melon chap

For the matrix M=

-e 0 d

e -n 0

0 n -d

I wrote the characteristic equation and found that one of the eigenvalues is zero and I'm trying to find the corresponding eigenvector s. So I wrote Ms=0 but then I'm not sure what the eigenvector is because each equation gives information including only two variables: so

from the 1st row we get d*z=e*x (with no information about y)

from the 2nd row we get e*x=n*y (with no information about z)

from the 3rd row we get n*y=d*z (with no information about x)

so.... What is the eigenvector?

Any help would be greatly appreciated.

Thanks very much!

so for example this word that I'm looking for would describe saying that in Roman times mobile phones existed.

Thanks

a ball of mass m ( initially at rest on a frictionless surface) is hit by a succession of small particles of mass δm and velocity v0 in the positive x direction. Note that δm<<m and each particle δm rebounds in the negative x-direction. We're asked to show that the speed,v, of the ball m after the nth collision is approximately given by

v=v0[1- exp(-an)] where a=2δm/m.

I tried this for the first collision with δm and found that the speed of m is given by

2δmv0/(m+δm)

but now I'm not sure what to do next (to get n in the equation). I have a feeling I have to integrate over something but I'm really not sure.

Any help would be much appreciated!

Thanks.

Hello,

I've been trying to find the sum of

S=1 + x^3/3! + x^6/6! +...

I've tried summing the Mclaurin's series for cos and sin and tried plugging in i here and there but I haven't been able to get anywhere. Some help would be greatly appreciated!

Thanks

A stationary muon has a half life of 2.2E-6s. Calculate the distance, in a lab's frame of reference, travelled by the muon in one half life given that its speed is 0.996c.

Now i know how to solve this using the time dilation equation but i need to know how to do this using the length contraction equation.

My book defines the proper length as the length measured by an observer who is stationary with respect to the event.

From my understanding, that means that the the distance travelled by the muon, in its frame of reference, is the proper length because if you're travelling at the same speed as the muon alongside it, you'd be stationary relative to it.

But it turns out that, to get the right answer, the proper length is in fact the distance measured in the lab frame of reference.

So this is how the calculation should be done:

l= 0.996x3E8x2.2E6= 657m

So, proper length, l0 =657( 1 - 0.996^2)^(-1/2)= 7360m

I am so confused! Why is the distance measured in the lab frame of reference considered the proper length? Someone please explain to me how i can figure out which length is the proper length!

Thanks so much in advance!

Here's the question:

A fixed solid sphere with a smooth surface has centre O and radius 0.8m. A particle P is given a horizontal velocity of 1.2ms-1 at the highest point on the sphere, and it moves on the surface of the sphere in part of a vertical circle of radius 0.8m.

Find the tangential component of the acceleration of P at the instant when OP makes an angle π/6 radians with the upward vertical. (You may assume that P is still in contact with the sphere.)

Now I know that you resolve tangentially to get

mgsin π/6 = ma => a=g/2

But why does this method give the wrong answer:

At top, v=1.2 so ω0=1.2/0.8=1.5 rads-1

At θ= π/6, v=1.88ms-1 (this is correct – it was found in a previous part of the question) so ω= 1.88/0.8= 2.35 rads-1

So using ω2= ω02 +2αθ => α=(ω2- ω02)/(2θ) = (2.352-1.52)/(π/3)= 3.13rads-2

So tangential acceleration= rα= 0.8x3.13= 2.51ms-2

But 2.51=/= 4.9 so why is the second method wrong? Is α not the same as d2θ/dt2? (if not, then what is it?)

Thanks in advance!

PS sorry i don't know how to get the super/subscript right on this.

how do the velocity and acceleration of a ball rolling down a curved surface with a decreasing gradient vary? please state and explain how you deduced the answer. I know the acceleration due to gravity stays the same and the velocity would increase if the ball were just free falling, but this curved surface is really confusing me!

Thanks a lot in advance

i want to get from (1- v/c)/√(1-v^2/c^2 ) to √((1-v/c)/(1+v/c))

I've tried several times now but i'm not getting anything. A method with all steps shown would be much, much appreciated!!!

Cheers!

integrate v / (9.8-v) dv

I thought the answer was -v ln(9.8-v) but that doesn't seem right.. Please help and explain!

Cheers!

My rabbit is a 9months old female and recently (for about 3 days now) she's been biting the metal bars of her pen and then making soft grunting noises when she's let out.

I make sure she always has enough food and hay and water in her pen and that the pen is cleaned every other day but she still keeps biting her pen's metal bars. I thought she might just want to be let out and run around so i let her out for about 3hrs everyday (i've read that that should be enough on a webpage). I've just let her out again now and she's making soft grunting noises and seems to be looking for something: she jumps around and licks things (including my arm). I don't know what's happening or what i should do! Please help!

Hi

My rabbit is about 6 months old and is a female - I've tried to litter train her but it's just not working! But i need to find a way because i'm feeling so bad for keeping her in her pen most of the day - she loves running and i can only let her do that in the garden when i get home - and that's only when the weather's nice (which is not often in London).

How can i get her to stop pooing and urinating everywhere?! Please please please help i really want to let her just run free all around the house without having to bleach the sofas and the carpet!

i.e. How can you make sure that what you're measuring is the diameter and not a cord? I was thinking that if i use a micrometer then i can find the parallel sides of the coin hence i would be measuring the diameter, but are there more 'solid' methods?

Thanks in advance!

I solved this question my way and then looked at the answers and my answer was wrong. Please explain to me why. Here's the question:

Each packet of Cruncho cereal contains one free fridge magnet. There are five different types of fridge magnet to collect. They are distributed, with equal probability, randomly and independently in the packets. Keith is about to start collecting these fridge magnets. Find the Probability that Keith collects all 5 types of fridge magnets by buying just 5 packets.

My (wrong) answer:

5C5 * (1/5)^5 = 0.000 32

which makes sense to me because (1/5) is the probability of getting each fridge magnet. Raising that to the power of 5 gives the probability of getting 5 magnets. Then multiply by 5 to get the number of possible ways of doing this.

The actual answer:

1*(4/5)*(3/5)*(2/5)*(1/5) = 0.0384

But how does that make sense? the question says probabilities are independent!

Please please help!

I called my network provider 3 times and no one could help me! I can connect to the WLAN at my college but I can't connect to my home wifi (WEP) - it doesn't even display it on the list of available wifi networks. When I enter it manually, it says it's 'out of range'.

Please please please help! I'm having to use my 3G all the time which is costing me a lot of money. Please advise me what to do or what to say when I call the network provider (because I am clueless in things to do with the internet, etc..)

Thanks for any help!

On wikipedia, it says that the argument of a complex number is worked as follows, depending on what quadrant the complex number lies within on an Argand diagram:

1. arg(z) if in 1st and 4th quadrants: arctan(y/x)

2. arg(z) if in 2nd quadrant: arctan(y/x)+pi

3. arg(z) if in 3rd quadrant: arctan(y/x) - pi

What I need to understand is why we need to add pi in the second quadrant and why we need to take away pi in the 3rd quadrant. It makes absolutely no sense to me!

Wouldn't it make sense to do pi - arctan(y/x) if the complex number is in the 2nd quadrant?

Someone please please please explain it to meeee!!!!

Any help would be much appreciated!

Thanks.

I'm planning to go to universities' open days (physics departments) and I would greatly appreciate it if someone could please tell me what I should look for and what questions I should ask. I know it might sound somewhat silly - asking you to tell me about what I should ask - but you've already had an experience at uni so you should know what the good things and the bad things are. I can give a full review of what makes a good sixth form college - but i'm clueless when it comes to unis because I've never been!

Thanks for your help!

is it the same thing? or is the 'electron neutrino' a different particle that just has a smiliar name?

I tried using the pen of my LG cookie (mobile phone) on my laptop's touchpad but it doesn't work. Is there any pen that I can use/buy? I've seen people on the internet who seem to be using such a thing (for example, Salman from the Khan academy on youtube).

So, could you please provide with a link/ advise me what to do?

Thanks in advance!

For example, a 2x2 identity matrix would be:

1 0

0 1

but can you also have an Identity matrix for a 3x2 matrix, for example?

If yes, please give me an example.

Thanks in advance!

I want to lose some body fat and I do both aerobic and anaerobic exercise. I don't just want to lose the fat but I also want to replace it with some muscles but I've been told that I shouldn't do anything such as weight lifting because that won't help me lose the fat, instead it'll make me 'bigger'.

So could someone explain to me what I should do and why?

Thanks.