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.
Greetings everyone,
I understand the derivation of the Lorentz transformations, and have not had trouble applying the concepts and the math to most elementary SR problems. However, something occurred to me recently which I have been unable to resolve.
Let’s say there are two tennis balls...
i am wondering when i read about planets or solar systems that are like 1million lightyears away, those that take into account length contraction, because if the light is traveling at the speed of light then the distance it has to go will contract.
also another (possibly) stupid question...
Hi,
I have been looking at hoop stresses and the information I have found hasn't been all that useful to me as I am having a hard time converting the thermal contraction of a system into a pressure for the equation (stress=a+b/r^2). This is the thick walled hoop equation
The disc is a few...
Homework Statement
I have a two part question where one has to solve for a velocity to make a moving clock run half the rate as one at rest. Then the second part is what velocity would an object have to move in order to make its length halved.
Homework Equations
t'=t\gamma...
Hi
I am trying to solve this problem. I will present my solution though I couldn't get the tension right.
At 40 Celsius , there is no tension in the wire. When the wires are cooled , they contract and the tension increases. But the tensile stress, which is force per unit area, will remain...
Homework Statement
Derive length contraction using Lorentz invariants.
Homework Equations
ds^2 = dx^2 +dy^2 + dz^2 - c^2 dt^2
The Attempt at a Solution
Consider a rod parallel to the x-axis and moving with velocity v in the x-direction. We can measure the length of the rod of...
I'm having a major mental block to special relativity - i understand it the principle of it but seem to be struggling with time dilation and lenth contraction. I've spent a while thinking that time dilation and length contraction happen both togethor like you can't get one without the other...
Homework Statement
We have the application h: (C[0,1], R) --> (C[0,1], R), defined by
h(f(x)) = \[\int_0^x cos(f(t))/2\, dt \]
Prove that h is a contraction.
Homework Equations
Need to prove there exists k, 0<k<1 s.t.
sup_(x in [0,1]) \left|\int_0^x (cos(f(t)) - cos(g(t)))/2\, dt...
Homework Statement
Let f be a function defined on all of R and assume there is a constant c such that 0<c<1 and |f(x)-f(y)<c|c-y|
a) Show f is continuous on all of R
b)Pick some point y1 in R and construct the sequence (y1,f(y1),f(f(y1)),...)
In general if y_(n+1)=f(yn) show that the...
This was probably asked some time ago. It involves a paradox of relativity and I hope someone can answer it for me:
Imagine a solid cylinder (call this the plunger) with a bar welded to one end making a T. The plunger fits just perfectly into a hollowed cylinder of the same length, and the...
Hey there, I'm having a real hard time understanding exactly how to manipulate tensors (let alone know what they actually are).
I learn brilliantly from example and repetition (the understanding comes later) but the internet and my lecture notes seem to be void of any kind of worked example...
A rod moves along x-axis with speed u and has length L relative to Inertial Frame S. What is its length L' relative to the other inertial S' that moves with speed v with respect to S.
I know the famous length contraction formula L=L' * sqrt(1-square(v/c))
but I confuse how to include...
When a moving observer views a stationary meter stick, it appears contracted. The stationary observer measures it at full length. Similarly, the stationary observer views a moving meter stick as contracted, and the moving observer views it as full length. This is conventional relativity. When a...
Homework Statement
How fast must a pion be moving on average to travel 25 meters before it decays? The average lifetime, at rest, is 2.6 x 10-8s.
Homework Equations
\Deltat =\Deltat0/ sqrt(1 - v2/ c2)
l = l0 * sqrt (1 - v2/ c2)
The Attempt at a Solution
I think that 2.6 x...
1. Homework Statement
Q1) Show that a contraction transformation from V to V has a diagonal matrix representation regardless of the basis given to V (same basis in domain and range).
!2) T(x1,x2,x3)=(x1,x2,x2*x3) find the kernel and range T for this transformation.
2. Homework Equations
3...
Bob, Ed, and Sussie are all observers, each in their own space-ship. Ed and Sussie accelerate on parallel paths to very near the speed of light. Bob sees both length contraction and an increase in mass of both Eds and Sussies ships. These effects are great enough that each ship achieves the mass...
Homework Statement
As a rocket ship moves by at 0.95c a mark is made on a stationary axis at the front end of the rocket and 9 × 10^−8 s later a mark is made on the axis at the back end. The marks are found to be 100 m apart. The rest length of the rocket is:
A. 31m
B. 78m
C. 100m
D...
Hello, I am not sure if I am doing this right or not. It seems to simple to be the right aswer, I feel I must have gone wrong somewhere. Many thanks :-) xxx
Homework Statement
Length Contraction Relativity Question?
An aeroplane is of length L’(m) precisely when measured in its rest...
Hello,
I was reading Einstein's RELATIVITY (his non-mathematical 1916 (or so) book).
Having shown the Lorentz transformation formulas, i.e.
t' = \gamma( t - vx/c^2)
x' = \gamma(x - vt),
he then talks about length contraction. He takes a meter-rod fixed in a certain coordinate system S'...
Homework Statement
Consider a universe in which the speed of light c is equal to 100 mi/h. A lincoln continental traveling at a speed v relative to a fixed radar speed trap overtakes a Volkswagen traveling at the speed limit of 50 mi/h. The lincoln's speed is such that its length, as...
Hi, i asked some quesitons about this before but i need a clarification. Generally we use vertical light clocks and compare the distances taken by light and since c is constant the longer path taken by the light means a dilation in time, from here we say every other type of clcok dilates in same...
I did more than one course of classical electromagnetism in college. Recently, however, after reading "How Relativity Connects Electric and Magnetic Fields" (http://galileo.phys.virginia.edu/classes/252/rel_el_mag.html) I was astounded to realize how little I knew about it! In college (if I...
http://cas.web.cern.ch/cas/Baden/PDF/Relativity.pdf
on pg 16, it says that a muon traveling at a relativistic velocity towards Earth would see the distance to Earth shorted by the gamma factor... i thought the length of the muon is all that is shortened by the factor of gamma? am i wrong here? :s
I'm doing some independent study with a professor at my university. He has taken one GR class and he said that it was not a good experience. So we are in a sense learning together as we pursue this.
We are using the book "A First Course in General Relativity" by Schultz. We are doing problem...
Homework Statement
A spaceship flies past a space station at 0.75c. Observers on the station measure the length of the ship to be 0.30 km. If the ship later docks alongside the station and its length is measured, what would this measured value be?
Homework Equations
d=d0/\gamma
The...
Hi,
I am aware that time dilation has been observed experimentally with atomic clocks on satellites etc. but after a few google searches I have not found anything about experimental confirmation of length contraction. Has this been observed at all? If so, how was it tested?
thanks.
If i have a rod of length L at rest . And there is a hole up ahead that is L/2 and I move the rod at a velocity which will contract it to half its rest length. Will the rod fall into the grate?
Well I think that from the rods point of view its still its rest length and it would appear...
Homework Statement
A meter stick moves with speed .8c relative to frame S. What is the length observed by a person in frame S if the stick is 60 degrees to v, as measured in S?
Homework Equations
L=observed length
l=proper length
y=1/sqrt(1-B^2)
L=l/yThe Attempt at a Solution
Sorry, I suck at...
Hi,
Suppose a stationary frame S' is observing frame S moving with velocity v=0.866c in the x-direction, and let points (4,0),(10,0) define the ends of a rod in S, so its distance is 6, but as measured from S' contracts to 3 because of the Lorentz factor gamma.
I'm unable to determine...
Hi folks,
This is my first post here. I hope this is the right forum for this question.
I am trying to come up with a linear transform to that will take as input a vector (x, y, z) and output a vector that is scaled in the direction of another vector.
For example:
Suppose I...
Assuming 300,000 km/sec for c;
I am in a spaceship which is 300 meters long traveling at 0.5c. A beam of light passes me and I want to measure how long it took to travel the length of my ship.
As c is the same in all frames of reference, I would work this out as distance (300 m) divided by...
Homework Statement
The starships of the Solar Federation are marked with the symbol of the Federation, a circle, whereas starships of the Denebian Empire are marked with the Empire's symbol, an ellipse whose major axis is n times its minor axis (a=nb in the figure ).
Homework Equations...
the proper length is the length where we can measure the length, with one clock( not moving)
and for someone looking at it as i moves it seems contracted.. how does this happen i do not under stand could someone explain
thanks in advance
Seto.
hello,
how is it possible to calculate the only GRAVITATIONNAL time dilation and length contraction factor in the Kerr metric and/or the Kerr-Newman metric, for an object falling but otherwise at rest, since there is frame dragging, and the metric contains dt^2 components but also dt.dphi...
I have a curiosity. I do not have a degree in science (going to university later this year) so this should be very simple to follow. I'm looking for a refutation (preferably with words and not unnecessary equations), confirmation, maybe a link to this sort of stuff.
I'm aware that as an...
Do fast moving objects in relative motion always observe length contraction regardless of their direction of travel? In every example I find the train or the rod appears to be “moving toward you.” I can’t find any thought experiments describing what happens after you pass the train and it...
So in Analysis I we explained the convergence of cos to a fixed value by Banach's contraction theorem. But is the cos a strict contraction? Is that obvious? (What is its contraction factor?)
The terms "length contraction" and "time dilation"
Is there a particular reason why we say length contraction but time dilation? A Lorentz transformation \Lambda=\gamma\begin{pmatrix}1 & -v\\ -v & 1\end{pmatrix} takes \begin{pmatrix}1\\ 0\end{pmatrix} to \gamma\begin{pmatrix}1\\...
Homework Statement
I've been reading a textbook on tensor analysis for a while. The book uses the conclusion of "covariant differentiation commutes with contraction" directly and I searched around and found most people just use the conclusion without proof.Homework Equations
For example...
My question is: why does Lorentz contraction happens?
I have a understanding of this but I don't know if it's correct, so I'll tell what I understand, if I'm wrong please correct me...
Suppose we have two observers A and B. If I say B is moving with respect to A then time is slower to B...
Homework Statement
Q1 http://www.maths.ox.ac.uk/system/files/private/active/0/b07.2_c7.2.pdf
Homework Equations
The Attempt at a Solution
How do I do the final bit that lead to the discrepancy and why does this occur? I have no idea where to begin.
By what factor would the radius parallel to the direction of travel contract for a 7 TeV proton, relative to an antiparallel 7 TeV proton, in the Large Hadron Collider?
Can length contraction be treated as a vector?
E.g.
Suppose I am traveling 10 degrees north of east. Will my length contraction with respect to the east direction be cos 10 times the appropriate Lorentz transformation (with respect to the direction of motion)?
Thanks.
My interest surrounds the qualities and affects of gravitational length contraction (GLC).
Like most other General Relativity circumstances GLC is difficult to measure because of frame of reference issues (such that a meter in space is longer than a meter on Earth but in both frames of...
Homework Statement
Consider the function g : [0,∞) → R defined by g(x) = x + e−2x.
Given |g(x2) − g(x1)| < |x2 − x1| for all x1, x2 ∈ [0,∞) with x1 ≠ x2.
Is g a contraction on [0,∞)? Why?
Homework Equations
I think we are intended to use the given equation and the CMT
CMT states that...
As I understand it, Lorentz Contraction states an object "contracts" relative to it's velocity to an observer.
So at a high velocity of speed, the meter stick (carried by the object moving relative to the observer) appears to contract (to the observer) and the observer measures less distance...
Hi
Homework Statement
As the sun evolved to the main sequence it contracted under gravity and its internal temperature changed from 3E4 K to 6E6 K. Assuming the sun is fully ionised at these temperatures estimate the energy radiated during this phase, stating your assumptions.
Homework...
Hi, i asked this before but i think i found a clearer way to define my quesiton. As i asked in the title, does length contradicts as a result of time dilation? Or time dilation and length contraction are equal?
When we deal with formulas generally we use the vertical clock and derive time...
Homework Statement
Suppose that the speed of light in a vacuum ( c), instead of being a whooping 3x108, was a rather sluggish 40.0 mph. How would that affect everyday life? Throughout this problem we are going to assume that c = 40.0 mph and that time dilation is in full effect. Let's start...