Minimum Definition and 1000 Threads

Homework Statement Suppose we have the following forces: F1=[5i]kN F2=[-4j]kN F3= unknown force 30 degrees from + y-axis. How do you determine the magnitude of F3 such that the resultant FR for all three forces is a minimum? Thanks in advance.

Homework Statement A civil engineer is asked to design a curved section of roadway that meets the following conditions: With ice on the road, when the coefficient of static friction between the road and rubber is 0.1, a car at rest must not slide into the ditch and a car traveling less...

Homework Statement Show that the smallest possible uncertainty in the position of an electron whose speed is given by \beta = v/c is \Delta x_{min} = \frac{h}{4 \pi m_0 c}\sqrt{1-\beta^2} The Attempt at a Solution Since \Delta x \Delta p \geq \frac{\hbar}{2} , we see that \Delta x_{min}...

Homework Statement A car is traveling at 51.0 mi/h on a horizontal highway. If the coefficient of static friction between road and tires on a rainy day is 0.100, what is the minimum distance in which the car will stop?Homework Equations \Sigma \vec{F} = m \vec{a}...

50kg of water at 0ºC have to be frozen into ice in a refrigerator. The room temp. is 20ºC. What is the minimum work input to the refrigerator to achieve this? (latent heat of fusion of water=3.33x10^5J/kg) ans:1.22x10^6J It is proposed to heat a house using a heat pump operating between the...

Homework Statement a football kicker can give the ball an initial speed of 25m/s. what are the least and greatest elevation angles at which he can kick the ball to score a field goal from a point 50m in font of the goalposts whose horizontal bar is 3.44 m above the ground. Homework...

Homework Statement a mountain climber plans to jump from A to B over a crevasse. Determine the smallest value of the climbers initial velocity Vo and the corresponding value of the angle alpha so he lands at B Homework Equations A to B is 1.8m horizontal distance and B is lower than A...

Homework Statement A 6 kg object sits on a horizontal surface with coefficient of friction = .8. What is the minimum force (not necessarily horizontal) necessary to make the object slide? Homework Equations Fsmax = u * Fn where Fsmax is the force that must be overcome to make an object move, u...

An electric hot water heater takes in cold water at 15.8°C and delivers hot water. The hot water has a constant temperature of 45.6°C, when the "hot" faucet is left open all the time and the volume flow rate is 5.0 multiplied by 10-6 m3/s. What is the minimum power rating of the hot water...

This is a tough question. I'd like to know if anybody can find a good solution. It isn't required for any of my classes, but I'd like to see a theoretical result. It seems like it should be a simple projectile motion problem, but it's not that easy. Let's say there's a building x1 meters away...

In a classic carnival ride, patrons stand against the wall in a cylindrically shaped room. Once the room gets spinning fast enough, the floor drops from the bottom of the room! Friction between the walls of the room and the people on the ride make them the “stick” to the wall so they do not...

Homework Statement Calculate the minimum vertical distance between the cubic y=x^3-x^2-4x+4 and the parabola y=-2x^2+16x-30, when x is positive. Homework Equations y=x^3-x^2-4x+4 y=-2x^2+16x-30 The Attempt at a Solution I have no idea at all how to work this out, so perhaps someone...

Homework Statement Suppose that you loft the ball with an initial speed of v = 13.5 m/s, at an angle of θ = 48.5° above the horizontal. At this instant your opponent is d = 10.0 m away from the ball. He begins moving away from you 0.350 s later, hoping to reach the ball and hit it back at...

hi, i probably don't need to give you all this information, but i will anyway :) i have a flyback transformer from a TV connected to a 30V 1A power supply via a transistor from a TV (a high power line output transistor), and the signal on the base of the transistor is around 100KHZ...

Homework Statement This seems to a reasonably basic question to go through but yet I seem to have a bit of a mental block on it. so any help in the right direction would be great.. An I-beam is 10mm thick on the web and flange, is 6m high and has a Young's modulus of 200 GN/m2. The design must...

Hi there. I am a student from Spain and I am about to join the University but I have to pass physics at High School. Here It is: The work of extracting an Eletron in a metal is 3.8 eV. Calculate the minimum frequency needed to start the electron. This is what I did. \[E = \phi + Ec\]...

Dear all, Is there a method to find the maximum and minimum dimension of an irregular closed loop? This is a problem when we want to define the full-width - half maximum of a image. The level contour of this image at its half maximum can be an irregular closed loop. Any reference or...

Homework Statement Find the maximum and minimum values of f(x)=x^4e^-x over [0,10] Homework Equations The Attempt at a Solution From what I remember is you set the f' equal to 0. And that will give you two more points to test. and then you put the 0 and 10 number into the...

I must put both of them because I want to have an idea of dynamics here, of scattering and of geometry at the same time. I will rewrite what I put in another thread: "Matter field is something that lives on a spin foam like electical fields on a electrical grid structure. Any possible...

Homework Statement 11. Maximize Q=xy, where x and y are positive numbers such that (4/3)x2 + y=16 Homework Equations The Attempt at a Solution I know how to do it. The first time I did it. I multiplied the (4/3)x^2 +y=16 by (3/4) and got x^2+y=12 and then y=12-x^2 when solving...

Homework Statement A fisherman yanks a fish straight up out of the water with an acceleration of 2m/s^2 using very light fishing line that has a "test value" of 50 pounds. the fisherman, loses the fish as the line snaps. What is the minimum mass of the fish? The answer given is...

Homework Statement A rope exerts a force of magnitude of 21 N, at an angle 31 degrees above the horizontal, on a box at rest on a horizontal floor. The coefficients of friction between the box and the floor are s=0.55 and k=0.50 . The box remains at rest. Determine the smallest possible mass...

How could you mathematically solve for the minimum amount of colors needed for each face of an icosahedron or any regular polyhedron to not touch? (E.g. a tetrahedron pyramid would need four unique colors.)

Can anybody help me understand the solution to the problem at http://www.tutorvista.com/q/to-qualify-in-a-competitive-examination-candidates-must-score-in-the/q53911_86449 ?

...assuming very slow adaptation is possible. How low can one go? And something else: if you're at very low pressure, water or blood would boil at RT (pressure is lower than the vapor pressure of water). Would this mean a relatively innocent cut wound would make you lose a lot of blood? The...

Homework Statement A metric on C[0,1] is defined by: d(f,g) = ( \int_0^1 \! (f(x) - g_t(x))^2 \, dx )^{1/2} Find t e R such that the distance between the functions f(x) = e^x - 1 and g_t(x) = t * x is minimal. Homework Equations Given above The Attempt at a Solution The first...

Dear Friends, I want to find an upper and lower bound for the expected value of the minimum of independent binomial random variables. What paper/book do you suggest for this problem? In other words, I need to find bounds for E(min(X1,X2,...,Xn)), where Xi 's are independent random variables...

Homework Statement A point lies on the plane x-y+z=0 and on the ellipsoid x^2 +\frac{y^2}{4} + \frac{z^2}{4} = 1 Find the minimum and maximum distances from the origin of this point. The Attempt at a Solution The two contraints g = x-y+z =h= x^2 +\frac{y^2}{4} +...

Homework Statement A box with mass of 45 kg is placed on a flat board. It starts moving when the board is inclined at 27 degrees. If the mass is doubled, what is the minimum angle needed so that it starts moving? Homework Equations Frictional force = mgsin\theta The Attempt at a...

What are the dimensions of the largest rectangle that can be drawn in the closed region bounded by the x- and y-axes and the graph of the function y = 8 - x3 A=lw=16 D= 2l + 2w = 2l + 16/l I started off by graphing the equation. The y-int was 8 and the x-int was 2. Thus, I established...

I'm having no end of trouble with this seemingly simple problem: Homework Statement What's the minimum mass of a black hole for which you could survive a fall through the event horizon without being ripped to shreds? Why would you be ripped to shreds for smaller black holes? Homework...

Homework Statement A fire-hose must be able to shoot water to the top of a building 35.0 m tall when aimed straight up. Water enters this hose at a steady rate of 0.500 m³.s¯¹ and shoots out of a round nozzle. (a) What is the maximum diameter that this nozzle can have? (4 marks) (b)...

Homework Statement prove: if f(x) bigger or the same as 0 on an interval I and if f(x) has a maximum value on I at x0(0 is written small beside the x), then sqrt of f(x) also has a maxsimum value at x0. Similarily for minimum values. Hint: Use the fact that sqrt of x is an increasing...

Calculate the minimum of PT = 16.8e0.0697t + 204e-0.356t PT' = 0.0697 x 16.8e0.0697t + -.356 x 204e-0.356t Stationary points occur when PT'=0. Therefore: 0=0.0697 x 16.8e0.0697t + -.356 x 204e-0.356t My final answer was that t = 4.29. However, the Graphics Calculator begs to differ...

Homework Statement An owl has good night vision because its eyes can detect a light intensity as small as 4.5 10-13 W/m2. What is the minimum number of photons per second that an owl eye can detect if its pupil has a diameter of 7.5 mm and the light has a wavelength of 503 nm...

Hi The minimum pressure acceptable in South African water reticulation systems is 24m. The maximum pressure acceptable is 900 kPa. http://www.mangaung.co.za/docs/Regulations-Water-Conservation.pdf I need to write write a training manual for the waterworks department, and I need to...

Good day, everyone! Lately I faced the necessity of solving a problem from a field I know literally nothing about. So I just made an online research but without success. Any help (hints, good sources, relevant equations) would be greatly appreciated! Homework Statement Gold nucleus (Au...

Homework Statement Consider an isosceles triangles with height x and a fixed incircle of radius R. Show that the minimum area of such triangle occurs when x = 3R Homework Equations None. The Attempt at a Solution Well, I know that have to express the area of the triangle in terms...

1. Predict the minumum speed of a 20.0MeV proton as it passes within 1.0x10^-13 meters of a lead nucleus having 82 protons. (Note: 1eV = 1.6x10^-19 Joules) 2. How do I start off? 3. All i can think of is to get a charge for the lead nucleus by using q=ne which is the number of...

Homework Statement A small flat circular disc of diameter 2mm and mass 5mg is lowered vertically to rest at the centre of a flat tray of width 10mm in the x direction and 50mm in the y direction. What is the minimum uncertainty in measuring the velocity of the particle in the x direction...

The question asks for local minimum of x^4-9x^3+9x^2+5x-4. The answer was x=-0.21 and 5.96. I thought 5.96 is the absolute minimum, since it gives the loweset y value on the open interval. Where am I wrong. Thanks.

Homework Statement Using a telescope with circular aperture of diameter 2.5 meters and wavelength 463 nm. The stars are 10E22 meters away from us. What does the distance between them have to be so we view them as two stars? Homework Equations angle = 1.22 x (wavelength/diameter) >...

I currently have a question that i am struggling with it is: Propose a mathematical model in the form of an equation desribing, in general terms, the relationship between a given volume for a cylindrical container and the minimum surface area of material required to make it.. i am...

Homework Statement 1000kg plane lands on a 2000kg barge on in a calm ocean. The only frictional force is equal to one quarter of the planes weight. What must the minimum barge length be to land safely if it hits the deck at 50m/s. Also there is no water friction/resistance. Homework...

Homework Statement Find the dimensions of an isosceles triangle of least area that can be circumscribed about a circle of radius R. Homework Equations Let a,b, and c denote the lengths of the sides of this triangle and c=b. Then the angles opposite these sides are A, B and C...

Hi everyone! I'm new to online math forums. I wonder if anyone can give me a hand on this - it would be greatly appreciated. Thank you in advance! Dave Homework Statement If a box with a square base and an open top is to have a volume of 160 cubic feet, find the dimensions of the box having...

36. A proton is confined in a uranium nucleus of radius 8 x 10^-15 m. Determine the proton's minimum kinetic energy according to the uncertainty principle if the proton is confined to a one-dimensional box that has length equal to the nuclear diameter. What's wrong with my equation and value...

Homework Statement Two towns, A and B are 5 km and 7 km respectively, from a railroad line. The points C and D nearest to A and B on the line are 6 km apart. Where should a station be located to minimize the length of a new road from A to B? Homework Equations a^2+b^2 = c^2, a=0.5bh(?)...

This is bugging me and maybe someon can help me find the obvious mistake: I want to calculate the minimum power needed to keep a mass of 1 kg floating in mid air. The naive approach is this: The mass falls 5 meters in one second so to get to the original position I have to invest an...

Homework Statement A ray of light is incident in air at an angle of 40 degrees to the normal to one face of a 60 degree glass prism. Calculate the angle through which the ray has been deviated by the time it emerges from the prism. (refractive index of glass wrt air is given as 1.50)...