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.
[SOLVED] Help: Length Contraction and changing Frames
Hi i have been learning about length contraction and i thought i understand how it works until i was given this question.
A very fast train of proper length Lo rushes through a station which has a plaform of length L(<Lo).
According to...
Homework Statement
A bar (lo = 10mm) is moving along the x-axis with speed v according to a referential R.
Meanwhile a table, parallel to the bar is moving along the z axis, with speed u. There's a circular hole in the table with radius = 5mm.
From R perspective the bar has l < 10mm and it...
Hi, I am an undergraduate, doing an experiment regarding of minor losses due to sudden contraction. However, I found that my theoretical loss is higher than the experimental loss.
The flow rate = 3.28*10^-4 (m^3/s)
(Inner diameter) D1= 3.652*10^-2 m
(Inner diameter) D2= 1.539*10^-2 m
by...
Bear with me. I am a lawyer, not a physicist... I understand how the light clock demonstrates time dilation with special relativity. I think I understand length contraction.
Here is my question: at relativistic speeds, why does length contraction not affect the distance traveled by the light...
I am not a physics student (my background is that of an engineer + MBA) but have read a lot about relativity and have built up a fair level of understanding.
I just thought up a situation regarding Lorentz contraction that has kind of confused my understanding of the same. Consider the...
So I have been trying to wrap my head around time dilation and length contraction... It is all good until i come to the point to derive length contraction from time dilation...
So we have
\gamma \Delta \tau = \Delta t
\gamma L = L_0
So now from my lecture notes i have an observer...
Hello, I recently learned of the Lorentz contraction and mass distortion effect in a physics
book, and for the sheer heck of it, I decided to see what it would be like if my dog, Little
Ann, were sped up to relativistic speeds. I decided to try to calculate it using the equations
provided by...
Problems on "Length contraction"
Homework Statement
This is a problem in my text. The idea is that a bar is moving with a high speed (say 0.5c) relative to us. We now want to know what will be the length appeared to us if the bar is parallel, perpendicular and 60 degrees tilted. And we are...
Homework Statement
The gravitational potential energy W of a self-gravitating sphere of mass M and radius R depends on the detailed distribution of mass within the sphere, but it is generally of order of magnitude -GM^2/R. For the Sun, W_sun = -2G(M_sun)^2/R. What is the timescale
t =...
Consider what happens when we accelerate a box filled with gas. We have to expend a certain amount of energy to accelerate the box, In Newtonian mechanics, this energy goes into the kinetic energy of the box: as its speed increases so does its kinetic energy.
This happens in relativity too, of...
why does the einstein field tensor have the riemann tensor contracted? I am confused as to what purpose it serves. I have seen an explanation that it gets rid of extra information about spacetime or something like that. and also is the Ricci scalar added to einstein tensor so that the covariant...
Textbooks I know derive the formula that accounts for the time dilation by measuring simultaneously the space coordinates of a moving rod.
Is there another way to derive it?
A rod of length 2l is at rest in frame O' with co-ords (x',y',z')=(±l,λ,0)
Observer O moves at speed u along the x axis.
The first part of the question is just to derive the length contraction - fine, O measures the length as 2l / γ
The next part has me stuck:
"Show that, at t = 0...
Please tell me if it is possible to derive the formula which accounts for the Lorentz contraction from the invariance of the space-time interval.
Thanks
Consider some material object, more or less rigid, with two ends, A and B, like
A---B
It is at rest at a point in time t_0 in my reference frame. Now I kick it a bit, i.e. I apply some force for a limited amount of time at A in the direction of B. After the kick, the whole object has a...
De Sitter relativity and Lorentz contraction
I need help in understanding the elements of a paper that I think could turn out to be quite important, namely http://arxiv.org/abs/0711.2274 de Sitter Relativity: a New Road to Quantum Gravity
R. Aldrovandi, J. G. Pereira)
Inter aliathey say...
Directly from the Peskin & Shroeder, page 63:
S_F(x-y) = \int\frac{d^4p}{(2\pi)^4}\frac{i(\displaystyle{\not}p + m)}{p^2-m^2+i\epsilon} e^{-ip\cdot(x-y)}
I'm slightly confused with the notation with the contractions. Things like \overline{\psi}(x)\psi(y) and \psi(x)\overline{\psi}(y) get...
Has it been shown that observed length contraction that occurs due to high relativistic speeds is any different from that that appear due to the additional time it take a signal from the trailing edge of object (as opposed to the leading edge) to reach an observer? If not, then obviously a...
Now, if I'm not mistaken, from the Lorentz transformations one derives the following equations for time dilation and length contraction, respectively:
T'=gT
L'=gL
Where g is the gamma factor, forgive my sloppy representations, but I'm not well versed in Latex.
However, the equation for...
Let Y_{1},..,Y_{k} be vector fields and let A be a tensor field of type ^{k}_{1}. Could you explain how applying k contractions to A\otimesY_{1}\otimes...Y_{k} yields A(Y_{1}...Y_{k})?
Actually, could you first explain why contraction of w\otimesY is equal to w(Y)?
Here, w is a 1-form and Y...
Homework Statement
Two lightning bolts strike the ends of a moving boxcar (Points A and B). The boxcar has length 2d and is moving at a speed v. A stationary observes both lightning bolts hitting the boxcar simultaneously. An observer in the car, however, claims that the front (position B') of...
Ive heard that length contraction does not occur when the movement of the object is perpendicular to the observer. Is this correct?
Say two identical rings were traveling at each other at relativistic speeds, whilst the observer is perpendicular to them. Ring A would see ring B contract and...
Homework Statement
A rod of length L_0 moves with a speed v along the horizontal direction. The rod makes an angle of \vartheta_0 with respect to the x'-axis.
(a) Show that the length of the rod as measured by a stationary observer is given by
L = L_0 [1-(v/c)^{2} cos ^{2} (...
question for the Lorentz's space contraction
I imagin this thought experiment: a train which travels with the speed of light is trying to enter a tunel which has absolutely the same form and dimmension like the train's shape, as if the the train goes slowly with his regular speed it will enter...
My impression was that only misinformed people argue that LQG discreteness is in conflict with Lorentz invariance. This was resolved a long time ago, i thought.
Does anyone disagree? Want to talk about it? Explain something to me that I am missing?
http://arxiv.org/abs/gr-qc/0205108
Reconcile...
car 2 is twice as long as car 1 when they are at rest
a stationary policeman observes that car 2 is the same length as car 1 as car 2 passes car 1 going through a speed trap.
car 1 is going 1/2 the speed of light
I tried to solve this with
L 1/sqrt(1-(1/2)^2) = 2L/sqrt(1-v^2/c^2) and...
Homework Statement
Supersonic jets achieve maximum speeds of about (3 *10^-6)*c.
By what percentage would observe such a jet to be contracted in length?
Homework Equations
The equations for these this problem would be : 1/gamma= L(proper)/Length = 1/sqrt(1-v^2/c^2) ; beta=v/c
The...
Hi all,
I'm teaching myself the algebraic side of tensors and I was wondering if you would be able to clarify a few things for me.
I prefer to think of a tensor in the set theoretic manner as a multi-linear mapping taking several copies of a vector space and its dual space to the base...
R' is an observer from I'. A rod is in a state of rest relative to him. He measures its proper length L(0). An observer R from I measures its Lorentz contracted length L related by
L=L(0)sqrt(1-vv/cc) (1). If we reverse the situation, R measuring the proper length of the rod R' measuring its...
Using the concept of length contraction and time dilation explain how is it possible to travel a distance of 1mln light years during the life of a single person?
thanks for any help
Based on the Michelson Morley experiment, Lorentz proposed already length contraction as an explanation of the negative outcome of the experiment.
a) Did he also propose time dilation?
b) How is width contraction ruled out: is that a necessary conclusion of the Michelson Morley experiment or...
A rod. having slope m relative to the x-axis of S, moves in the x direction at speed u. what is the rod's slope in the usual second frame S'? (S is at rest realtive to S' which moves along the x direction with velocity v).
well obviously the horizontal length of the rod is contracted or...
If I can explain a special relativistic effect with both Lorentz-Fitzgerald Contraction and Time Dilation, then which one is the correct answer?
Because, for example in the experiment with the muons coming from the atmosphere, the explanation was Time Dilation, but we can explain it with...
Hello,
I am working on the following problem and cannot figure out if I am doing the problem incorrectly or if my professor gave us the wrong answer. (I think that the former is the issue.)
1. Homework Statement [/b]
To a stationary observer two frogs at opposite ends of a 100m long lake...
Here is the question
--------
Give an example of a function f:[a,b] \to \mathbb{R} which is continuously differentiable and which is a strict contraction, but such that |f'(x)| = 1 for at least one value of x \in [a,b].
--------
Continuously differentiable means that the first derivative is...
Here is the question from our book:
-------
Let (X,d) be a complete metric space, and let f:X\to X and g:X\to X be two strict contractions on X with contraction coefficients c and c' respectively. From the Contraction Mapping Theorem we know that f has some fixed point x_0, and g has some fixed...
Hi...
I know that this question will be found little bit stupid, but unfortunatly I can't see where I made a mistake.
Let's have stick with light sources on both ends. In stick's reference frame the flashes from both sources are simultaneous. In laboratory ref. frame they are not. However...
Homework Statement
Two powerless rockets are on a collision course. They are moving with speeds 0.800c (ship 1) and 0.600c (ship 2) and are initially 2.25*10^12 m apart. The ships are both 50m in length as observed by a stationary observer on earth.
a) what are their respective proper...
as the sun evolved it contracted, its internal energy changing fro x to y. what's the total energy radiated, assuming luminosity is comparable with present?
I understand that the rate of change of the internal energy = rate at which energy is radiated away by the star.. but i have been...
I have some questions about the relative factor:
1/'root'1-v^2/c^2
If an object moves close to the speed of light, the length contraction becomes significant.
I hear this "paradox": (that was said not to be a paradox, but I didn't understand it) A train of 100 meter moves at a speed...
Homework Statement
An electron travaels in an accelerator tube at a speed of 0.997 c relative to Earth. In the frame of reference of the electron, the length of the tube is 1.20 m. What is the length of the tube relative to earth?
Homework Equations
L = Lo / γ
Textbook answer: 15.5 m...
Homework Statement
The distance between the Earth and Alpha Centauri is 4.2 light years (1 light year is the distance traveled by light in one year). If astronauts could travel at v = 0.95c, then we on Earth would assume that the trip would take the astronauts 4.2 / 0.95 = 4.4 years. The...
Time dilation and length contraction are expressed by the following equations:
L=L'*sqrt(1-(v^2/c^2))
T=T'/sqrt(1-(v^2/c^2))
However, according to the principle of relativity, you can't tell which is the fixed frame of reference and which the moving frame, so you can swap L and L' and T...
Hello guys. Here I am, bothering all of you again...
I am having troubles proving the following:
For v \in V and \omega \in \Lambda^k(V), show that if v_1,v_2,...,v_n is a basis of V with dual basis \phi_1,\phi_2,...,\phi_n then
i_{v_j}(\phi_{i_1}\wedge ... \wedge \phi_{i_k})=\left\{...
consider a rod of proper length Lo located along the overlapped OX(O'X') axes of the I and I' inertial reference frames in the standard arrangement I' moving relative to I' with speed V. The rod moves with speed U relative to I and with speed U' relative to I'. The measured length of the rod is...
A short question this time :
Is the gravitational length contraction an effect which acts parallel as well as perpendicular to the direction of the gravitational field ?
I suppose it is not occurring perpendicular to it, but I might be wrong and I didn't find a good reference on it.
if you have a row of blocks, all touching each other in your frame, then when observed from a frame moving relative to you in the direction of the blocks will the contraction make the blocks look as if they're not touching - each one will be shorter but the total length of the row will be almost...
Relativity
Two balls move with speed v along a line toward two people standing along the same line. The proper distance b/w the people is L, and the proper distance b/w the ball is γL [Note: γ is gamma]. Due to length contraction, the people measure the distance b/w the ball to be L, so the...
What does the factor that you get when you plug the length contraction and time dilation of a moving object back into the form of meters/second represent?