The other lights wouldn't be affected?
:/
Answer:
muddy water is a heterogeneous mixture, which is Suspension.
Answer:
ω = √(2T / (mL))
Explanation:
(a) Draw a free body diagram of the mass. There are two tension forces, one pulling down and left, the other pulling down and right.
The x-components of the tension forces cancel each other out, so the net force is in the y direction:
∑F = -2T sin θ, where θ is the angle from the horizontal.
For small angles, sin θ ≈ tan θ.
∑F = -2T tan θ
∑F = -2T (Δy / L)
(b) For a spring, the restoring force is F = -kx, and the frequency is ω = √(k/m). (This is derived by solving a second order differential equation.)
In this case, k = 2T/L, so the frequency is:
ω = √((2T/L) / m)
ω = √(2T / (mL))
Answer:
F=8.0*10^{-10}N
Explanation:
See the attached file for the masses distributions
The force between two masses at distance r is expressed as

since the masses are of the same value, the above formula can be reduce to

using vector notation,Let use consider the force on the lower left corner of the mass due to the upper left side of the mass is

The force on the lower left corner of the mass due to the lower right side of the mass is

The force on the lower left corner of the mass due to the upper right side of the mass is

The net force can be express as
![F=\frac{Gm^{2}}{r^{2} }j +\frac{Gm^{2}}{r^{2} }i +\frac{Gm^{2}}{d^{2} }cos\alpha i +\frac{Gm^{2}}{d^{2} }sin\alpha j\\\\F=Gm^{2}[\frac{1}{r^{2}}+ \frac{1}{d^{2}cos\alpha }]i + Gm^{2}[\frac{1}{r^{2}}+ \frac{1}{d^{2}sin\alpha }]j\\\alpha=45^{0}, G=6.67*10^{-11}Nmkg^{-2}](https://tex.z-dn.net/?f=F%3D%5Cfrac%7BGm%5E%7B2%7D%7D%7Br%5E%7B2%7D%20%7Dj%20%2B%5Cfrac%7BGm%5E%7B2%7D%7D%7Br%5E%7B2%7D%20%7Di%20%2B%5Cfrac%7BGm%5E%7B2%7D%7D%7Bd%5E%7B2%7D%20%7Dcos%5Calpha%20i%20%2B%5Cfrac%7BGm%5E%7B2%7D%7D%7Bd%5E%7B2%7D%20%7Dsin%5Calpha%20j%5C%5C%5C%5CF%3DGm%5E%7B2%7D%5B%5Cfrac%7B1%7D%7Br%5E%7B2%7D%7D%2B%20%5Cfrac%7B1%7D%7Bd%5E%7B2%7Dcos%5Calpha%20%7D%5Di%20%2B%20Gm%5E%7B2%7D%5B%5Cfrac%7B1%7D%7Br%5E%7B2%7D%7D%2B%20%5Cfrac%7B1%7D%7Bd%5E%7B2%7Dsin%5Calpha%20%7D%5Dj%5C%5C%5Calpha%3D45%5E%7B0%7D%2C%20G%3D6.67%2A10%5E%7B-11%7DNmkg%5E%7B-2%7D)
if we insert values we arrive at
![F=6.67*10^{-11}*2.5^{2}[\frac{1}{1^{2}}+ \frac{1}{\sqrt{2}^{2}cos45 }]i + 6.67*10^{-11}*2.5^{2}[\frac{1}{1^{2}}+ \frac{1}{\sqrt{2}^{2}sin45}]j\\F=5.643*10^{-10}i+5.643*10^{-10}j](https://tex.z-dn.net/?f=F%3D6.67%2A10%5E%7B-11%7D%2A2.5%5E%7B2%7D%5B%5Cfrac%7B1%7D%7B1%5E%7B2%7D%7D%2B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%5E%7B2%7Dcos45%20%7D%5Di%20%2B%206.67%2A10%5E%7B-11%7D%2A2.5%5E%7B2%7D%5B%5Cfrac%7B1%7D%7B1%5E%7B2%7D%7D%2B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%5E%7B2%7Dsin45%7D%5Dj%5C%5CF%3D5.643%2A10%5E%7B-10%7Di%2B5.643%2A10%5E%7B-10%7Dj)
if we solve for the magnitude, we arrive at

Hence the net force on one of the masses is
