Ratio Definition and 1000 Threads

1. A ball of mass m and radius R is both sliding and spinning on a horizontal surface so that its rotational kinetic energy equals its translational kinetic energy.What is the ratio of the ball’s center-of-mass speed to the speed due to rotation only of a point on the ball’s surface? The moment...

Homework Statement Determine whether the series converges or diverges. \sum (\sqrt {k} - \sqrt {k - 1})^k Homework Equations The Attempt at a Solution (a_k)^\frac{1}{k} = \sqrt{k} - \sqrt{k - 1} What do I do here..? = \frac{1}{\sqrt{k} + \sqrt{k-1}} \to 0 ?

Suppose we've got the setup as shown in the figure (see attachment). The idea is that the motor transfers its speed and force (rotary) to the actuator force and speed (linear) via some gears and a spindle. Here: R = radius [m] J = inertia [kg m^2] n = rotary to linear transmission [---]...

Whar is selectivity ratio and skirt selectivity?? what is the -30 dB point??

Hi, I need to calculate \Gamma(7/3)/\Gamma(1/3) is there some trick to doing this type of problem? I'm finding it really hard to do from first principles. Any help would be great, thanks!

Homework Statement Two resistors of resistances R1 and R2 , with R2>R1 , are connected to a voltage source with voltage V0 . When the resistors are connected in series, the current is Is . When the resistors are connected in parallel, the current Ip from the source is equal to 10Is Let r be...

Homework Statement The problem is to find the inverse laplace of \frac{s^2-a^2}{(s^2+a^2)^2} I am supposed to use the residue definition of inverse laplace (given below) The poles of F(s) are at ai and at -ai and they are both double poles. Homework Equations f(t) =...

Homework Statement Two resistors R1 and R2, where R1 > R2, are connected to a voltage source with voltage V. When the resistors are connected in series, the current is Is. When the resistors are connected in parallel, the current from the source is Ip = 8.0Is. What is the ratio R2/R1? I have...

Let ∑ak be a series with positive terms. Ratio test: Suppose ak+1/ak -> c. If c<1, then ∑ak converges. If c>1, then ∑ak diverges. If c=1, the test is inconclusive. What if ak+1/ak diverges (i.e. ak+1/ak->∞)? Do we count this as falling into the case c>1? Can we say whether ∑ak converges...

Homework Statement Hint: Disregard any dissipative effects of the atmosphere of the planet. A projectile is launched from the surface of a planet (mass M, radius R) with a launch speed equal to 61 percent of the escape speed for that planet. The projectile will rise to a maximum height...

Homework Statement Prove: If the limit inf as k goes to infinity of abs(ak+1 / ak) > 1 then the sum from 1 to infinity of ak diverges Homework Equations The Attempt at a Solution So far I have this: Suppose lim inf abs(ak+1/ak) >1 then, there exists an r such that lim inf...

Homework Statement Prove: If the limit inf as k goes to infinity of abs(ak+1 / ak) > 1 then the sum from 1 to infinity of ak diverges Homework Equations The Attempt at a Solution So far I have this: Suppose lim inf abs(ak+1/ak) >1 then, there exists an r such that lim inf...

Hi, my task is to calculate the ratio (gamma) between the specific heats of a gas (Cp and Cv). The only information I have is a table of data for the pressures and volumes of the gas at different temperatures. I don't know if its monatomic, diatomic etc. (it's a later task to determine this)...

what is the maximum "compression ratio" lease visit this link http://www.starrotor.com/Engines what is the maximum "compression ratio", so to speak, achievable by compressors? i don't think it is very high.

4clue

Homework Statement The Helmholtz coil current = 2.45 A, the magnetic field = 1.91 x 10^(-3) T, the accelerating voltage = 295 V, and the beam radius = .03m. a) Calculate the e/m ratio of an electron. Show that e/m = 2V / r²B² b) During the initial use of this experiment, physicists also...

Hi All, This is a similar post to one before, but that didn't offer much more than i know already. a = width of cell - depth of cell c= height of cell c/2 = height of central atom So i have various formula for a few isosceles lengths, namely a/2*cos30 for the base line of the vertical...

Homework Statement Two astronauts are floating in space. Astronaut A's mass is 1.89 times greater as that of astronaut B. IF astronaut A pushes astronaut B, what is the ration of their accelerations, Ab/Aa. Homework Equations F=ma MaAa=MbAb (M is the mass, A is acceleration)...

Aspect ratio of cylinder floating in water? Hi, Basically the question is: What is the aspect ratio (h/d) for a cylinder of specific gravity 0.65 above which it will float vertically? (Note use GM = I/V - BG) So i found a solution that is simliar and can help solve the problem. (please...

please could you help me understand this is very simple terms. 1.0 x 10-2 = 1:100 (as in ten to the power of minus 2) i do not understand what i need to do to get it into a ratio.

Hi everybody: I am trying to solve this question: [PLAIN]http://imageshugger.com/images/wviidazp3mf06ej32.jpg I have made the following: u=y v=xy Calculated the Jacobian, which is |-y|=y then as I know that is unnormalized I need to normalized first using a double integral as a...

Just out of curiosity : Consider a transformer with winding ratio of 1 : 10. What happens when AC 120 v is applied on primary and on secondary we apply DC voltage of 120 v from a battery source is series or in parallel? What will be the output in both cases?

If the phase angle for a block-spring system in SHM is φ and the block's position is given by x = xm cos(ωt+φ), what is the ratio of the kinetic energy to the potential energy at time t = 0? State your answers in terms of the given variables. x =xm Cos(wt + phi) v = -w(xm)sin(wt +phi)...

Hi, I am doing a project on communications engineering. I've done some background reading on CDMA and spread spectrum technologies such as Direct Sequence and Frequency Hopping. My project supervisor has asked me to find out the equation for the signal to interference ratio of CDMA systems...

I'm a bit confused about power output and gear ratios. I think it's best to explain by going by my example (imperical units, sorry Americas & Brits): Mass: 1300kg max. power: 128 kW @ 5500 rpm max. torque: 245 Nm Gear ratios (from a slightly different car type, but should be similar): 1st...

Homework Statement Determine whether the series below is convergent or not: \sum 7*\frac{n!}{n^{n-10}} n=8 and the series goes to infinity (Sorry, I couldn't get the formatting correct.) Homework Equations n/aThe Attempt at a Solution Well, originally I thought the series was divergent...

Homework Statement I have often heard that given say, ds/dt=k, that it is not entirely rigorous to say that ds=kdt. Why is that? If I view the derivative as nothing more than a ratio of the differentials, that seems perfectly reasonable. Also I see this done all the time, with acknowledgment...

Homework Statement Two tubes carry the same incompressible fluid with viscosity 1.5 Pl. They have lengths L1 = 6 and L2 = 22 m and diameters d1 = 1.2 and d2 = 4.5 cm. What is the ratio of their flow rates F1/F2? Homework Equations Poiseuille's law: 8nLI/(pi*r^4) while n is viscosity L...

Homework Statement Calculate the ratio of the kinetic energy to the potential energy of a simple harmonic oscillator when its displacement is half its amplitude. Homework Equations KE=1/2mv2 = 1/2kA2sin2(wt) U=1/2kx2 = 1/2kA2cos2(wt) KEmax=1/2kA2 Umax=1/2KA2 The Attempt at a...

electron is deflected in a circular path electron speed = 2.7 x 10^8 m/s diameter = 3cm magnetic field = 0.24T 1. work out charge to mass ratio - 7.5 x 10^10 2. the textbook value is 1.76 x 10^11 - comment on this value The answer is given as electron traveling close to speed of...

So I've read that phi (1.6) has been found at the quantum level, and from what I've been told this is a major breakthrough. But I fail to see the relevance. I was wondering if anyone felt that this is a major breakthrough, and could explain this to me? edit: posting link to article...

Here is a problem involving ratio , and the answer plus work as given by my textbook. I get a little lost at the underlines part. I don't understabnd how we arrived at a ratio of 24:9. Can anyone help me out? Mr Smith starts a business with $50,000. 3 months later, Mr Jones joins the...

Why do we take the "probability of an event" ratio as favorable / possible outcome If A is an event, then probability that A will occur is given by P(A)= no. of favorable outcomes / total no. of possible outcomes Is this just a definition, or is there some special significance in taking...

Hi, Could anyone explain to me why it is that cosmic radiation supplies slightly more positive than negative muons? I know that negative muons disappear a little faster than the positive ones as they can decay or be captured, but I don't know if this would have any impact on what I'm asking...

Calculate the heat capacity ratio for a diatomic ideal gas. ---- Using the equipartition theorem, I calculate: Cp / Cv = (Cv + R) / Cv = (7/2 R + R) / (7/2 R) = (9/2 R) / (7/2 R) = 9/7 ~ 1.286 According to the equipartition theorem, I assign each vibrational degree of freedom 1 R and...

All the LCDM models with variations (see http://lambda.gsfc.nasa.gov/product/map/current/parameters.cfm ) have similar ratios of dark matter: baryonic matter density of very close to 5:1. Is this ratio determined from WMAP data such as angular size of a peak, or is it a not very tightly...

v = \epsilontrans/ \epsilonaxial where ν is the resulting Poisson's ratio, \epsilontrans is transverse strain \epsilonaxial is axial strain and Poissions Ratio have range and its not more then 0.5 and not less then -1? so my question is how its value can turn "-1"? As...

Homework Statement let f: R->R be a continuous function Suppose k>=1 is an integer such that lim f(x)/x^k = lim f(x)/x^k = 0 x->inf x->-inf set g(x)= x^k + f(x) g: R->R Prove that (i) if k is odd, then g is surjective (ii) if k is even, then there is...

I'm building pairs of coils with standard core heights and diameters and linking each pair with a yoke. The magnets all run at 6V DC with windings of 24 AWG magnet wire in 6/8/10 layers. Is there a ratio of coil core mass to yoke mass for maximum efficiency? (shown below)

What substance has the highest expansion ratio? (liquid:gas)

Homework Statement I'm supposed to determine e/m using Zeeman effect. B=0.45 T Difference between two spectral lines is also known (0.649x10^10 Hz)Homework Equations Normal or anomalous Zeeman effect? How you know it? I'm guessing normal, so \Delta E = m_{l} \frac{e \hbar}{2m_{e}}B \Delta E =...

1. Uranium has two naturally occurring isotopes. 238U has a natural abundance of 99.3% and 235U has an abundance of 0.7%. It is the rarer 235U that is needed for nuclear reactors. The isotopes are separated by forming uranium hexafluoride, which is a gas, then allowing it to diffuse through a...

Homework Statement Harry and Sally are sitting on opposite sides of a circus tent when and elephant trumpets a loud blast. If Harry experiences a sound intensity level of 65dB and Sally only 55dB, what is the ratio of the distance between Sally and the elephant to the distance between the...

Homework Statement Work out the branching ratio of (W --> e-Ve) The book uses fermi's golden rule to do it, but I am wondering if my different solution is also valid? Homework Equations Γ = 1/τ and ΔEΔT = hbar The Attempt at a Solution If ΔEΔT = hbar, then i can write ΔT =...

Homework Statement The problem is looking for the radius of convergence sum(5^n)((x-3)^n)/n n=1 Homework Equations The Attempt at a Solution

Hi, my question is about determining the damping ratio for the upper spring-damper part of the system given in the link. Is it still r2/(2*sqrt(k2*m2)) or something equivalent should be determined? http://img217.imageshack.us/img217/3148/sprdampmass.png Thank you!

Homework Statement Calculate the ratio of the magnitude of the attractive gravitational force to the repulsive electrostatic force between two protons. Homework Equations Mass of proton = M = m = 1.672e-27 kg g = 9.80665m/s2 Q = q = 1.60219e−19 C k = 8.9875e9...

Homework Statement Statement: If Jupiter emitted just as much energy per second (as infared radiation) as it receives from the Sun, the average temperature of the planet’s cloud tops would be about 107 K. Given that Jupiter actually emits approximately twice this much energy per second...

Homework Statement Given: (1/2) mol N2 + (3/2) mol H2 -> NH3 change in H = -46.11 kJ/mol If the number of moles of N2 are changed to 10 and the number of moles of H2 to 35, how much heat is generated if only 10% of the Nitrogen reacts? The Attempt at a Solution After setting...

Homework Statement I am asked to provide an anti vibrational support mount for equipment mounted on turbo-prop aircraft. The equipment has a mass of 40kg. the vibrational response of the equipment to the environmental disturbances will need ot satisfy a safety limit prescribed by the...