What is Linear density: Definition and 26 Discussions
Linear density is the measure of a quantity of any characteristic value per unit of length. Linear mass density (titer in textile engineering, the amount of mass per unit length) and linear charge density (the amount of electric charge per unit length) are two common examples used in science and engineering.
The term linear density is most often used when describing the characteristics of one-dimensional objects, although linear density can also be used to describe the density of a three-dimensional quantity along one particular dimension. Just as density is most often used to mean mass density, the term linear density likewise often refers to linear mass density. However, this is only one example of a linear density, as any quantity can be measured in terms of its value along one dimension.
I attached a drawing of the problem for a better understanding and my attempted solutions.
The first point is fairly simple but there's something that I can't figure out.
dq=λdx=kxdx
Q=∫ k x dx from 0 to L -> Q=k[x^2/2]0-L -> Q=(L^2/2)k -> k=2Q/L^2
This is what I came up with. I integrated...
I am trying to choose Elevator wire, chart shows max load reading in KG/m. Does it mean if length increases weight will increases as well ?
Example;
If max load of wire is 0.492kg/m.
And i am using 2 meter does it mean capacity of wire would be 0.984 kg/m.
Given a square with a linear mass density of:
λ(x) = a * x (see image below where black is high density and white is low density)
how would you deduce what the surface mass density is?
I get confused for the following reason:
To me it seems that the surface mass density should depend on x...
Homework Statement
A charged, straight line/rod of infinite length has a Discrete uniform distribution of charge, has a linear density of λ and is at a distance d from a sphere with a radius of R.
Find the entirety of the Electrical Flux that is caused by this charged rod, which passes...
Homework Statement
A line charge with a uniform linear charge density Lambda lies along the x-axis and extends from -∞ to 0. Determine the X-component, and Y-component of the E-field at a point P, a distance 'a' from the origin on the positive y-axis.
Homework Equations
dE= (k*dq/r^2)* r(hat)...
Homework Statement
I need to find the final impact speed of the flame of a non-uniform candle. I am given that the mass per unit length increases linearly from top to bottom starting with 1kg/m at the bottom and 10kg/m at the top. I need to find how fast the candle flame is moving once the...
Homework Statement
The figure shows two masses hanging from a steel wire. The mass of the wire is 60.5 g . A wave pulse travels along the wire from point 1 to point 2 in 24.0 ms .
https://session.masteringphysics.com/problemAsset/1383975/6/knight_Figure_20_80.jpg
//What is mass m?
Homework...
Homework Statement
A geologist is at the bottom of a mine shaft next to a box suspended by a vertical rope. The geologist sends a signal to his colleague at the top by initiating a wave pulse at the bottom of the rope that travels to the top of the rope. The mass of the box is 20.0 kg and the...
Would it be correct to assume that if the linear density of a rope changes by a factor of k, then the amplitude of a wave traveling on the rope would change by a factor of \frac{1}{\sqrt{k}}? (Assuming tension and frequency are fixed.)
I get this by assuming the average power of the wave is...
The string on the violin with the highest pitch is the note E, which has a frequency of 329.6 Hz and a wavelength of 1.032 m. If the string has a mass of 180.0 g and a length of 32.0 cm and is currently producing a wave of frequency 328.1 Hz, how much do you need to change the tension in the...
Homework Statement
A rod with charge linear density λ is located at the long axis of a cylinder with charge linear density 2λ. With this information use Gauss's law to find (a) the charge linear density on the interior and exterior surfaces of the cylinder (b) the electric field outside of the...
Please look a picture.
I think the book made a mistake.
The answer should be 89.9N/m.
Why? Because they calculated the linear density μ wrongly. They should have done $$\frac{75*10^{-3}kg}{1.8m}$$
I hope someone can point me in the right direction on how to solve this, and hopefully I can explain it properly.
Given a rod with a known length, mass and center of mass, how can I find the linear density at a given location (x) along the length of the rod. I want to say 'instantaneous'...
Homework Statement
It's for our termpaper thing and i can't get any reliable sources on the net, so might get a shot at asking it here, What are the Differences between Area and Linear Density?
Homework Equations
The Attempt at a Solution
Homework Statement
If you were given the
- linear density 1 = 2g/m
- linear density 2 = 4g/,
- total length of the strings = 4m
- Length 1 > Length 2
- the fact that when a pulse is sent from a knot in the strings it reaches the ends at the same time
How would you go about working...
Homework Statement
A metal rod is 50cm long. Its linear density at the point x cm from the left end is given by the equation p(x)=1/(100-x) gm/cm. Find the mass and center of mass for the rod.
Homework Equations
mass = \int p(x)dx
center of mass = moment / mass
The Attempt at a...
Homework Statement
The mass of part of a wire is x(1+sqrt(x)) kilograms, where x
is measured in meters from one end of the wire. Find the
linear density of the wire when x=4m.
2. The attempt at a solution
Actually what i did was put in x = 4 in the mass equation given and divide...
Homework Statement
An infinite slab of charge with thickness d (from x=0 to x=d) in the x direction has a charge density corrosponding to rho (x) = Ax+B where A and B are positive consants.
Find the electric field at point x1<d
Homework Equations
I know i have to find some guassian...
Unit Cell -- Linear Density -- BCC&FCC
Homework Statement
Calculate the linear density for the most densely packed directions in BCC and FCC. Note the difference in linear density. Note the difference in linear density.
Homework Equations
LD = #of atoms/length
The Attempt at a...
Homework Statement
The wave speed on a string is 155 m/s when the tension is 84.0 N.
What tension will give a speed of 182 m/s?
Homework Equations
velocity= Squareroot(tension/linear density)
linear density = mass/length
The Attempt at a Solution
Well, what I did was...
Homework Statement
In Fig. below, a string, tied to a sinusoidal oscillator at P and running over a support at Q, is stretched by a block of mass m.The separation L between P and Q is 2.30 m, and the frequency f of the oscillator is fixed at 142 Hz. The amplitude of the motion at P is small...
Homework Statement
A long line carrying a uniform linear charge density + 50.0*10^-6C/m runs parallel to and 10.0 cm from the surface of a large, flat plastic sheet that has a uniform surface charge density of - 100*10^-6C/m^2
Find the location of all points where an alpha particle would...
(Sorry I cannot follow the question format because this question is related to a problem, but is not the problem itself.)
I am talking about the linear density μ that appears in this equation:
v = sqrt(T/μ)
.. used usually for musical instruments, where μ = m/L
Now, I am wondering which...
Waves on a String "linear density?"
Two steel guitar strings have the same length. String A has a diameter of .5mm and is under 410N of tension. String B has a diameter of 1.0mm and is under a tension of 820N. Find the ratio of the wave speeds, v_a/v_b, in these two strings.
Linear...
Would anyone be able to give me a hint for this question? Do I take the integral? I have possible answers but I am unsure.
A rod of length 30.0 cm has a linear density given by:
D = 50.0g/m + 20.0xg/m^2
where x is the distance from one end measured in meters. a. What is the mass of...