You are working for a manufacturing company, which is mathematically given as
<h3>What is the
value of m that will place the
movable bead in equilibrium at x-a a ....?</h3>
a)
Generally, the equation for the force of equilibrium is mathematically given as
F=2fcos\theta
Therefore
![K(npq^2/a^2)=2\frac{kmpq^2}{a\sqrt{2}^2}0.5\\\\np=mP/ \sqrt{2}\\\\where n=3](https://tex.z-dn.net/?f=K%28npq%5E2%2Fa%5E2%29%3D2%5Cfrac%7Bkmpq%5E2%7D%7Ba%5Csqrt%7B2%7D%5E2%7D0.5%5C%5C%5C%5Cnp%3DmP%2F%20%5Csqrt%7B2%7D%5C%5C%5C%5Cwhere%20n%3D3)
![m=3\sqrt{2}](https://tex.z-dn.net/?f=m%3D3%5Csqrt%7B2%7D)
b)
By force equilibrium
![K(npq^2/(2a^2))=2*\frac{kmpq^2}{a\sqrt{5a}^2}* \frac{2a}{\sart{5a}}](https://tex.z-dn.net/?f=K%28npq%5E2%2F%282a%5E2%29%29%3D2%2A%5Cfrac%7Bkmpq%5E2%7D%7Ba%5Csqrt%7B5a%7D%5E2%7D%2A%20%5Cfrac%7B2a%7D%7B%5Csart%7B5a%7D%7D)
Therefore
![n/4=2/5*m*2/\sqrt{5}\\\\m= \frac{5\sqrt{5}}{16}\\\\\\\\](https://tex.z-dn.net/?f=n%2F4%3D2%2F5%2Am%2A2%2F%5Csqrt%7B5%7D%5C%5C%5C%5Cm%3D%20%5Cfrac%7B5%5Csqrt%7B5%7D%7D%7B16%7D%5C%5C%5C%5C%5C%5C%5C%5C)
![m=\frac{15\sqrt{5}}{16}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B15%5Csqrt%7B5%7D%7D%7B16%7D)
c)
![K(npq^2/x^2)=2\frac{kmpq^2}{a\sqrt{x^2+a^2}^2}0.5*x/\sqrt{x^2+a^2}](https://tex.z-dn.net/?f=K%28npq%5E2%2Fx%5E2%29%3D2%5Cfrac%7Bkmpq%5E2%7D%7Ba%5Csqrt%7Bx%5E2%2Ba%5E2%7D%5E2%7D0.5%2Ax%2F%5Csqrt%7Bx%5E2%2Ba%5E2%7D)
x^2+a^2=(14/3)^{2/3}x^2
x=a/1.338
x=0.747a
d)
By force equilibrium
![K(npq^2/x^2)=2\frac{kmpq^2n}{\sqrt{x^2+a^{3/2}}^2}\\\\n/x^2=\frac{2mx}{(x^2+a^2)^{3/2}}](https://tex.z-dn.net/?f=K%28npq%5E2%2Fx%5E2%29%3D2%5Cfrac%7Bkmpq%5E2n%7D%7B%5Csqrt%7Bx%5E2%2Ba%5E%7B3%2F2%7D%7D%5E2%7D%5C%5C%5C%5Cn%2Fx%5E2%3D%5Cfrac%7B2mx%7D%7B%28x%5E2%2Ba%5E2%29%5E%7B3%2F2%7D%7D)
![m/n=\frac{(x^2+a^2)3/2}{x^3}](https://tex.z-dn.net/?f=m%2Fn%3D%5Cfrac%7B%28x%5E2%2Ba%5E2%293%2F2%7D%7Bx%5E3%7D)
Read more about electric fields
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The total mass of the mixture would not change.
Think about it as a mix of marbles. Suppose you have a group of 10 marbles. 5 marbles are red, and 5 marbles are blue. If you separate the marbles into 2 different groups by color, you still have 10 marbles in total, but they are separated and no longer a mixture of colors.
Answer:
C. C
Explanation:
A wave can be defined as a disturbance in a medium that progressively transports energy from a source location to another location without the transportation of matter.
In Science, there are two (2) types of wave and these include;
I. <u>Electromagnetic waves</u>: it doesn't require a medium for its propagation and as such can travel through an empty space or vacuum. An example of an electromagnetic wave is light.
II. <u>Mechanical waves</u>: it requires a medium for its propagation and as such can't travel through an empty space or vacuum. An example of a mechanical wave is sound.
A crest can be defined as the highest (vertically) point on a waveform.
On a related note, a trough is the lowest (vertically) on a waveform.
An amplitude can be defined as a waveform that's measured from the center line (its origin or equilibrium position) to the bottom of a trough or top of a crest. Thus, the vertical axis (y-axis) is the amplitude of a waveform i.e it's measured vertically.
In this scenario, waveform C which is represented by a blue curvy line has the smallest amplitude in comparison with the other waveforms because it has the minimum height when measured from the origin.
In contrast, waveform A represented by a purple line has the highest amplitude because it has the maximum height when measured from the origin.
Mathematically, the amplitude of a wave is given by the formula;
x = Asin(ωt + ϕ)
<u>Where;</u>
- <em>x is displacement of the wave measured in meters.</em>
- <em>A is the amplitude.</em>
- <em>ω is the angular frequency measured in rad/s.</em>
- <em>t is the time period measured in seconds.</em>
- <em>ϕ is the phase angle.</em>
Hello
we can use the equation
E=mc️T
If we rearrange this to get the mass our new equation is
E/cT=mass
We have
E as 650J
c as 130J/kg⁰
️T as 45-19=26⁰
E/c️T=m
650/(130*26)=0.19 kg
That's your answer, hope it helps!
Also just a note T here is denoted as delta T showing change in temperature