Minimum Definition and 1000 Threads

Homework Statement (see attachment) An iron rod of length L is hung at a common point with threads of length \ell which are attached to the two ends of the rod. The rod is displaced a bit in the plane of the threads. What is the length of the threads if the period of the swinging of the rod...

Homework Statement Gus is at end of rope. He needs to reach roof. His friend fires cannon ball horizontally hitting Gus and get stuck in belt. Find minimum speed of cannon ball for Gus to reach roof. 50m is rope. 99kg is Gus. 1kg is ball. 45° angle in diagram Homework Equations...

I’ve encountered a relationship that, if true, could show that there are an infinite number of twin primes. It involves the minimum number of twin primes to be found between 3 and any higher odd number squared. However, I don’t know if this relationship holds true in all cases. We start with...

It is a well-known fact that Harvard university (arguably the most prestigious college in the United States) only accepts the very top highest-performing high school graduates in the country. What is Harvard's minimum accepted high school GPA, number of AP credits, and SAT/ACT scores? I...

Author: Leonard Susskind, George Hrabovsky Title: The Theoretical Minimum: What You Need to Know to Start Doing Physics Amazon Link: https://www.amazon.com/dp/046502811X/?tag=pfamazon01-20 Prerequisities: Contents:

Leonard Susskind's the Theoretical Minimum was released today to go along with his Stanford Courseware lectures. Has anyone gotten there hands on a copy yet? I am very excited for this publication because I am very pro-self-education (if you could call it that). I am debating whether to order a...

When you write an action and then you calculate its minima, how can you be sure that they are minima and not maxima? Thanks

Right so, I actually know the math, my problem is that I think, I am getting confused with wording. I will explain better where I show you where my problem lies. Question: Show that 2x^2-36x+175 mat be written in a(x-b)+c where the values a,b,c are to be found. state, with reason, the...

deriving equation for minimum height in projectile motion with two give me's :) Homework Statement A ball is launched at a 45 degree angle and lands 152.4 m away. What is the maximum height the ball will reach during its flight. I Know the answer, what I need is to find a way to derive an...

Homework Statement The coefficient of static friction between the box (6.75 kg) and the ramp (30 degree incline) is 0.500. What is the magnitude of the minimum force, F, that must be applied to the box perpendicularly to the ramp to prevent the box from sliding? Homework Equations...

Consider an m x n table containing single digits 0 to 9. So each cell contain the digits 0 to 9. My goal is to make sure that all combinations from 000 to 999 can be found in the table in adjacent cells. A cell is adjacent to the cells around it (i.e. above, below, to the left, to the right...

Homework Statement What is the minimum velocity required to throw a ball over a house with a pitched roof ( See attachment for the figure) You can choose the throwing point as needed The Attempt at a Solution (Choose throwing point standing near a and facing left) Assuming b is...

What is the minimum amount of power needed to charge a small lithium ion battery of 3.4 V and 2100 mAh?

[SIZE="4"][FONT="Times New Roman"]Let X_1, X_2 \sim Exp(\mu) and Y = min(X_1, X_2) then find E[Y]. My attempt is as follows: $$E[Y] = E[Y/X_1<X_2]P(X_1<X_2) + E[Y/X_1>X_2]P(X_1>X_2) \\ = \frac{1}{2} (E[X_1/X_1<X_2] + E[X_2/X_1>X_2] ) \\ = \frac{1}{2} (1/\mu + 1/\mu) \\ = 1/\mu$$ But, we know...

Homework Statement Hello, I have a question what is What is the minimum of Ʃ^{n}_{i=1}\left|x_{i}-z\right| x_{i} are constants Homework Equations Not Much The Attempt at a Solution I split the sum to 3 sums Ʃ^{}_{x_{i}>z}(x_{i}-z) +...

Hi Wasn't sure where to post this, hope it's ok in here! I've gotten myself very confused as to how to find the minimum yield strength for an element. I have used Mohrs circle to find sigma1 and sigma2, then plugged that into the von mises equation to find sigma-von = 636.8MPa. The...

Homework Statement Object A of mass 10 kg moving at 10 m/s [E] interacts with (but does not touch) Object B of mass 8 kg moving at 12 m/s [N]. What is the minimum possible kinetic energy of the system after the collision? Homework Equations M1V1o + M2V2o = M1V1f + M2V2f KE = (.5)(m)(v2)...

Homework Statement A boy ties a 3.00kg rock to a 0.70 m string and begins spinning it around in a horizontal circle at a constant speed. If the string will break if the tension is greater than 80.0 N, what is the minimum period for the rock to spinning in a circle. How do i solve this...

Homework Statement I'm stuck on part b) of the question, but this includes the whole thing: A farmer wants to make a rectangular paddock with an area of 4000m^2. However, fencing costs are high and she wants the paddock to have a minimum perimeter. a) Show that the perimeter is given...

Homework Statement Explain why f(x) = 1/x must have a minimum on [1,2] but not on [-1,2].Homework Equations The Attempt at a Solution I don't know what to do. First, I took the x values from the given points and plugged them back into the function but the results do not coincide with the y...

Homework Statement An electron is confined to a nucleus of radius 4 femtometres. Estimate its minimum energy. Homework Equations ΔxΔp_x=h/4\pi E^2=p^2c^2 + m^2c^4 As the electron's rest energy will be much less than it's kinetic energy, E=pc The Attempt at a Solution So I...

New to this and was thinking about extreme cases to help me get my head around how this all works...need help.. Imagine we have an object with mass moving along. Not that this is possible, but what if all other mass in universe was somehow utilized in some nuclear reaction so ALL energy in...

Calculate the density at which the available thrust of a jet propelled aeroplane is equal to the minimum drag for the full fuel load case. Use the simplest assumption for the variation of engine thrust with density. Wing area, S = 29.5 Weight, W = 88000 CD,0 = 0.02 k = 0.044 Max thrust...

Hi, Satellites A and B are traced at a particular moment by a space base located at the origin, with respect to which they move at constant velocities: A0 = (a1,0,a3); B0 = (0,b2,b3) V of satellite A = (Va,0,0); V of satellite B = (Vb,Vb,0) Is the minimum distance between the satellites...

Homework Statement I have a hill with a roller coaster cart on it and it goes down and around a loop-the-loop the radius of the loop is 10m Diameter=20m What is the minimum speed the cart needs to go to keep it on the track? There is no friction, what is the height of the hill...

A space base has traced stallites A and B at a particular moment at: A0 = (a1,0,a3) B0 = (0,b2,b3) whereas the base itself is located at the origin (0,0,0) and the satellites move at constant velocities with respect to the base: Va = (Va,0,0) Vb = (Vb,Vb,0) The minimum distance...

Homework Statement Suppose a truck is going up a hill and the maximum acceleration while braking is 9 m/s2. Find the minimum angle of the hill such that the driver can brake at maximum rate without the refrigerator on back slipping. (coefficient of static friction between truck and...

Homework Statement A heavy sled is being pulled by two people as shown in the figure. The coefficient of static friction between the sled and the ground is μs = 0.603, and the kinetic friction coefficient is μk = 0.395. The combined mass of the sled and its load is m = 291 kg. The ropes are...

prove that for any graph G, kappa (G) ≤delta (G).

Homework Statement In a deuteron, a proton and a neutron are very weakly bound by the strong nuclear force with an average distance between the particles of about 5fm. Due to the uncertainty principle, the particles have a minimum momentum and hence a minimum kinetic energy of ...? Which...

Homework Statement A charge of 3.0 μC is distributed uniformly throughout the volume of plastic sphere with a radius of 10.0 cm. An identical plastic sphere with charge 3.0 μC is shot directly at the center of the first sphere, from very far away. The mass of each sphere is 5.0 X 10^-5...

Homework Statement Assume that the polynomial P(x) has exactly two local maxima and one local minimum, and that these are the only critical points of P(x). Sketch possible graphs of P(x) and use them to answer the following. (e) What is the sign of the leading coefficient of P(x)? positive...

Homework Statement A beam (note: part of a truss, I chose to use the beam in the truss with the most force and length for my calculations, which I assume is the correct thing to do) of length 6m with a force of 9N is being constructed out of a material with a Young's Modulus of E = 70 \times...

Homework Statement Determine the longest wavelength of light emitted from this atom. Homework Equations \lambda=\frac{hc}{E} The Attempt at a Solution I calculated the lowest energy of the light emitted: E_{min}=2.1(eV) Then the longest wavelength would be...

Homework Statement Assume that a particle travels with a certain known (average) velocity ##v = \left\langle\hat{p}/m\right\rangle##. You know it's position with an uncertainty ##Δx##. Use the uncertainty principle to determine the least possible value for the article's kinetic energy...

The question is: A ball of a mass 4kg is attached to the end of a 1.2m long string and whirled around in a circle that describes a vertical plane..what is the minimum speed that the ball can be moving at and still maintain a circular path? i try solve it by use T+mg=mv*2/r.But i can't find...

Homework Statement What are the maximum and minimum values that can be represented using a 7s complement representation in base 7, using a 5 digit number? Homework Equations The Attempt at a Solution Would you divide the numbers so that any number starting with an odd digit is...

1. The muzzle speed for a Lee-Enfield rifle is 630 meters per second. Suppose you fire this rifle at a target 700 meters away and at the same level as the rifle. a - In order to hit the target, you must aim the barrel at a point above the target. How many meters above the target must you aim...

Say we have two particles of mass m which repel each other, V = V(seperation). Let these particles be constrained to move on a circle of radius r. The particles want to stay at opposite sides of the circle because they repel each other. We want to treat this as a quantum problem so the particles...

Homework Statement A gazelle leaps over a 2.1m fence. Assuming a 45° takeoff angle, what is the minimum speed?Homework Equations 1. x=v0x * t 2. y = v0y * t - 1/2gt2 3. vy = v0y - gt 4. vy2 = v0y2 - 2gΔyThe Attempt at a Solution I assumed at the top of the leap, vy=0 m/s, so I used equation 4...

Clever guy that I am, I am writing a small paper on Celestial Mechanics...simplified...really really simplified. However, if I bore a tunnel through the Earth and drop a watermelon through it, the watermelon returns to my hand in 76 minutes. This is an example of an elliptical orbit of e=1 But...

1. A blue car pulls away from a red stop-light just after it has turned green with a constant acceleration of 0.9 m/s2. A green car arrives at the position of the stop-light 4 s after the light had turned green. What is the slowest constant speed which the green car can maintain and still catch...

Homework Statement Assume there is a wall located 100m downrange (x=100) from the projectile launching position (x=0) that is 55m (y=55) high. What is the minimum initial velocity of the projectile launched at what angle necessary to clear the wall? Homework Equations h=(v^2sin^2α)/2g...

So I've read that super Earth's masses 2-10 can be habitable hold thick atmosphere and generate plate tectonics. So I am wondering the absolute minimum mass an exoplanet or moon can be to stay habitable in the liquid H2O zone? I guess these would be called subEarth's.

For each real number x, let f(x) be the minimum of the numbers 4x+1, x+2, and -2x+4. What is the maximum value of f(x)?

i know this is a basic calculus question, but i can't seem to get two answers. G(x) = 1/2 x^2sin2x+1/2 xcos2x - 1/4 sin2x find the maximum and minimum values for G(x) on the interval [0,pi/2] i found G'(x)= x^2 cos2x and i know that there is a global max at pi/4 but i can't find the...

Hi guys I have a problem to solve, I'd like to find the minimum distance between a point and a geometric locus described in closed form, for example the intersection of two circles: p= point coordinate p1= center coordinate circle 1 p2=center coordinate circle 2 r1=radius of circle 1...

What is the minimum distance between Earth and Mars in course of their rotation in orbits? I need the derivation and analytic calculation. If we assume the plane of rotation is different for Earth and mars, the problem become to complicated. So the orbits may be assumed co-planner.Please...

Homework Statement A heat engine operating between freezing and boling points of water takes 20 cycles to raise a mass of 1000kg through a height of 3m. Calculate the minimum energy per cycle that must be extracted from the hot reservoir in order to achieve this. Homework Equations...

Homework Statement Photoelectric experiment show that about 5eV of energy are required to remove an electron from platinum, if light of 150nm wavelength is used, what is the velocity of the emitted electron?Homework Equations de broglie's equation, E=hvThe Attempt at a Solution Tried by using...