Gravitational force of moving objects
Hello guys!
According to relativity, objects with higher kinetic energy have larger mass. Would that affect the gravitational force of the object?
Or in other words, if a neutron moves faster, would it attract other things more strongly?
tyvm
According to relativity, objects with higher kinetic energy have larger mass. Would that affect the gravitational force of the object?
Or in other words, if a neutron moves faster, would it attract other things more strongly?
tyvm
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Poisson Distribution w/ book errors
1. The problem statement, all variables and given/known data
In a lengthy manuscript, it is discovered that only 14% of the pages contain no typing errors. If we assume that the number of errors per page is a random variable with a Poisson distribution, find the percentage of pages that have: Exactly one typing error, At the most 2 typing errors, Two or more typing errors. Also compute the mean and variance of the number of typing errors per page.
2. Relevant equations
3. The attempt at a solution
I know for a Poisson distribution np=λ
the problem states that p=14% of pages with 0 errors, but don't I also need to know 'n' which would be the number of pages??? Anyone got a hint?
In a lengthy manuscript, it is discovered that only 14% of the pages contain no typing errors. If we assume that the number of errors per page is a random variable with a Poisson distribution, find the percentage of pages that have: Exactly one typing error, At the most 2 typing errors, Two or more typing errors. Also compute the mean and variance of the number of typing errors per page.
2. Relevant equations
3. The attempt at a solution
I know for a Poisson distribution np=λ
the problem states that p=14% of pages with 0 errors, but don't I also need to know 'n' which would be the number of pages??? Anyone got a hint?
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MoI of a Sphere using Spherical Coordinates
1. The problem statement, all variables and given/known data
Calculate the moment of inertia of a uniformly distributed sphere about an axis through its center.
2. Relevant equations
I know that
$$I= \frac{2}{5} M R^{2},$$
where ##M## is the mass and ##R## is the radius of the sphere. However, for some reason,
when I do this integration in spherical coordinates, I do not get this result.
3. The attempt at a solution
The density is
$$ \rho= \frac{M}{V}= \frac{3M}{4 \pi R^{3}}.$$
Then the moment of inertia is
$$I= \int r^{2} \,dm= \rho \iiint_{V}r^{2} \,dV
= \rho \int_{0}^{2 \pi} \int_{0}^{ \pi} \int_{0}^{R} r^{4} \sin(\theta) \, dr \, d\theta \, d\phi
=4 \pi \rho \, \frac{R^{5}}{5}
$$
$$=4 \pi \frac{3M}{4 \pi R^{3}} \, \frac{R^{5}}{5}= \frac{3}{5} \, MR^{2}.$$
Where is my error?
I know, I know: all the derivations of this result I can find split the sphere up into
disks. I understand those derivations: I want to know where this one is wrong.
Calculate the moment of inertia of a uniformly distributed sphere about an axis through its center.
2. Relevant equations
I know that
$$I= \frac{2}{5} M R^{2},$$
where ##M## is the mass and ##R## is the radius of the sphere. However, for some reason,
when I do this integration in spherical coordinates, I do not get this result.
3. The attempt at a solution
The density is
$$ \rho= \frac{M}{V}= \frac{3M}{4 \pi R^{3}}.$$
Then the moment of inertia is
$$I= \int r^{2} \,dm= \rho \iiint_{V}r^{2} \,dV
= \rho \int_{0}^{2 \pi} \int_{0}^{ \pi} \int_{0}^{R} r^{4} \sin(\theta) \, dr \, d\theta \, d\phi
=4 \pi \rho \, \frac{R^{5}}{5}
$$
$$=4 \pi \frac{3M}{4 \pi R^{3}} \, \frac{R^{5}}{5}= \frac{3}{5} \, MR^{2}.$$
Where is my error?
I know, I know: all the derivations of this result I can find split the sphere up into
disks. I understand those derivations: I want to know where this one is wrong.
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Convergence of Series Sinx/x
1. The problem statement, all variables and given/known data
Determine whether the series Ʃ(1 to infinity) sinx / x converges or diverges.
2. Relevant equations
This question appears in the integral test section, but as far as i know the integral test can only be used for decreasing functions, right?
3. The attempt at a solution
Using the ratio test, limx->infinity sin(x+1)/(x+1)*(sinx/x)=limx->infinity x*sin(x+1)/((x+1)(sinx))
This is where i got stuck-this limit oscillates between positive infinity and negative infinity.
Using the root test, i need to find the limit of (sinx)^(1/x) as x approaches infinity, which also gets me nowhere.
we have not done taylor series yet so i'm sure there is a relatively simple approach to this question...please help?
Determine whether the series Ʃ(1 to infinity) sinx / x converges or diverges.
2. Relevant equations
This question appears in the integral test section, but as far as i know the integral test can only be used for decreasing functions, right?
3. The attempt at a solution
Using the ratio test, limx->infinity sin(x+1)/(x+1)*(sinx/x)=limx->infinity x*sin(x+1)/((x+1)(sinx))
This is where i got stuck-this limit oscillates between positive infinity and negative infinity.
Using the root test, i need to find the limit of (sinx)^(1/x) as x approaches infinity, which also gets me nowhere.
we have not done taylor series yet so i'm sure there is a relatively simple approach to this question...please help?
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Homomorphisms of Languages
Hey, I was thinking of this generalization of homomorphisms. You have a language [itex]L_1 = (A, B)[/itex] where [itex]A[/itex] is a set of symbols and [itex]B[/itex] is a set of sequences of symbols in [itex]A[/itex]. Given languages [itex]L_1 = (A, B)[/itex] and [itex]L_2 = (C, D)[/itex] a function [itex]f: A \rightarrow C[/itex] is defined to be a homomorphism of languages if, given any sequence [itex]a_1 a_2 ... a_n \in B[/itex], we have [itex]f(a_1) f(a_2) ... f(a_n) \in D[/itex].
This is seen as a generalization. For example, if [itex]A[/itex] is a set of group elements, and [itex]B[/itex] is a set of sentences of the form "[itex]a_1 a_2 a_3[/itex]" (the multiplication table, [itex]a_1 * a_2 = a_3[/itex]), then every homomorphism of languages from [itex]A[/itex] to the alphabet of another language set up like this corresponds to a group homomorphism.
Another example: if [itex]A[/itex] is a set of ring elements together with special elements * + =, and [itex]B[/itex] is a set of sentences of the form "[itex]a_1 * a_2 = a_3[/itex]" (the multiplication table), unioned with a set of sentences of the form "[itex]a_1 + a_2 = a_3[/itex]" (the addition table), then homomorphisms of languages that map * to * and + to + and = to = correspond to ring homomorphisms.
To look at it in general, [itex]A[/itex] is a set of objects, and [itex]B[/itex] is a set of true statements about elements of [itex]A[/itex]. A homomorphism of languages [itex]f : A \rightarrow C[/itex] induces a map from statements in [itex]B[/itex] to corresponding statements in [itex]D[/itex] that "maps truth to truth" (doesn't generate false statements, i.e. strings outside of [itex]D[/itex]).
What do you think? Have you heard of this?
This is seen as a generalization. For example, if [itex]A[/itex] is a set of group elements, and [itex]B[/itex] is a set of sentences of the form "[itex]a_1 a_2 a_3[/itex]" (the multiplication table, [itex]a_1 * a_2 = a_3[/itex]), then every homomorphism of languages from [itex]A[/itex] to the alphabet of another language set up like this corresponds to a group homomorphism.
Another example: if [itex]A[/itex] is a set of ring elements together with special elements * + =, and [itex]B[/itex] is a set of sentences of the form "[itex]a_1 * a_2 = a_3[/itex]" (the multiplication table), unioned with a set of sentences of the form "[itex]a_1 + a_2 = a_3[/itex]" (the addition table), then homomorphisms of languages that map * to * and + to + and = to = correspond to ring homomorphisms.
To look at it in general, [itex]A[/itex] is a set of objects, and [itex]B[/itex] is a set of true statements about elements of [itex]A[/itex]. A homomorphism of languages [itex]f : A \rightarrow C[/itex] induces a map from statements in [itex]B[/itex] to corresponding statements in [itex]D[/itex] that "maps truth to truth" (doesn't generate false statements, i.e. strings outside of [itex]D[/itex]).
What do you think? Have you heard of this?
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Thermal Engineering_Heat Transfer
Hi,
I am new to this Forum... So please let me know this is not the correct sub heading under which i am suppose to post the question...
I would like to the basic relation between the Air density, Air Mass Flow Rate and heat Transferred to air by Convection...
Changing the Air Flow Rate from 0 to say 0.001, the heat transferred, mass flow rate and the air density changes... why and what is the relation???
RV
I am new to this Forum... So please let me know this is not the correct sub heading under which i am suppose to post the question...
I would like to the basic relation between the Air density, Air Mass Flow Rate and heat Transferred to air by Convection...
Changing the Air Flow Rate from 0 to say 0.001, the heat transferred, mass flow rate and the air density changes... why and what is the relation???
RV
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interference and entanglement
Sorry if the question is too basic.
What happens when a pair of entangled particles are sent through a double slit? (Same time) ....in case they are
1. Only momentum entangled
2. Only position entangled
3. Only spin entangled
What happens when a pair of entangled particles are sent through a double slit? (Same time) ....in case they are
1. Only momentum entangled
2. Only position entangled
3. Only spin entangled
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Maximum perpendicular height above an inclined plane
1. The problem statement, all variables and given/known data
A particle is projected from a point o with initial velocity u up a plane inclined at an angle 60° to the horizontal. The direction of projection makes an angle ∅ with the horizontal. The maximum perpendicular height is H.
prove that H = u^2( sin^2(∅) ) / g
2. Relevant equations
v = u + at
s = ut + .5(a)(t^2)
3. The attempt at a solution
the horizontal axis ( i axis ) is the line of greatest slope of the inclined plane. The j axis is perpendicular to the i axis.
splitting the u vector into horizontal and vertical components along the i and j axis'.
i axis.............. ucos( ∅ - 60 )
j axis..............usin( ∅ - 60)
force of gravity split into component vectors along and perpendicular to the inclined plane
i axis = gsin(60) = √3/2
j axis = (1/2)g
the object will have reached its maximum perpendicular height when its vertical velocity(Vy) is 0
Vy = usin(∅ - 60) - (1/2)gt = 0
t = 2u( sin( ∅ - 60 ) )/g
The maximum perpendicular height Sy = H
Sy = ut + (1/2)at^2
Sy = usin(∅-60)(2u)(sin(∅-60)/g -(1/2)(1/2)g(4u^2)( sin^2(∅-60)/g^2 )
simplify
Sy = u^2( sin^2( ∅ - 60 ) ) /g
when I simplify using
sin(A-B)=sin A cos B - cos A sin B
It just makes the equation more awkward
I think I was right using ∅ - 60 since both angles are taken from the horizontal so you have to subtract to get the angle between the objects line of projection and the plane.
Any help would be appreciated.
A particle is projected from a point o with initial velocity u up a plane inclined at an angle 60° to the horizontal. The direction of projection makes an angle ∅ with the horizontal. The maximum perpendicular height is H.
prove that H = u^2( sin^2(∅) ) / g
2. Relevant equations
v = u + at
s = ut + .5(a)(t^2)
3. The attempt at a solution
the horizontal axis ( i axis ) is the line of greatest slope of the inclined plane. The j axis is perpendicular to the i axis.
splitting the u vector into horizontal and vertical components along the i and j axis'.
i axis.............. ucos( ∅ - 60 )
j axis..............usin( ∅ - 60)
force of gravity split into component vectors along and perpendicular to the inclined plane
i axis = gsin(60) = √3/2
j axis = (1/2)g
the object will have reached its maximum perpendicular height when its vertical velocity(Vy) is 0
Vy = usin(∅ - 60) - (1/2)gt = 0
t = 2u( sin( ∅ - 60 ) )/g
The maximum perpendicular height Sy = H
Sy = ut + (1/2)at^2
Sy = usin(∅-60)(2u)(sin(∅-60)/g -(1/2)(1/2)g(4u^2)( sin^2(∅-60)/g^2 )
simplify
Sy = u^2( sin^2( ∅ - 60 ) ) /g
when I simplify using
sin(A-B)=sin A cos B - cos A sin B
It just makes the equation more awkward
I think I was right using ∅ - 60 since both angles are taken from the horizontal so you have to subtract to get the angle between the objects line of projection and the plane.
Any help would be appreciated.
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Transition from Mech. Eng (undergrad) to Comp Science (masters)
Hello everybody.
As the title suggests, I received my undergraduate degree in mechanical engineering. I was accepted into a mechanical engineering master's program, specifically in the field of dynamics and control. All of a sudden, an opportunity jumps at me. I learned about a program that I did not know existed at my university. It's an expanded M.S. Computer Science program aimed at students who have an engineering/math/science/non-CS background.
The first semester is a foundational semester with the following 3 classes:
Computer Systems Organization
Foundations of Artificial Science
Introduction to Programming Systems Design
I have to average a 3.0 to stay in the program, or else I fall back to the dynamics and control program (not a bad plan B, but it is a wasted semester of time and tuition).
Anyways, I extremely excited for the opportunity as Computer Science is a subject that I have always been fascinated by. Through my internship work this summer, I have been exposed to satellite flight software written in C. On my own, I've done minor mobile application development in C#/XAML. But overall, the only formal education I've had for a programming language is MATLAB.
I guess I'm making this thread to see if anybody went through a similar situation. I'm extremely excited but extremely nervous! I'm spending the next few weeks working through the book "Invitation to Computer Science" 6th edition and even paid for the extra lab course that comes with it.
Thanks!
As the title suggests, I received my undergraduate degree in mechanical engineering. I was accepted into a mechanical engineering master's program, specifically in the field of dynamics and control. All of a sudden, an opportunity jumps at me. I learned about a program that I did not know existed at my university. It's an expanded M.S. Computer Science program aimed at students who have an engineering/math/science/non-CS background.
The first semester is a foundational semester with the following 3 classes:
Computer Systems Organization
Foundations of Artificial Science
Introduction to Programming Systems Design
I have to average a 3.0 to stay in the program, or else I fall back to the dynamics and control program (not a bad plan B, but it is a wasted semester of time and tuition).
Anyways, I extremely excited for the opportunity as Computer Science is a subject that I have always been fascinated by. Through my internship work this summer, I have been exposed to satellite flight software written in C. On my own, I've done minor mobile application development in C#/XAML. But overall, the only formal education I've had for a programming language is MATLAB.
I guess I'm making this thread to see if anybody went through a similar situation. I'm extremely excited but extremely nervous! I'm spending the next few weeks working through the book "Invitation to Computer Science" 6th edition and even paid for the extra lab course that comes with it.
Thanks!
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Can't get Fortran code to give me desired output file
Hey everyone,
I have written a Fortran code for a project I am working on, but am having an issue: I can't get the code to output my data to the file I have opened. Here is what I am trying to do.
I am setting up a Monte-Carlo code that selects a random x- and y-value. These values are then used to calculate the value of a Gaussian distribution (gauu_dist) at that point. Then another random value (z) is found, and compared as 0 is greater than or equal to z, and z is less than equal to gauss_dist at that point. If so, then the x- and y- values are to be written to my file jet_dist.dat (I do not care what z is after this, nor do I care what the gauss_dist value is anymore. ) For some reason I cannot get the resulting data to be put into my .dat file. If I ask the code to wirte my x- and y-values as soon as they are found, and comment out the lines of my if/then statement and my gauss_dist line, I can get the code to write my x- and y-values. I really can't figure out what I am missing!
Hopefully this is clear enough for someone to assist me. The following is my code, if you need further clarification, please let me know. Oh, and I am compiling using gfortran on an Ubuntu (most recent distro) platform.
program jetdist
implicit none
integer N, i
real x, y, z, gauss_dist, a, a2, z_min, e
real x_acc, y_acc, z_max
real, dimension(1100, 1100, 1100, 1100) :: jet_dist
open(unit=3, file="jet_dist.dat", status="unknown")
N = 1000
a = 3
a2 = a*a
e = 2.718
! need to insert print/write command so that N/-values can be changed for different runs of code
a2 = a*a
x_acc = 0
y_acc = 0
z_min = 0
z_max = 1.25
do i = 1, N
x = (rand()-0.5) * 26
y = (rand()-0.5) * 26
z = (rand())
gauss_dist = e**(-(x*x + y*y)/a2)
if (z_min .ge. z .and. z .le. gauss_dist) then
write(3,*) x, y
end if
end do
close(3)
return
stop
end
I have written a Fortran code for a project I am working on, but am having an issue: I can't get the code to output my data to the file I have opened. Here is what I am trying to do.
I am setting up a Monte-Carlo code that selects a random x- and y-value. These values are then used to calculate the value of a Gaussian distribution (gauu_dist) at that point. Then another random value (z) is found, and compared as 0 is greater than or equal to z, and z is less than equal to gauss_dist at that point. If so, then the x- and y- values are to be written to my file jet_dist.dat (I do not care what z is after this, nor do I care what the gauss_dist value is anymore. ) For some reason I cannot get the resulting data to be put into my .dat file. If I ask the code to wirte my x- and y-values as soon as they are found, and comment out the lines of my if/then statement and my gauss_dist line, I can get the code to write my x- and y-values. I really can't figure out what I am missing!
Hopefully this is clear enough for someone to assist me. The following is my code, if you need further clarification, please let me know. Oh, and I am compiling using gfortran on an Ubuntu (most recent distro) platform.
program jetdist
implicit none
integer N, i
real x, y, z, gauss_dist, a, a2, z_min, e
real x_acc, y_acc, z_max
real, dimension(1100, 1100, 1100, 1100) :: jet_dist
open(unit=3, file="jet_dist.dat", status="unknown")
N = 1000
a = 3
a2 = a*a
e = 2.718
! need to insert print/write command so that N/-values can be changed for different runs of code
a2 = a*a
x_acc = 0
y_acc = 0
z_min = 0
z_max = 1.25
do i = 1, N
x = (rand()-0.5) * 26
y = (rand()-0.5) * 26
z = (rand())
gauss_dist = e**(-(x*x + y*y)/a2)
if (z_min .ge. z .and. z .le. gauss_dist) then
write(3,*) x, y
end if
end do
close(3)
return
stop
end
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Do you use encryption? According to NSA = Potential Terrorist
And on top of that; if you speak a language that is out of place for the region you are in You are probably a terrorist! And on top of that; if you search the web for suspicious stuff (like Osama bin Laden) You are MOST LIKELY a TERRORIST!!
Cant believe this is true ... sigh ... Lloyd Christmas and Harry Dunne couldnt have come up with a safer bet.
This of course explains why they didnt caught Tamerlan Tsarnaev and Dzhokhar Tsarnaev the brothers spoke English in Boston (without encryption)!! :grumpy:
Has NSA never heard of the HTTPS protocol?? They say its like encrypted sort of, but what do I know... and its supposed to be quite common, like banks and Visa and other terrorist stuff...
Enjoy the most enlightening training material in human history - Training materials for the XKeyscore program:
Conclusion: NSA is looking for encrypted German terrorists in Pakistan that search for suspicious stuff. This far they have found 300. Not bad for HTML language tags.
This is nuts, and its your tax money they burn on high-tech personnel and gigantic Linux clusters.
Which guy do you trust?
http://www.youtube.com/watch?v=lqZWRdNih8E
http://www.youtube.com/watch?v=H5q6XyXnESc
Say goodbye to metadata:
XKeyscore: NSA tool collects 'nearly everything a user does on the internet'
(To the mentors: This is not supposed to be a computer/technical thread, but something that concerns all people that ever use internet, VoIP, etc, which should be pretty general, I hope...)
Cant believe this is true ... sigh ... Lloyd Christmas and Harry Dunne couldnt have come up with a safer bet.
This of course explains why they didnt caught Tamerlan Tsarnaev and Dzhokhar Tsarnaev the brothers spoke English in Boston (without encryption)!! :grumpy:
Has NSA never heard of the HTTPS protocol?? They say its like encrypted sort of, but what do I know... and its supposed to be quite common, like banks and Visa and other terrorist stuff...
Enjoy the most enlightening training material in human history - Training materials for the XKeyscore program:
Quote:
Quote by Page 15
|
Quote:
Quote by Page 19
|
Conclusion: NSA is looking for encrypted German terrorists in Pakistan that search for suspicious stuff. This far they have found 300. Not bad for HTML language tags.
This is nuts, and its your tax money they burn on high-tech personnel and gigantic Linux clusters.
Which guy do you trust?
http://www.youtube.com/watch?v=lqZWRdNih8E
http://www.youtube.com/watch?v=H5q6XyXnESc
Say goodbye to metadata:
XKeyscore: NSA tool collects 'nearly everything a user does on the internet'
(To the mentors: This is not supposed to be a computer/technical thread, but something that concerns all people that ever use internet, VoIP, etc, which should be pretty general, I hope...)
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Is it ok to commit fraud if it's widespread?
If an employer offers you a deal to give you $400/month without needing you to do work for his/her institution, so you're getting money for doing nothing for him/her, would you accept that offer? do you think that there's anything morally wrong with this?
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