A helix (), plural helixes or helices (), is a shape like a corkscrew or spiral staircase. It is a type of smooth space curve with tangent lines at a constant angle to a fixed axis. Helices are important in biology, as the DNA molecule is formed as two intertwined helices, and many proteins have helical substructures, known as alpha helices. The word helix comes from the Greek word ἕλιξ, "twisted, curved". A "filled-in" helix – for example, a "spiral" (helical) ramp – is called a helicoid.
Can you by any type of rotations or transformations turn a left handed helix into a right handed or vice versa? If yes why? And if no, why not?
For example if you have a 2 d triangle like the one in the picture:
You can turn it in 3 dimensions 180 degrees in a sense mirroring it and you will...
I honestly have such a dumb question- it says “a pitch angle” but cannot find that in relation to a helix. It is not defined in the textbook. Looking on google I found a helix angle, but is that different than the pitch angle? Can anyone draw me a picture of where the pitch angle is?
I assumed...
If a particle is in a magnetic field ##\vec{B} = B\hat{z}## with velocity ##\vec{v} = v_x \hat{x} + v_y \hat{y} + v_z \hat{z}##, then in Cartesian coordinates we can obtain the pair of differential equations $$\ddot{x} = \frac{qB}{m}\dot{y}$$$$\ddot{y} = -\frac{qB}{m}\dot{x}$$which give the...
I was thinking about a situation related to Galilean relativity but couldn't come up with a solution to the problem. I would be very grateful if someone can explain it to me.
So, I was thinking of a situation where I am in the reference frame of a block moving at velocity u along the x-axis and...
I thought that a nearly parallel entry path would result in a helix of very small, but constant, radius. I would not expect the electrons to focus at a point, but continue along the infinite helix. What have I missed?
I attempted to use the relation that B = gradient crossed with A; however, I'm strguggling with how to setup the question. I think that alternatively the problem can be solved using the Poisson equation that A(r) = (mu/4pi)integral{(J(r)/r}dtau; however, here to I am struggling with the setup.
I asked this question on SO, but I am having problems with it (I cannot even get into my account now). It seems that people using the IP I am using are asking a lot and that limits the number of questions I can ask. Please have a look at my question. Here's the link:
[Moderators note: bold large...
Hello all,
I have a question with the helix path of proton in a magnetic field that I am a bit stuck on.
Question:
Equations:
F = qv X B
F = mv^2/r
d=vt
My Attempt:
Think the graph drawn is good enough for questions (a). However, I am stuck on (b) and (c).
Firstly I am not entirely sure...
In a problem in Landau’s mechanics (end of section 9) he asks for the quantity conserved in the field of “an infinite homogenous cylindrical helix.”
The solution is that the Lagrangian is unchanged by a rotation of dΦ together with a translation of hdφ/(2π) (about and along the symmetry axis)...
Homework Statement
The Reason for the Double helical Structure of DNA is the operation of -
A) Van Der Waals Forces
B)Dipole Dipole Interactions
C)Hydrogen Bonding
D)Electrostatic Attraction
2. Background of question
This question ,is part into the home work asignment my chem tracher...
Let's say you have a helix defined parametrically as
r(t) =<sin(t), cos(t), t>
Is it possible to eliminate t and write an equation for this helix just in terms of x, y, and z?
Homework Statement
Homework Equations
$$\mathcal{L}=T-U$$
$$\omega= \frac{d\phi}{dt}$$
$$I=mr^{2}$$
The Attempt at a Solution
My problem is not finding the Lagrangian. But finding the kinetic energy! The translational kinetic energy would obviously be the following:
$$K.E...
Homework Statement
When a particle moves along the helix shown, the componentsof its position vector are
x=Rcosωt , y = Rsinωt , ##z=-\frac h {2π} ωt##
where ω is constant. Show that the velocity and acceleration have constant magnitutes,
and compute their values if R=1.2m, h=0.75m, and...
Hi,
I'd like to build a homopolar generator. Since generating magnetic fields of uniform density of any useful size is very tricky to do with off the shelf permanent magnets (I've tried!) I had the idea to use DC solenoids instead. But with a rotating helical plate in place of the cylindrical...
Homework Statement
A small bead of mass m is constrained to move on a helix: r (θ) = (R cos(θ), R sin(θ), q θ) where R and q are constants, and θ=θ(t) describes the position of the bead along the helix at time t. The bead is also subjected to a gravitational acceleration g downward (-z...
Hello. I use a group of 4 helix antennas in the band of 1420 MHz. It works fine but by nature directivity is very poor ( around 50° at -3 dB). Is there a way to improve directivity using mechanical, electrical ... devices ?
How do I find the force acting on the helix of a thread.
Say if I'm using a torque wrench to tighten a nut and compress a gasket between nut and a mating piece and give 100 ft.lbs of torque how much of it will be available on the helix of the thread (say a helix angle of 0.67 degrees)...
Hello, I have a problem that seems to have beaten me.
I want to make a cable-driven reduction system between a threaded rod (pinion) and a larger threaded cylinder. Because of string walking, the string between the two has to stay at all times straight, parallel to the ground so that...
Hello dear physics masters on earth, I am very grateful to be priviliged to ask you a question regarding electric fields and potential of a single-cpin helix. It is portrayed as below.
It is a line of uniform charge, and 1-turn helix with radius R and height H. I have came to ugly answers, and...
Hi,
##x(s)=\cos\frac{s}{\sqrt{2}}##
##y(s)=\sin\frac{s}{\sqrt{2}}##
##z(s)=\frac{s}{\sqrt{2}}##,
it is a unit-speed helix. Its curvature is ##\kappa=||\ddot{r}||=\frac{1}{2}##. Principal unit normal is ##{\mathbf n}=(\cos\frac{s}{\sqrt{2}},\sin\frac{s}{\sqrt{2}},0)##. So far so good...
But the...
I was just trying for the ninetieth time to try and understand the sort of physicality Euler's formula and the role i plays in the way so many equations work - it's always been such an obstacle to reading so many of them. I mean what the heck is that i doing there. Progress, maybe, but... no...
I believe what I am attempting to do is not possible but here goes. I want to design a fixed overall length coil which I can manually adjust the pitch on. Optimally one would be able to grab the coil and by twisting it in place would be able to change it's pitch by changing its diameter but not...
Dear physicist,
my task is to calculate the acceleration of a particle of mass m which moves without friction in the Earth's gravitational field on a helix:
The helix is parameterized as shown:
x(\phi)=a cos \phi
y(\phi)=a sin \phi
z(\phi)=c \phi
formed with a radius a,gradient c as constants...
I'm a new user to both PF & Maxwell 3D. I've been having a lot of problems trying to draw a helical coil in Maxwell 3D v11.
the problem is how to connect the two tub in 3D
here is the image imported MAXWELL...
Homework Statement
A generalized helix is a space curve whose unit tangent makes ##T## makes a constant angle ##\theta## with the a fixed unit vector ##A## in Euclidean space, I.e ##T \cdot A = \cos \theta = \text{const}##. Prove that if the torsion ##\tau \neq 0## everywhere then the space...
Homework Statement
Evaluate the integral
∫
(x2 − yz) dx + (y2 − xz) dy + (z2 − xy) dz, C(A→B)
where C(A → B) is a piece of the helix
x = a cos φ, y = a sin φ, z = h φ, (0 ≤ φ ≤ 2π),
2π
connecting the points A(a, 0, 0) and B(a, 0, h).
Homework Equations
[Hint: The problem could...
Consider the case of a right circular helical curve with parameterization \(x(t) = R\cos(\omega t)\), \(y(t) = R\sin(\omega t)\), and \(z(t) = v_0t\). Find the curvature and torsion curve.
http://img30.imageshack.us/img30/7828/gwi.png
We can then parameterize the helix
\begin{align*}...
Hello,
I am approximating a helix by parts of torus, to build an optical fiber wrapped around a cylinder simulation. Due to the software limitations, there is no easier way.
So I take a part of the torus, rotate it so the one end points slightly up, connect similar part of the torus to the...
Homework Statement
don't know the line integral latex code but;
\int\underline{r}\timesd\underline{r}
from (a,0,0) to (a,0,2∏b) on the circular helix \underline{r} = (acos(λ), asin(λ), bλ)
The Attempt at a Solution
Its the multiple use of the position vector r in the question...
Homework Statement
A charge Q is uniformly distributed with linear density λ over a helix parameterized as \vec{r}=acos(\theta)\hat{x}+asin(\theta)\hat{y}+ \frac{ h\theta}{2 \pi}\hat{z}, where a and h are positive constants, and 0<∏<2∏.
a) Find the charge Q
b) Find the electric field on...
Homework Statement
A proton moves with a speed of 4300 m/s in a direction 76.0° above positive x axis. It enters a region where a magnetic filed of 25x10^-6 Tesla exists in the positive x direction. Find the radius of the helix formed by the protons path and the distance between adjacent...
Homework Statement
When riding a roller coaster, when you enter a double helix why does it feel as if you're speeding up? I'm in the rotational dynamics section, so the answer will most likely be about Conservation of Angular Momentum or something along those lines. I am really interested but...
I have a question about one of the methods used to draw the alpha helix structures in proteins.
This is a typical drawing from Wikipedia of a small protein transcriptional activator Myb;
http://en.wikipedia.org/wiki/File:Protein_MYB_PDB_1guu.png
Now that drawing looks typical of any...
Homework Statement
DoCarmo Section 1.5 problem 1 part d. Show that the lines containing n(s) and passing through a(s) [a is the curve, and n(s) is the unit normal vector] meet the z axis under a constant angle of pi/2.
Helix: a(s) = (a cos(s/c_, a sin(s/c), b*s/c), so I computed n(s) =...
Homework Statement
I'm doing past a past exam (2003) and I'm stuck on the first exercise. Here it is:
Consider a helix centered in the z-axis, of radius R and fixed step a, given in cylindrical coordinates by z=\frac{a\theta }{2 \pi }, r=R.
A particle of mass m slides without rolling over the...
Homework Statement
A uniform magnetic field of magnitude 0.137 T is directed along the positive x axis. A positron moving at a speed of 5.40 106 m/s enters the field along a direction that makes an angle of θ = 85.0° with the x-axis (see figure below). The motion of the particle is expected...
i have the curve a(t) = (3t, 2t2, 2t3) and that a'(t) = (3, 4t, 6t2). my textbook tells me to verify that the tangent lines make a constant angle with the line y = 0, z = x so basically the vector (1, 0, 1).
using the definition of the dot product a * b = |a| |b| cos(\theta) i have...
If I have an elastic formin a helix which I've turned N times and have a radiu r... it connect two masse m (one of them is fixed) - the natural length of the ropes are X_0 (the distance between the masses)
what are the equation of motion X(t) and (Theta)(t) ??
Can DNA adopt an A-form helix, and can RNA adopt a B-form helix. If so, under what conditions, and if not, why not?
The only idea I have so far is that low humidity will help form the A form, and high humidity forms the B form. However, can humidity change in our bodies? I'm lost here.
Homework Statement
r(t)=cos(t^2)\hat{i}+sin(t^2)\hat{j}+t^2\hat{k}
Compute the arc length integral from t=0 to t=\sqrt{2 \pi}Homework Equations
Arclength = \int_{a}^{b}||v(t)||\, dtThe Attempt at a Solution
I did the following:
\\r'(t)=-2tsin(t^2)\hat{i}+2tcos(t^2)\hat{j}+2t\hat{k}\\...
This question is about variable end points in calculus of variations. I understand the basic principle of how you would find the various equations, but I embarrasingly keep getting stuck on when determining the constants.
Question: Find the equation of a frictionless wire between the point...
Homework Statement
I'm a little confused as to how exactly a protein folds into an alpha helix...like what causes it exactly to assume that conformation...does it fold spontaneously in water (like i know hydrophobic R groups cause the protein to fold where the hydrophobic groups are faced...
Is this doable, a calculation to go from A to B on a helical path?
To simplify the problem we could consider A and B being parallel planes so that the end location of the helix is not of prime importance, it could end anywhere on the plane at B.
It is easy to determine the length of a...
Rank the following base pairs according to their stability.
Rank from most to least stable. To rank items as equivalent, overlap them.
-------------
I have found out that the first one is thymine-adenine pair and the second one is a cytosine-guanine pair. The third one is cytosine...
Hi all,
I have a circular helix with any point on the helix defined using the Frenet tnb triad.
t- tangent, b- binormal and n-normal acting towards the axis of the host circular cylinder.
The tangent of the helix t is oriented at angle A with respect to the base of the cylinder.
Now...
Hello
A wheel rolling on a shallow rotating helix can be used to provide off vehicle power to a moving vehicle.
Does anyone know of any applications where this is used, or know of any research into the matter?
Thanks
Homework Statement
An object weighing 1.2 pounds travels along a helix given by x=cost, y=sint, z=4t, 0<=t<=8pi. Find the work done by the object.
Let's keep this in ft.
Homework Equations
g=32.174 ft/s2
f=m*g
f=w*d
The Attempt at a Solution
r(t)=cos(t)i+sin(t)j+4(t)k
I know I need an F...