.8 on page 226 I understand that by reversing the direction of the current, sign of B is switched. but i can't get it that highlighted part. and why B doesn't have z-component? Homework EquationsThe Attempt at...

Homework Statement A particle with charge q and kinetic energy K travels in a uniform magnetic field of magnitude B. If the particle moves in a circular path of radius R, find expressions for speed, v, and mass, m.. (Use any variable or symbol stated above as necessary.) Homework Equations...

Homework Statement Find the potential outside a charged metal sphere (charge Q, radius R) placed in an otherwise uniform electric field E0. Explain clearly where you are setting the zero of potential. 2. The attempt at a solution So for this problem I figured I could exploit superposition and...

Homework Statement "Julie drives 100 mi to her Grandmother's house. On the way, she drives half the distance at 40 mph and half the distance at 60 mph. On her return trip, she drives half the time at 40 mph and half the time at 60 mph." Homework Equations a. "What is Julies average speed on...

Homework Statement A particle with a mass of 1.5×10−5kg and a charge of +2.9 μC is released in a (parallel plate) uniform horizontal electric field of 11 N/C . How far horizontally does the particle travel in 0.40 s ? Homework Equations I think some of the kinematic equations are needed, but...

Ok we know that the electric field(uniform or non uniform) is a conservative field. Imagine three horizontal electric field lines in '+X' direction separated by unequal distances let's say line 1 and 2 is separated by distance 'a' and line 2 and 3 is separted by some distance 'b' such that...

Homework Statement Use the principle of moments and take moments about A to show that the weight of the object O is 19 N.Homework Equations Moment=Force x perpendicular distance The Attempt at a Solution Vertical component of tension= TsinA...

Hi, I have a quick question. If both X and Y are uniformly distributed on the unit interval [0, 1]. Can we prove that the joint distribution of (X, Y) is uniform on the unit square [0, 1]×[0, 1]? Do we need any condition to ensure the result, such as Independence between X and Y? Thanks.

Not sure that I've phrased the question correctly. If you have a series of p values from a series of tests, and they're all meant to be uniformly distributed, why do you have to do a KS test on that, and not another Chi-squared test? The following is an extract from a test program's output:-...

Homework Statement i was going through uniform circular but a confusion popped out of my head . as i have read before the Rutherford atomic model was only rejected due to the fact that electrons moving in circular orbits need to accelerate constantly to maintain a uniform speed but the...

Homework Statement Kim has her coffee cup on her car's dash when she takes a corner with radius 4 m and 20 km/h. What is the minimum coefficient of static friction which would allow the coffee cup to stay there without slipping? Homework Equations Can someone show me the steps in how they...

Homework Statement A particle is moving along a straight line such that when it is at the origin it has a velocity of 5m/s. If it begins to decelerate at a rate of a=(-2.5v^(1/2)) m/s^2, where v is in m/s, determine the distance it travels before it stops Homework EquationsThe Attempt at a...

Homework Statement Find the coordinates of the centroid of the uniform area. Homework Equations equations for centroid coordinates at the top of my paper. The Attempt at a Solution

This technically isn't a coursework or homework problem: I have a uniform Joint density function for the lifetimes of two components, let's call them T1 and T2. They have a uniform joint density function, both are positive it follows, and the region is 0<t1<t2<L and L is some positive constant...

Homework Statement Random variable X is uniformly distributed on interval [0,1]: f(x)=\begin{cases} 1 & \text{ if } 0\leq x\leq 1\\ 0 & \text{ else} \end{cases} a) Find probability density function ρ(y) of random variable Y=\sqrt{X} +1 I tried like this. Is it good, if no why not...

<< Mentors have notified the OP to show their Attempt at a Solution >>[/color] 1. Homework Statement A uniform rod of length L1 = 1.5 m and mass M = 2.8 kg is supported by a hinge at one end and is free to rotate in the vertical plane. The rod is released from rest in the position shown. A...

I recently took an exam in my engineering mechanics class and passed the exam except for one question. I have been trying to solve this question after the fact and determine the solution, however neither I nor several engineering tutors have had any success. The professor refuses to give...

Find the Range of Uniform convergence of $ \zeta\left(x\right) = \sum_{n=1}^{\infty}\frac{1}{{n}^{x}} $ Using the Weierstrass-M test, I get this converges for $ 1 \lt x \lt \infty $ But the book's answer is $ 1 \lt s \le x \lt \infty $? I have scoured the book but can't see why they say it...

Homework Statement A police officer in hot pursuit drives her car through a circular turn of radius 356 m with a constant speed of 70.9 km/h. Her mass is 57.1 kg.What are (a) the magnitude and (b) the angle (relative to vertical) of the net force of the officer on the car seat? (Hint: Consider...

Homework Statement A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At time t1 = 3.30 s, it is at point (5.10 m, 6.80 m) with velocity (3.90 m/s)## \hat j ## and acceleration in the positive x direction. At time t2 = 9.90 s, it has velocity...

Homework Statement A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At time t1 = 3.30 s, it is at point (5.10 m, 6.80 m) with velocity (3.90 m/s) ## \hat j ##and acceleration in the positive x direction. At time t2 = 9.90 s, it has velocity...

Homework Statement A 0.020-kg mass is attached to a 1.2-m string and moves in a horizontal circle with a constant speed of 1.50 m/s, as shown in the figure. What is the measure of angle θ? What is given: m = 0.020kg v = 1.50 m/s L = 1.2 m Homework Equations Lengths L = 1.2m Lsinθ = r...

I would appreciate it if someone could explain the steps in the reasoning of the following statement. This is not a homework assignment or anything. Let ##U \subseteq R^{n}## be compact and ##f:U\to R## a continuous function on ##U##. However f is not uniformly continuous. Then there exists an...

Homework Statement A particle moving along a straight line can have nonzero acceleration even when its speed is zero (for instance, a ball in free fall at the top of its path). Can a particle moving in a circle have nonzero centripetal acceleration when its speed is zero? If so, give an...

Homework Statement An object is moving uniformly in circles with a radius of 5m and a frequency of 2 Hz. What is its instantaneous velocity? Homework Equations [/B]The Attempt at a Solution The problem i am dealing with is the frecuency. I am not here for an answer or to cheat. I am...

Homework Statement This isn't a homework problem, but I was just thinking of the following question: Suppose that a merry go round spins with a constant speed (so its radially accelerating towards the center), and a man want to jump onto the merry go-round while its spinning. In what way...

I noticed that uniform continuity is defined regardless of the choice of the value of independent variable, reflecting a function's property on an interval. However, if on a continuous interval, the function is continuous on every point. It seems that the function on that interval must be...

1. The problem The answer is A. Homework Equations x = Acoswt y = Asinwt The Attempt at a Solution C is not correct because the x & y positions are in terms of sin & cos, so the acceleration can't be constant. D is not correct because x & y are oscillating in value. E is not correct because...

The uniform bar in the attached diagram pivoted onto a wall on its center of mass and rotated an angle theta>0 from the horizontal should theoretically stay in static equilibrium because all torques are balanced, right? How come trying to do this in real life usually leads to the bar swinging...

It's hard to type this out as there is a diagram and notation I can't find on the key board so I've attached an image of the question and answer. I've explained my solution below however I've also attached an image if it's too confusing with the lack of symbols! Problem involves uniform...

Currently doing my A2 Levels and have just been revising over electromagnetic induction. The general consensus seems to be that current can only be induced in a changing magnetic flux.The textbook I'm using constantly refers to cutting a magnetic field, i.e. moving a wire relative to a field, to...

Problem statement, equations, and work done: A perfectly conducting cube is placed in a uniform electric field in the x direction (see attached). Step1 : Use Gauss's law to determine the electric field inside the cube.##\phi_E = 2E(r)A = \frac{q}{\epsilon_0} →...

Is an exact solution to Einstein's Field Equations known for the interior of a sphere of uniform density (to approximate a star or planet, for example?)

Homework Statement An electron moves through a uniform magnetic field given by B = Bx i + (3.68 Bx) j . At a particular instant, the electron has velocity v = (1.88 i +4.86 j) m/s and the magnetic force acting on it is (2.43 × 10-19) N. Find Bx. Givens B = [Bx i + (3.68 Bx)] v = (1.88 +...

What does the metric look like for constant uniform acceleration, say in the x-direction? ds^2 = g_tt (cdt)^2 + g_xx (dx)^2 g_tt = ? g_xx = ?

My reasoning: The magnetic force on charge q is Fm = qv x B B does not change |v|. Therefore, |Fm| is constant at time t > 0 and Fm is always perpendicular to the direction of movement of charge q. Fm behaves as a centripetal force, and thus the charge moves along the circumference of a...

Consider a total charge of q = 3.50 10^-9 C spread uniformly over a thin rod of length L = 0.8 m as shown. Point P is a distance H = 0.6 m away from the midpoint of the rod. Find the magnitude of the electric field at point P. Relevant equations: E = k \int \lambda dx/r^2 where \lambda =...

Homework Statement \[/B] Joey spins a laptop then he releases it, at an angle. Assuming no wind resistance, the laptop (has a rubberized case) hits the concrete and drags across the concrete for 5.3 seconds. What is the coefficient of friction between the rubber and concrete and what distance...

Homework Statement An electron is fired at 4.0 x 10^6 m/s horizontally between the parallel plates, as shown, starting at the negative plate. The electron deflects downwards and strikes the bottom plate. The magnitude of the electric field between the plates is 4.0 x 10^2 N/C. The separation...