Search results

Almost right, the air resistance isn't the resultant force. The resultant force is the air resistance + the weight. When the air resistance is equal to the weight, the resultant force is zero and so there is no acceleration.

Yeah, so you have 31.8 N up, and 33.42 N down, so what is the net force?

Momentum is conserved, i.e. for any process, the total momentum before = the total momentum afterwards. Basically the woman and skateboard can be considered as one object moving with speed v after she has jumped on, whose total momentum must be the same as the momentum before (of the two objects...

Problem looks like units, assuming you were supposed to give your answer in Newtons. If you want the force in Newtons, you need the mass to be given in kg.

The best way to see this (IMO) is this: If you accept (or look up a proof) that rotational K.E. is given by 0.5Iω^{2}, and that T = I dw/dt. If you think about the change in rotational K.E. : d(0.5Iω^{2})/dt = Iω dw/dt = Tω

The principle states that no two identical fermions in a system can be in the same quantum state, but what I don't fully understand is how you define a "system". For example when you apply statistical thermodynamics to a gas of non-interacting fermions you say that a maximum of one can occupy...

I see, thanks very much this is a lot clearer now.

Thanks very much. Is there a way you could explain the justification for using the rest frame of the CMB?

Hi, I've just been wondering about something so if anyone coudl explain it that'd be great. You often come across the statement that we believe the universe to be 13.7 billion years old, but I was wondering how this calculation is made? My main problem is that I'm confused as to whether every...

Homework Statement A system of 10 oscillators, characterised by a \beta^ parameter of ln(3/2) is in equilibrium with a heat bath. Determine the probability that the system should possesses Q quanta. Homework Equations p(Q) proportional to e^(-Beta*Q) The Attempt at a Solution I have seen a...

actually looking at the problem the best thing to do I think is to evaluate how far they've both moved from tom's initial position after 20s (because at this point they're both traveling with constant velocity). Then work out their velocities at this time, and from that you can easily work out...

For a) you could try to work out the position of tom and jane (relative to tom's start position) as a function of time and then find how long it takes jane to reach the end (375m) and compare this to how long it takes tom. for (b) just consider the vertical velocity, which is initially 0 and...

I don't have the Blundell book, and I haven't got that far yet no. I think I've figured this out though, but again confirmation would be good: work will be the same as \DeltaSgas is the same therefore \DeltaQ is the same. As T is constant \DeltaE is 0 so \DeltaQ=-\DeltaW as before.

Homework Statement (a) A piston is used to compress an ideal gas quasistatically from volume Vi to volume Vf . If the gas is in thermal contact with a heat bath at temperature T, such that the compression is carried out isothermally, calculate the work done on the gas, the change in entropy of...

I think something you need to get your head around is that there is nothing fundamentally that you can measure velocities with respect to. On Earth we tend to measure velocities w.r.t the earth, but when you consider the universe as a whole there is nothing you can do this with. It therefore...

OK been thinking about this a bit and have come up with this: if Z is the position of the bottom of the circuit, Z(t) = 1/2*g*t2 the change in magnetic flux through the surface, d\phi/dt = d/dt \intB.ds = -V (potential difference). I think then that \intB.ds = BlZ = 0.5 Blgt2...

Homework Statement 1) a circuit is composed of a square wire of side length l, mass m, resistance R and thermical capacity c. It is placed on the xz plane, with corners at the points (0,0), (0,l), (l,0), (l,l). The magnetic field is 0 for positive values of z, aligned along the y-axis and...

sorry I messed that up, wherever I put y I meant z. so i found v(z)

Homework Statement I have a problem where I have a force and therefore acceleration which depends on position, z. Using z'' = dv/dt = dv/dy * dy/dt = v*dv/dy I was able to find velocity as a function of position. It nows asks for z(t). I'm having a bit of a mental block here and don't know...

Ah ok, so what you're saying is if the equation has definite parity you can always find solutions which have definite parity? Thanks very much for your help!

but because you don't know the parity of y, which is a function of x would this not mean it's impossible to tell the parity of the equation?

and so substituting -x' in I get: -x'3d2y/dx'2 - x'2dy/dx' + x'(x'2+1)y=0 I don't understand how parity is defined from this though.

hmmmm I think: d^2/dx^2 = dx'/dx d(-d/dx')/dx' = -dx/dx' d^2/dX'^2 = d^2/dx'^2 so this will allow me to make the proper transformation, I'm still not sure how this will determine the parity of the equation

OK I don't think I understand how to express the derivatives in terms of -x'. Would it just be substituting in -x' instead of x for d^2y/dx^2 and dy/dx? Sorry for being so slow, I appreciate your help!

right so if they are equal (when you use x and -x') that would mean the equation is even? And if the equation using -x' is equal to the original equation times -1 it would be even, basically just f(x)=f(-x) and -f(x)=f(-x) right? So from that the equation doesn't have well defined parity, not...

are you sure? I don't think I have, but even if I have I'm still not sure as to how this would help?

-x'3y'' +x'2y' + x'(x'2+1) = 0 sorry I don't see how this helps

Homework Statement How do you tell whether a differenital equation has well defined parity or not? The equation I have is: x3y'' + x2y' - x(x2+1)y=0 and it asks: "Does this equation have a well-defined parity? What does this imply for the solutions of the equation?" My instinct would be...

Homework Statement I have this equation and need to find |F|2 (which should be real). I thought you did this by multiplying by the complex conjugate which was just replacing all i with -i, but this doesn't seem to work. What am I doing wrong? Thanks Homework Equations The...

Homework Statement Consider the following vector field in cylindrical polar components: F(r) = rz^2 r^ + rz^2 theta^ By directly solving a surface integral, evaluate the flux of F across a cylinder of radius R, height h, centred on the z axis, and with basis lying on the z = 0 plane. Using the...

Homework Statement [PLAIN]http://img408.imageshack.us/img408/7163/partialdifferent.jpg [Broken] So this means differentiate w.r.t y first, so I want dz/dy, and then w.r.t x right? so I rearrange so that y=z3/3 + xz and differentiate w.r.t z to get dy/dz, and then do 1 over this which i...

or rather: Re[e^(2*e^(i0))]

ok, I think I have it. Is it the Maclaurin series for e^(2*Re[e^(i\theta)]) that seems to work I think :s, meaning that the sum is just what's written above right?

cos(x)... sorry it's been a long day! Still not sure how to use that to get any further.

Yeah but I was thinking that it looked like something to do with e^(i\theta) to the power of n which would give terms of cos(n\theta). I'm not sure, if not how do I go about tackling the problem?

well it looks like a maclaurin series, but I don't really know how to work out what it's a Maclaurin series of.

Homework Statement [PLAIN]http://img263.imageshack.us/img263/9336/seriesgay.jpg [Broken] In the previous part of the question we had to show where the taylor expansion comes from, and calculated the maclaurin series for e^x, sin x and cos x. From that we had to prove De Moivre's theorem and...

mgh=\\frac{1}{2}m(v_{man}^2+v_{stairs}^2) For a start this assumption is wrong (just by putting in the numbers) and also as there is no set speed for vman, he could start off fast and finish slowly. Work can be defined as change in kinetic energy, but there is not necessarily a net gain of...

OK so how do I work out the limits of z? It can't just be from 0-2 because that would make it a cylinder? Still a bit confused.

Homework Statement A conical container with radius 1, height 2 and with its base centred on the ground at the origin contains food. The density of the food at any given point is given by D(r) = a/(z + 1) where a is a constant and z is the height above the base. Using cylindrical polar...

Homework Statement the gas scale temperature is defined as: T=273.16 lim Ptp->0 (P/Ptp) The bulb of a constant volume gas thermometer is immersed in an ice-water-vapour mixture and the recorded pressure is 0.500 atm. It is then immersed in a boilng liquid and the pressure is 0.720 atm...

OK I was thinking that must be the only way. Thanks :)

Homework Statement A radioactive source emits electrons. The number of electrons emitted per second N(t) decreases with time according to the equation: dN/dt = −1.8 × 10−5N(t) , where t is expressed in seconds. If N = 12 electrons/sec at t = 0, after what time t has N fallen to the value...

Homework Statement OK, so I have defined: n=[0:1:100]; p=1.01; (but later will make this so it is inputted by user as a function) dx1=100*(p-1)/(p^101-1); dxn=p.^n*dx1; I need to define y1-y100 like: y0=1 y1=1/(1+dxn(1)) y2=1/(1+sum(dxn(1:2))) y3=1/(1+sum(dxn(1:3))) etc is...

Homework Statement A modified form of the trapezium rule for calculating the area under a curve makes use of strips of varying width: by using narrower strips where the gradient varies more rapidly, better accuracy can be achieved. Create a function to perform the integral \int1/x dx between 1...

I really don't think that works because the answer you get is far too small, I worked it out manually with a calculator and the answer is near £50,000

I don't think this accounts for the fact that you add another £1000 at the beginning of each year though

The way I would go about it is to say Smith has invested $50,000 for 12 months, multiplying gives 600,000. Jones has invested $25,000 for 9 months, multiplying gives 225000. Divide $11,000 by the sum of these, and then multiply by 600000 for Smith's share and 225000 for Jones' share

Homework Statement If you invest £1000 on the first day of each year and interest is paid at 5% on your balance at the end of each year how much money do you have after 25 years? Homework Equations The Attempt at a Solution Been a while since I did series, and I was never very...

Homework Statement There is a mass attached to two springs on a table. Coefficients of static and sliding friction between the mass and table are equal with the value \mu. The particle is released at time t=0 with a positive displacement x0 from equilibrium. Given that 2kx0 > \mumg write...