ganeshie8
  • ganeshie8
classic yet interesting question about roller coaster : find the minimum height from which the car needs to fall so as to complete the loop safely. The diameter of loop is 100m and the mass of car is 1000kg.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
ganeshie8
  • ganeshie8
|dw:1443166269719:dw|
inkyvoyd
  • inkyvoyd
EWWWW I might have this problem on my test!
Jhannybean
  • Jhannybean
|dw:1443166523518:dw|\[\sum F_y = ma_{cp} = F_{N} + F_{g} = N + mg=\frac{mv^2}{r}\]

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Jhannybean
  • Jhannybean
Well that's technically a little wrong because the vector for the normal force should be longer than the force of gravity, but still....
inkyvoyd
  • inkyvoyd
I think it's more wrong because your bottom circle is elliptical and thus does not obey rules of circular motion ;)
ParthKohli
  • ParthKohli
haha, vertical circle looks like you've fallen in the trap that physics is :)
ParthKohli
  • ParthKohli
Try to prove that the minimum velocity at the bottom is \(v_{min} = \sqrt{5gR}\) and thus the minimum kinetic energy is \(\frac{5}{2}mgR\) which can be equated to the initial potential energy to find the minimum height.
inkyvoyd
  • inkyvoyd
in the course of a few years parth has learned like 4 times as much physics as me.
Jhannybean
  • Jhannybean
\[N = \frac{mv^2}{r} -mg\]um... at the top of the roller coaster the normal force is neither more than the gravitational force, and nt less, but equal to it, therefore \(N=0\) \[mg = \frac{mv^2}{r}\]
IrishBoy123
  • IrishBoy123
why do we need to know the mass :-)
Jhannybean
  • Jhannybean
I wasnt there yet haha
ParthKohli
  • ParthKohli
Exactly, no need to know the mass. Jhanny is almost there. To be precise, \(N \ge 0\) to complete the vertical circle. At the minimum value of \(N\), we also get the minimum value of \(v\) at the top.
ParthKohli
  • ParthKohli
anyway the answer is \(h_{min} = 5R/2\)
ganeshie8
  • ganeshie8
that looks really nice and simpler! i think mass is given so that we can assume that newton mechanics works just fine but it is amazing how mass disappears after the calculations in most of these problems!
IrishBoy123
  • IrishBoy123
yeah, Galileo and Neil Armstrong!!
ganeshie8
  • ganeshie8
is that tesla in ur dp
IrishBoy123
  • IrishBoy123
yes if anyone loads up an Edison avatar, there's gonna be blood!!
ParthKohli
  • ParthKohli
no this is a dog
IrishBoy123
  • IrishBoy123
lol!
ganeshie8
  • ganeshie8
so a naive q, do roller coasters really work like this? without any chains hooked to the tracks?
Jhannybean
  • Jhannybean
\[g=\frac{v^2}{r} \implies v^2 = gr\] Yeah the mass is relevant when we're finding the change in work done, but this is where I get a little lost every time. :( \[U_i +K_i = U_f + K_f\]
DanJS
  • DanJS
Just from the back of my mind, i think Walter Lewin did this in one of the 8.01 lectures on MIT OCW
DanJS
  • DanJS
been a couple years since watching those
ganeshie8
  • ganeshie8
they had removed all his lectures from MIT after some controversy
ParthKohli
  • ParthKohli
in ideal conditions, they can work like that
DanJS
  • DanJS
:-O, well good thing i dl them all, hehe
ParthKohli
  • ParthKohli
yeah, he harassed a young female student on one of his MOOCs it's still a shame, because he did know his physics pretty well
DanJS
  • DanJS
hell yes, his lectures and feynman spiked my interest
ganeshie8
  • ganeshie8
watching top 5 rolller coaster accidents https://www.youtube.com/watch?v=mM0HE7DKTvg
DanJS
  • DanJS
i am pretty sure the acceleration at the top of the circle is zero for one instant to 'just' make it over... maybe not
ParthKohli
  • ParthKohli
https://www.youtube.com/watch?v=HN8nv4tVFuA
DanJS
  • DanJS
maybe a way to do it with just energy conservations
IrishBoy123
  • IrishBoy123
|dw:1443168272771:dw|
ParthKohli
  • ParthKohli
yes, as Jhanny said - the velocity at the top of the roller coast is \(\sqrt{gR}\) at least so if we look at the energies at the top and at the bottom at the top: \(mg(2R) + \frac{1}{2}m(gR)\) at the bottom: \(\frac{1}{2}mv_{\rm min, \rm bottom}^2 \)
IrishBoy123
  • IrishBoy123
in practise i think roller coasters go faster and you are pushed into your seat (upwards) by your inertia
Jhannybean
  • Jhannybean
\[U_i + K_i = U_f + K_f \\K_i = 0 \]\[mgh = \frac{1}{2}mgr +2mgr\]\[h=\frac{r}{2}+r\]\[h=\frac{3}{2}r\]
ParthKohli
  • ParthKohli
of course they go faster because here we're calculating the minimum velocity
Jhannybean
  • Jhannybean
I just figured out why \(U_f = mg(2r)\) lol... -_-
ParthKohli
  • ParthKohli
\(r/2 + 2r = 5r/2\)
IrishBoy123
  • IrishBoy123
|dw:1443168775694:dw|
Jhannybean
  • Jhannybean
Yah I cant either. That's not eve important. Pfft.
Jhannybean
  • Jhannybean
Oh I just realized something
DanJS
  • DanJS
ah gravity doesn't matter
DanJS
  • DanJS
isn't that convenient
Jhannybean
  • Jhannybean
We had \(v^2=gr\) when we simplified our forces in the y-direction. We could have multiplied both sides by \(\dfrac{1}{2}m\) to associate the forms of kinetic and potential energies!! Whoops.
IrishBoy123
  • IrishBoy123
@DanJS so if g = 0 ??!!
ParthKohli
  • ParthKohli
ganeshie try solving this question about vertical circles... it'd really test your knowledge.
DanJS
  • DanJS
The initial potential energy from the minimum height will be equal to the sum of the potential energy at height of 2R + the kinetic energy from the min velocity to make it around
DanJS
  • DanJS
2.5R min height to start
Jhannybean
  • Jhannybean
\[h=\frac{5}{2}r \qquad r=\frac{D}{2} = \frac{100}{2} = 50~m\]\[h_{min} =\frac{5}{2}(50) = 125~m \]
Jhannybean
  • Jhannybean
Yeah that's another way to look at it , @DanJS , and sorry I got a little mixed up in the Kinetic energies part... i'm not as practiced in physics anymore :\
ganeshie8
  • ganeshie8
Yes PK, post... today it is going to be a gravity/uniform circular motion day for me!
Jhannybean
  • Jhannybean
Maybe you can also post the breaking-of-the-plate momentum question, another classical physics question involving vectors and momentum. I always had trouble with those.
ParthKohli
  • ParthKohli
can I have that extension, ganeshie? you know, the drawing one.
ParthKohli
  • ParthKohli
yeah I have a huge collection of questions so no worries
ganeshie8
  • ganeshie8
send me meeting id in teamviewer it would be simpler if i install it
Jhannybean
  • Jhannybean
Back to eating my kichadi.
ParthKohli
  • ParthKohli
whatever... I found an image that does suit my purpose.
1 Attachment
DanJS
  • DanJS
https://www.youtube.com/channel/UCliSRiiRVQuDfgxI_QN_Fmw/playlists someone uploaded em
Jhannybean
  • Jhannybean
I asked my physics professor that problem parth, he solved in probably a minute tops. then gave me the death stare as to why I had forgotten how to solve it using component methods.... =_=
ParthKohli
  • ParthKohli
in that image, let \(d = L/2\) and \(\theta = 90^{\circ}\) now if I release it that way, find the maximum height reached by the pendulum bob before the string becomes slack
IrishBoy123
  • IrishBoy123
treasure trove https://www.youtube.com/watch?v=7E34VOj8Elc&index=182&list=PLERGeJGfknBR3pXCPlV3bgb_qHCSNOdBf
ganeshie8
  • ganeshie8
that is a very useful collection, i hope they don't delete his lectures from youtube too thanks @DanJS
Jhannybean
  • Jhannybean
@DanJS Im saving this.
ParthKohli
  • ParthKohli
Walter Lewin himself has uploaded it on his own channel BTW https://www.youtube.com/channel/UCiEHVhv0SBMpP75JbzJShqw
DanJS
  • DanJS
download those playlists to disk
ganeshie8
  • ganeshie8
|dw:1443169569982:dw|
Jhannybean
  • Jhannybean
I have a friend attending MIT that's met him.
ParthKohli
  • ParthKohli
this thread is really slow for me so can we move to another one?
ganeshie8
  • ganeshie8
okiee
Empty
  • Empty
http://datagenetics.com/blog/march42014/index.html
Jhannybean
  • Jhannybean
oh, never knew it was called a trifecta.
DanJS
  • DanJS
@irishboy123 Where is gravity ever zero in this universe .. infinite range
Empty
  • Empty
Well gravity is practically zero at the center of the earth or in free fall :D
DanJS
  • DanJS
hmmm, free fall means you do not sense the gravity, it is still there and it matches your acceleration of falling
ganeshie8
  • ganeshie8
\[F \propto \dfrac{mM}{r^2} \] so the Force is not defined at \(r=0\) right
DanJS
  • DanJS
man i discussed this awhile back, about how you can not have zero distance.. been too long
DanJS
  • DanJS
strong force repulsion or something
Jhannybean
  • Jhannybean
Ah, yes. that's true, @ganeshie8
DanJS
  • DanJS
EM repulsion
DanJS
  • DanJS
you can't be sure r=0 by uncertainties in position
IrishBoy123
  • IrishBoy123
nah, inside the earth gravity is pulling you outwards. zero at centre - theoretically
Empty
  • Empty
Yeah, I mean an astronaut living in the space station is for all intents and purposes living with no gravity.
IrishBoy123
  • IrishBoy123
the r assumes a point mass and works outside the sphere that is the earth or any body
Jhannybean
  • Jhannybean
And that's why their bone structure slowly decomposes over time - he gravity that acts on them!
DanJS
  • DanJS
microgravity, they are moving very fast and falling around the earth
Empty
  • Empty
Yep
DanJS
  • DanJS
like a super cannon that fires so fast the ball falls slower than the horizon curves away
DanJS
  • DanJS
or the same rate
DanJS
  • DanJS
@IrishBoy123 Is the gravity at the center of a uniform Ball zero?
IrishBoy123
  • IrishBoy123
@Jhannybean that's 2 degrees of separation, i think it's called ie w/ Lewin
IrishBoy123
  • IrishBoy123
yes, if you look at it classically.
DanJS
  • DanJS
In the real universe there is gravity everywhere, i think, i can idealize a empty space void, no gravity
Empty
  • Empty
@ganeshie8 When you have the \(1/r^2\) dependence and end up at the center of the earth, this is actually a kind of false division by zero since your model was assuming we could just look as though the center of mass was good approximation. But once you're inside the earth, the outer mass doesn't affect you anymore, so this model only applies for distance for r>Radius of the earth. Just imagine yourself at the center of the earth, look at the contribution of a tiny bit of force from each tiny bit of mass, and integrate over the sphere which we can approximately see to cancel out since all the little vectors will be in equilibrium! ;D
IrishBoy123
  • IrishBoy123
OK if we are playing with words, the gravity *due to the sphere* is zero at the centre of the sphere according to Newton's law of gravitation :p
Jhannybean
  • Jhannybean
I don't like playing with words one bit.
IrishBoy123
  • IrishBoy123
but i agree totally that a force that has unlimited reach much reach everywhere :-)
Empty
  • Empty
Can we measure the gravitational pull of planets outside of our solar system?
DanJS
  • DanJS
Does that have something to do with a metal sphere and charge concentrated on the surface...
IrishBoy123
  • IrishBoy123
@DanJS but i only know classical physics so if it reaches back on itself .... :p i dunno
Empty
  • Empty
@DanJS Yeah, because Coulomb's law is of a similar form. I think the Divergence formulation of gravity and electric force makes a lot more sense since it naturally gives rise to the 1/r^2 term. Just like a balloon being blown up has the same amount of rubber as you blow it up, it just gets stretched out thinner and thinner with increasing radius 1/r^2 since the surface area is r^2.
DanJS
  • DanJS
the electric field in the center is
IrishBoy123
  • IrishBoy123
isit a conducting sphere?!
ganeshie8
  • ganeshie8
it is like, there exists a point between earth and moon where the force would be 0
DanJS
  • DanJS
yes, just recalling barely, i have no numbers , just concepts
IrishBoy123
  • IrishBoy123
@Empty hit nail on head, the inverse square law and the surface area of a sphere ...
Jhannybean
  • Jhannybean
basic E&MM concepts?
IrishBoy123
  • IrishBoy123
so you get the same stuff happening. \(\dfrac{stuff}{r^2}\)
DanJS
  • DanJS
omg i have to sleep, the gravity at center of earth from earth, just made me think of a hollow conductive sphere with uniform charge density, and the electric field at the center... bye bye
IrishBoy123
  • IrishBoy123
@Jhannybean basic to anyone with only 2 degrees of separation from Walter Lewin!
Empty
  • Empty
https://en.wikipedia.org/wiki/Gauss%27s_law_for_gravity#Differential_form Yeah this is what I am specifically referring to, this should remind you of one of Maxwell's equations I think? :P
DanJS
  • DanJS
so you can think of earth as all mass distributed around circumference then in that state?
IrishBoy123
  • IrishBoy123
@DanJS as long as you are oustide the radius, it can be a point mass or a shell. the maths works out beautifully.
IrishBoy123
  • IrishBoy123
@Empty cracking link!
Astrophysics
  • Astrophysics
Is what you're talking about have to do with Poisson's equation @Empty ?
DanJS
  • DanJS
right,
DanJS
  • DanJS
goodnight
Astrophysics
  • Astrophysics
It has to do with gravitational fields with results of electrostatics from Maxwell's equation
Empty
  • Empty
Yeah, the Poisson equation is saying that gravity is a conservative vector field because it is the divergence of a scalar potential
DanJS
  • DanJS
lol, this all started because i said the universe has gravity throughout..
Empty
  • Empty
Haha well in all fairness I think gravity is technically not a force anymore, but it's still effectively a force to play around with :D
DanJS
  • DanJS
and if you could supercompute to unreasonable levels, you can calculate classically the gravity at any point from the net effects of every particle in the universe
IrishBoy123
  • IrishBoy123
does gravity "travel" at the speed of light ?!
Empty
  • Empty
Yeah
Empty
  • Empty
@DanJS I thought earlier you were arguing that 0 distance doesn't exist due to uncertainty, but if you were to calculate gravity from every particle, I think that the uncertainty in that would end up throwing away all of the information you'd get since planck's constant is on the order of \(10^{-34}\), which basically means anyone who's memorized 100 digits of \(\pi\) is wasting time since that's 3 times as much as we could ever measure xD
DanJS
  • DanJS
newtonian gravity
DanJS
  • DanJS
just some thoughts, i never got to take anything beyond relativity. Need to know quantum mechanics and the basic standard model interactions stuff.. maybe someday
Empty
  • Empty
This has really helped me a lot lately in learning QM: https://www.youtube.com/watch?v=lZ3bPUKo5zc&index=1&list=PLUl4u3cNGP61-9PEhRognw5vryrSEVLPr
IrishBoy123
  • IrishBoy123
+1 Allan Adams is cool
Empty
  • Empty
Most of the time when I have tried to learn QM I always sorta feel skeptical of the teacher and so I can't get very far, but I definitely can watch him, accept what he's saying is as best as we as lil human beings can do at this point in time lol.
Astrophysics
  • Astrophysics
As I just started relativity recently, and haven't got into it too much so I'll probably get this wrong, doesn't Einstein's theory of gravity concerns with space being distort, for example earth going around the sun, it's not because of "gravity" but of space being warped? So how does this relate to gravity and speed of light? Unless you mean space itself is being treated as "gravity" and space time travelling at speed of light, haha but I don't really know if any of this is true, as this has to do with general relativity, and that's a bit advanced.
Empty
  • Empty
As I understand it, objects travel through geodesics in space time, which are effectively 'straight lines'. The mass of the sun is bending space around it in such a way that the earth believes it's going in a straight line, it's just that the space is messed up so there's an effective curve to the path. So 'gravity' travelling at the speed of light is more like curvature of spacetime moving, which can't propagate faster than the speed of light, I think this is a pretty famous thought experiment so you can look into it, like "if the sun disappeared would the earth keep going around the sun for a while or would it instantly feel it?" and gravity waves are two things to look into. I am not an expert in any way for the record lol.
Astrophysics
  • Astrophysics
Ha, right!
IrishBoy123
  • IrishBoy123
about 8mins and the lights go out

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