New answers tagged string
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Solving for deceptively simple two-block pulley system
We can analyse the forces acting on each pulley, which must add up to $0$ assuming the ropes and pulleys have no mass. It is obvious that there’s no physical solution to this problem without ...
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Solving for deceptively simple two-block pulley system
Let's define coordinates: $m$ has $x_1$, $2m$ has $x_2$ and the block above $m$ has $x_0$. Overall length of the string will therefore be expressed:
$$ l = 2x_2 + x_1 - x_0 $$
Differentiating this ...
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How can we prove that tension on both sides of string will be equal?
The string is massless and inextensible; so if there is a net force on any part of the string it will cause its acceleration.
Since m approaches zero, acceleration for even a small unbalanced force ...
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How can we prove that tension on both sides of string will be equal?
Let me put it one more way:
If the tensions at two points of the string were different, the string piece between these two points would experience a net force from the tension difference.
There are no ...
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6
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Accepted
How can we prove that tension on both sides of string will be equal?
$\dots$ the tension on both sides of mass $m$ will be equal $\dots$ if there is no friction between the bead and the string.
If there are no frictional forces then the fact that the string is massless ...
- 93.4k
4
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How can we prove that tension on both sides of string will be equal?
The phrase "inextensible string" and the fact it's tied down at a point, is what determines that the tension at every point along the string is the same:
"Inextensible" doesn't ...
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8
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How can we prove that tension on both sides of string will be equal?
"A massless inextensible string wearing a bead of mass m"
From this line I assume there is only one string used throughout, and is passed through the hollow centre of the bead.
As long as ...
1
vote
Accepted
Newton's globe experiment with linear acceleration?
To ensure that there is no relative motion in the case of linearly accelerated motion, the same amount of force must act at every point of the moving body. If this is the case, there is no noticeable ...
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Three masses connected by a string (momentum conservation)
Note sure why you think A will collide with B, or what "collide without contact" means. My interpretation of the scenario is that B moves in the positive $y$ direction, A and C are pulled ...
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0
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Accepted
Three masses connected by a string (momentum conservation)
Firstly, the net external force acting on the system (all 3 bodies) is zero, which means that you are free to use the laws of conservation of energy and momentum.
You need to understand that the ...
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How is the curvature of a vibrating string defined in classical mechanics?
By definition curvature is differential angular displacement vs differential arc length.
$\kappa = \frac{d \theta}{ds}$
$\tan \theta = y'\implies \sec ^2\theta (d\theta /dx) = y''\implies \frac{d \...
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How is the curvature of a vibrating string defined in classical mechanics?
I am not sure to understand the question. Also because two comments by Ghoster already implicitly answered the same. However, the curvature is, by definition, the inverse of the curvature radius. The ...
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Determining the equations of motion for a 2 DOF in 2 directions
You are correct in trying to establish the equivalent mass of the pulley $m_p$ and place it inline with the rest of the system
You can work out what $m_p$ should be by taking the pulley at rest and ...
- 37.4k
2
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Where would a string with multiple points of equal weakness break?
As you pull from both ends, the string begins to accelerate and stretch slightly. The stretching force propagates through the string at the speed of sound - there is a period of time where the middle ...
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Where would a string with multiple points of equal weakness break?
Force propagates through the string at the speed of sound (in the string). So your final assumption would be correct. The outermost weak points will feel the pull before the more distant weak points ...
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Tension in a vibrating loop
Your first equation that states frequency is velocity divide by wave length. But this is not a basic law of motion but in fact is just a definition. It assumes there is a trigonometric function. Then ...
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String vibration and damping
First, the question contains an error because it assumes the initial condition of the string is determined by an “arbitrary initial condition” but the initial condition is the string length and ...
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How does a string thickness affect the frequency of its harmonics?
The ideal string has:
$$ f_n = nf_0 $$
for the $n$-th harmonic.
Including a finite thickness modifies that to:
$$ f_n = nf_0\sqrt{1+Bn^2}\big(1+\frac 2{pi}\sqrt B
+ \frac 4{\pi} B\big) $$
with
$$B = \...
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0
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Deriving the longitudinal sound wave from the transverse string vibration
The sound waves are produced by a moving surface that is the minimum surface of revolution formed by the string orbit. Your graph has the correct curve but the orbit of the string is that curve ...
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How does a string thickness affect the frequency of its harmonics?
Generally you try to excite many harmonics when you play an instrument. You can see this by the fact that a piano hammers the strings near the end. Likewise a guitar or violin.
The strings do not ...
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