Is their a multiple choice to choose from I'm not sure the answer I got is even right.
That would be very helpful.
Answer:
![F=18.58\times 10^{-11}\ N](https://tex.z-dn.net/?f=F%3D18.58%5Ctimes%2010%5E%7B-11%7D%5C%20N)
Explanation:
Given:
mass of first particle, ![m_1=6.7\ kg](https://tex.z-dn.net/?f=m_1%3D6.7%5C%20kg)
mass of second particle, ![m_2=5.1\ kg](https://tex.z-dn.net/?f=m_2%3D5.1%5C%20kg)
mass of third particle, ![m_3=3.7\ kg](https://tex.z-dn.net/?f=m_3%3D3.7%5C%20kg)
coordinate position of first particle in meters, ![(x_1,y_1)\equiv(4.2,0)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%5Cequiv%284.2%2C0%29)
coordinate position of second particle in meters, ![(x_2,y_2)\equiv(0,2.8)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%5Cequiv%280%2C2.8%29)
coordinate position of third particle in meters, ![(x_3,y_3)\equiv(0,0)](https://tex.z-dn.net/?f=%28x_3%2Cy_3%29%5Cequiv%280%2C0%29)
<u>Now, gravitational force on particle 3 due to particle 1:</u>
![F_{31}=G\frac{m_1.m_3}{r_{31}^2}](https://tex.z-dn.net/?f=F_%7B31%7D%3DG%5Cfrac%7Bm_1.m_3%7D%7Br_%7B31%7D%5E2%7D)
![F_{31}=6.67\times 10^{-11} \times \frac{6.7\times 3.7}{4.2^2}](https://tex.z-dn.net/?f=F_%7B31%7D%3D6.67%5Ctimes%2010%5E%7B-11%7D%20%5Ctimes%20%5Cfrac%7B6.7%5Ctimes%203.7%7D%7B4.2%5E2%7D)
![F_{31}=9.37\times 10^{-11}\ N](https://tex.z-dn.net/?f=F_%7B31%7D%3D9.37%5Ctimes%2010%5E%7B-11%7D%5C%20N)
towards positive Y axis.
<u>gravitational force on particle 3 due to particle 2:</u>
![F_{32}=G\frac{m_2.m_3}{r_{21}^2}](https://tex.z-dn.net/?f=F_%7B32%7D%3DG%5Cfrac%7Bm_2.m_3%7D%7Br_%7B21%7D%5E2%7D)
![F_{32}=6.67\times 10^{-11} \times \frac{5.1\times 3.7}{2.8^2}](https://tex.z-dn.net/?f=F_%7B32%7D%3D6.67%5Ctimes%2010%5E%7B-11%7D%20%5Ctimes%20%5Cfrac%7B5.1%5Ctimes%203.7%7D%7B2.8%5E2%7D)
![F_{32}=16.05\times 10^{-11}\ N](https://tex.z-dn.net/?f=F_%7B32%7D%3D16.05%5Ctimes%2010%5E%7B-11%7D%5C%20N%20)
towards positive X axis.
<u>Now the net force</u>
![F=\sqrt{F_{31}\ ^2+F_{32}\ ^2}](https://tex.z-dn.net/?f=F%3D%5Csqrt%7BF_%7B31%7D%5C%20%5E2%2BF_%7B32%7D%5C%20%5E2%7D)
![F=\sqrt{(10^{-11})^2(9.37^2+16.05^2)}](https://tex.z-dn.net/?f=F%3D%5Csqrt%7B%2810%5E%7B-11%7D%29%5E2%289.37%5E2%2B16.05%5E2%29%7D)
![F=18.58\times 10^{-11}\ N](https://tex.z-dn.net/?f=F%3D18.58%5Ctimes%2010%5E%7B-11%7D%5C%20N)
<em>For angle in counterclockwise direction from the +x-axis</em>
![tan\theta=\frac{9.37\times 10^{-11}}{16.05\times 10^{-11}}](https://tex.z-dn.net/?f=tan%5Ctheta%3D%5Cfrac%7B9.37%5Ctimes%2010%5E%7B-11%7D%7D%7B16.05%5Ctimes%2010%5E%7B-11%7D%7D)
One of Kepler's laws is that the orbits of planets are elliptical. It's not a suggestion.
BTW, circles are ellipses too, but so special that their likelihood is close to zero.
The use of pesticides in farming land is example of non-point source pollution. The area of emitting of pollution is very large. That is why, it is difficult to monitor and control this type of pollution.
Americans get their water for everyday use through aquifer. Aquifers can be conserve by avoiding high amount of chemical uses and reducing household waste. Also the sustainable use of water cause conservation of natural resource.
Aquifer are basically underground water present in ground pores. The structure of aquifer just look like sponge. The water moves through the porous surfaces of the ground.
The Earth is a sphere is a statement to describe a scientific law