Muscle contraction is the activation of tension-generating sites within muscle cells. In physiology, muscle contraction does not necessarily mean muscle shortening because muscle tension can be produced without changes in muscle length, such as when holding a heavy book or a dumbbell at the same position. The termination of muscle contraction is followed by muscle relaxation, which is a return of the muscle fibers to their low tension-generating state.Muscle contractions can be described based on two variables: length and tension. A muscle contraction is described as isometric if the muscle tension changes but the muscle length remains the same. In contrast, a muscle contraction is isotonic if muscle tension remains the same throughout the contraction. If the muscle length shortens, the contraction is concentric; if the muscle length lengthens, the contraction is eccentric. In natural movements that underlie locomotor activity, muscle contractions are multifaceted as they are able to produce changes in length and tension in a time-varying manner. Therefore, neither length nor tension is likely to remain the same in muscles that contract during locomotor activity.
In vertebrates, skeletal muscle contractions are neurogenic as they require synaptic input from motor neurons. A single motor neuron is able to innervate multiple muscle fibers, thereby causing the fibers to contract at the same time. Once innervated, the protein filaments within each skeletal muscle fiber slide past each other to produce a contraction, which is explained by the sliding filament theory. The contraction produced can be described as a twitch, summation, or tetanus, depending on the frequency of action potentials. In skeletal muscles, muscle tension is at its greatest when the muscle is stretched to an intermediate length as described by the length-tension relationship.
Unlike skeletal muscle, the contractions of smooth and cardiac muscles are myogenic (meaning that they are initiated by the smooth or heart muscle cells themselves instead of being stimulated by an outside event such as nerve stimulation), although they can be modulated by stimuli from the autonomic nervous system. The mechanisms of contraction in these muscle tissues are similar to those in skeletal muscle tissues.
Homework Statement
Show that the following linear transformation matrix is a contraction mapping.
\begin{bmatrix}
0.5 & 0 & -1 \\
0 & 0.5 & 1 \\
0 & 0 & 1
\end{bmatrix}
I don't know how to make that into a matrix, but it is a 3x3 matrix. The first row is [.5 0 -1] the second row is [0...
Hi all,
Page 94 of Special relativity by AP French has a worked out example that puzzled me.
This is the example:
Frame S’ has a speed v=0.6c relative to S. Clocks are adjusted so that t=t’=0 at x=x’=0. Two events occur.
Event 1 occurs at x1=10m, t1=2E-7s (y1=0, z1=0).
Event 2 occurs...
I'm confused. If t=γ*t0 and L0=γ*t how does the equation x=v*t hold for x0=v*t0, for constant velocity (Let t0 be the time in the stationary reference frame and t the moving frame, the same for length)? Then v would be equal to γ^2*v... Perhaps I'm missing something here.
I've recently been thinking more about special relativity, and while I understand the Lorentz factor and how to apply it to find correct solutions, I'm still stuck on the link between the effects of length contraction and time dilation, are they permutation of the same thing from different...
I've recently been thinking more about special relativity, and while I understand the Lorentz factor and how to apply it to find correct solutions, I'm still stuck on the link between the effects of length contraction and time dilation, are they permutation of the same thing from different...
I understand the concepts of time dilation and length contraction in SR. I also understand the concept of time dilation in a gravitational field. But what about length contraction in a gravitational field? Is there such a thing and can it be derived from the Schwarzschild metric?
If I am moving through space, things in front of me contract in the direction parallel to my movement. Does this also occur to objects behind me? For example, I look behind me, would things be contracted?
As always, thanks.
Lets say we have an infinite charged wire with a line charge \lambda
on it. Now when I move with respect to this wire the E field will increase do to length contraction. And there will also be a B field that we could calculate with ampere's law.
But the increased E would make it seem...
Mach's principle is considered falls by many because mass anisotropy would not be consistent with the Huges-Drever experiments, which showed the isotropy of nuclear resonance. However, anisotropy appears as well in GR in the form of radial length contraction, which can be interpreted as increase...
My understanding is that as I move, from my FoR all objects and space itself (according to Einstein) contract along the direction of my movement. This length contraction occurs for all space and objects in front of me for an infinite distance. Furthermore, relative motion is relative, and the...
I am confused about these two concupiscences of the consistency of light.
One of my books/notes says that time dilation and length contraction do not happen at the same time because they are 'the same thing' which kind of makes sense but the other says "when we reach relativistic velocities both...
Unfortunately, my knowledge on this is limited to wiki which I trust is relatively correct but I would like to clear up some ambiguity. (I don't mind technical but please back it up with a general explanation since I am completely new to this. The general explanations I value more.)
Wiki...
http://https://www.physicsforums.com/attachment.php?attachmentid=56297&stc=1&d=1362318192 problem:-
The situation is shown in attachment.
the right angled frame of rods (in stationary ) is moving at speed v perpendicular to its hypotenuse.
according to length contraction the corresponding...
Special Relativity states that a ruler flying by at near the speed of light will appear to be shortened as observed by a stationary observer in the lab frame. This is, of course, exactly what happens to macroscopic objects. The question is how far can we push this into microscopic realm...
Hi
I am struggling to see how the relation:
(df:U)(dh:V)-(dh:V)(df:V) (1)
can be rewritten as:
U(fdh:v)-V(fdh:U)-fdh:[U,V] (2)
I have tried expanding (1) out by making a scalar vector product of Udh:V but i don't think that is right and i am just not sure how best to proceed. It was...
according to special relativity theory, any object that has relative
velocity also has lorenz- contraction L' = L0 *sqrt (1-(v/c^2))
it sounds odd that this is only kind of length contraction known to exist.
why there are no other kind of length expansions or contractions, or are them...
Homework Statement
Hey All; I am trying to follow along with the following example in my book, but I am getting lost somewhere.
"We can perform another gedanken experiment to arrive at the same result (showing that length contraction is described as L=Lo/γ; this time we lay the meterstick...
f:[1,infinity)->[1,infinity)
$f(x)=x^{0.5}+x^{-0.5}$
I thought about using MVT but it doesn't work and I've tried showing it conventially but i can't reduce it to k|x-y|
A body with a mass of 2 kg is released from rest a height of 0.4m above the edge of a vertical rested spring with k= 1960 N/m. Assume there is no energy loss in the collision:
1. what's the maximal contraction of the spring?
2. to what height will the body reach back?
about 2 - Because I...
suppose I have a horizontal problem where I have a spring attached to a wall, a body that moves toward it in some inital speed and the surface isn't smooth so I have friction along the surface towards the spring and also while the body contracts the spring. I'm asked what's the maximal...
This is a very common topic especially regarding the apparent slowing down of time, the twins paradox etc.
I have come across the figures for a muon and the relativistic effects that allow it to reach the Earth's surface despite its very short life.
The relevant transforms show length...
Consider observer A at rest, seeing observer B traveling in a rocket at high speed towards a star C. Star C is at rest w.r.t. A.
A in his frame sees B's rocket to be length contracted. B considers his distance to C to be shorter than (contracted) compared to what A sees.
I seem to be...
Am I correct in thinking that the quantum mechanical de broglie wavelength explains relativity's contraction of matter? because lambda = h/p, as the velocity of say a proton increases, the momentum also increases, and the wavelength should get smaller because lim p-->infinity of h/p = 0. At very...
Double contraction of curvature tensor --> Ricci scalar times metric
I'm trying to follow the derivation of the Einstein tensor through double contraction of the covariant derivative of the Bianchi identity. (Carroll presentation.) Only one step in this derivation still puzzles me.
What I...
Hello,
in my other topic members on the forum helped me to understand time dilation by using Minkowski spacetime diagram. Now i would also need some assistance with explaining length contraction in Minkowski spacetime diagram.
I have observer Žiga in his frame ##x,ct## and observer Ranja...
I am on a spacecraft as it makes a journey between two planets. I use a lightpulse to measure the distance before I set off, I then accelerate to a speed that is close to the speed of light and measure the distance again. I find that the distance when I am stationary (relative to the planets)...
Hi, this isn't really a homework problem... but I'm just wondering
I see the time axis as c*t, now people say that its to scale the time axis so that the world line of light is 45 degrees. But if you were to multiply time by the speed of light, wouldn't you just get the units metres or...
Here's a scenario:
A rod shaped object 1m in diameter and 300m in length is moving through space at a velocity of .999994444429013c (picked that velocity arbitrarily for the 300:1 length contraction). The Lorentz factor is 300 for this problem. So the equation to figure length contraction is...
Hi
Consider a spaceship at rest in space, this ship is equipped with a bomb connected to two rings. Once the rings connected to each other, the bomb explodes making the ship also explodes. The proper distance between the rings is one meter. Now consider a conducting rod of proper length one...
Inspired by Aziza's question i came up with a similar, seemingly puzzling question.
Imagine a space-platform with a big cylinder on it. The cylinder has a hole drilled in, with a bomb-button at the end of the hole, which would trigger a bomb destroying the whole galaxy.
A terrorist is on that...
Length Contraction "Ether wind"
Homework Statement
Due to the ether wind, anything that moves along it is "contracted".
The Attempt at a Solution
Taking L1 to be contracted length,
(L1)2
= (L1x)2 + (L1Y)2
= (L10,X/γ)2 + (L10,Y)2But what they wrote is the opposite..
from wikipedia - "The Bohr radius is a physical constant, approximately equal to the most probable distance between the proton and electron in a hydrogen atom in its ground state."
in Planck units bohr radius (a0) = (mp/me).(1/\alpha).(lp)
the 1st 2 terms of the RHS of the equation are...
A spaceship with an arbitrarily large quantity of fuel cells departs Earth and accelerates away from it with a fixed trajectory until it reaches .9c. It continues to accelerate, but never reaches c because that is impossible for any object with mass.
From the frame of reference of the crew...
Hi, I have a question that's been bugging me. For simplicity, assume everything is inertial.
Let's say I take off in a spaceship from Earth towards a distant galaxy at .99999999C - so basically, the trip will be very fast, and let's say in one week time in my reference frame, it will appear...
If I am moving through space at a velocity that is a significant fraction of c, are all objects ahead of me in my path contracted in the direction of my travel for an infinite distance? In other words, are planets and stars from right in front of me to the edge of the known universe contracted...
Would it be possible for a truck, measuring 5ft tall when stationary, to pass under a 4ft barrier by accelerating towards the speed of light?
If so what would a spectator see if standing next to the barrier, would the spectator see the truck shrink? What would you see of the barrier from the...
Hi,
I have attempted the following questions but I am unsure of my answers/method. Could you guys please help me through?
A super fast spacecraft is moving at a speed of 0.80c with respect to the observers on Earth. The spacecraft leaves Earth in May 2004 on its way to a distant solar...
U is the universal rest frame. A and B space ships pass U at t=0, moving at v. Both experience equal length contraction in the x direction.
If length contraction is a result of em deformation in response to acceleration, then length expansion should be the response to deceleration. If the B...
Suppose you've just established the existence of time dilation using Einstein's 1905 postulates and the light clock. Is there any nice, easy way to go on and prove length contraction?
Here are a couple of incorrect arguments that I've been guilty of using in the past:
Symmetry: The Lorentz...
Homework Statement
Two momentarily coincident observers approach a small and distant object. One measures the object to be twice as large as the other's measurement. Find their relative velocity.
Homework Equations
Lorentz Transforms
L/L_0 = \sqrt(1 - \beta^2)
The Attempt at...
Homework Statement
A spaceship moves past you at speed v. You measure the ship to be 300 m long, whereas an astronaut on the ship measures a length of 356 m. Find v.
Homework Equations
L=L1sqrt(1-v^2/c^2)
The Attempt at a Solution
I have tried this by using the above formula. I...
Preparing for a classical prelim by going over previous exams.
Homework Statement
A relativistic meter stick moves with speed v in the lab. It collides head on with an impenetrable wall completely inelastically, thereby coming to rest in the lab frame. What is the maximum length of the stick...
In this thread in another forum, I calculated the coordinate speed of light as measured by a distant observer. As far as I understand it, the length contraction in GR is only in the radial direction, right? None tangent, correct? The time delay of light found, though, trying different examples...
If two clocks with observers attach to them move away from each with symmetrical acceleration, they will experience symmetrical time dilation, meaning they both see the rate of each other's clocks slow down relative to their own. However, if the acceleration is asymmetrical, the time dilation...
1: Does an observer, standing on the moon, see a brick, that is falling straight down, to contract?
2: Does an observer, standing on the moon, see a light pulse, that is falling straight down, to contract?
Homework Statement
The picture shows the settings of the experiment.The aim of this experiment is to investigate about the expansion and contraction of gas.
When the boiling tube is put into boiling water,the coloured water rises as air in the tube expands when heated
When the boiling tube...
OK, I've found a great explanation of the derivation of the Lorentz transformation, with
x' = γ [ x - v t ]
t' = γ [ t - ( v / c2 ) x ]
so if I take the other term as 0, there is
x'( t = 0 ) = γ x
t'( x = 0 ) = γ t
but the problem is that the time dilation & length...
Homework Statement
Two spaceships having rest length 100 m pass each other traveling opposite directions with a relative speed of 0.901 c As the front of the spaceships just cross, each pilot sets off a small flare at the back of her own ship, synchronized to the same instant (t=0 in her own...