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
Answer:
B
Volume decreases due to less molecular motion of the gas inside the football.
Explanation:
Assuming that the atmospheric pressure (and therefore, the pressure of the air inside the football) remains constant, this means that we can apply Charle's law, which states that:
"For a fixed amount of gas kept at constant pressure, the volume of the gas is proportional to its absolute temperature"
Mathematically:
where
V is the volume of the gas
T is its absolute temperature
In the winter month, the air becomes colder, which means that the temperature of the air (and of the gas inside the football) decreases. As the average kinetic energy of the molecules of a gas is proportional to its absolute temperature, this also means that there will be less molecular motion in the gas, and therefore (as stated by Charle's law) the volume of the gas also decreases.
The "c) percent efficiency" could not be used to find the mechanical advantage of an inclined plane. There are two formulae that could be used to determine the mechanical advantage of an inclined plane which stated as MA = Length/rise and Wout=Win. MA is the mechanical advantage, Wout is the output force, Win is the input force, and "rise" is the height of the inclined plane<span>.</span>
The pumping work has the equation written below:
W = mΔh,
where m is the mass
Δh is the difference in height
We determine the mass from the density of water which is 62.5 lb/ft³.
Density = Mass/Volume
Mass = m = Density*Volume
m = (62.5 lb/ft³)(π/4)(24 ft)² = 9,000π
The lb is in lbm or pound-mass. To convert it to pound-force, lbf, we use the g/gc conversion factor which is equal to 1 lbf/lbm. Thus,
W = (9,000π lbm)(5 ft - 4 ft)(1 lbf/lbm) = 28,274 lbf·ft
Answer:
Methane, which generally produces more heat and energy got decreased in the Earth's system, leading to less energy in the Earth system and less energy absorbed by Earth's surface.
Explanation:
Methane produces a great deal of energy than any other gas that plays a role in the greenhouse effect. In several billions of years ago, humans were not engaging in activities that could increase the amount of methane in the earth's system most especially the atmosphere. Such activities that were not done include burning fossil fuel, raising livestock as we have now, and waste disposal. Natural process which includes natural air reduces some amount of methane in the atmosphere.
