Answer:
x = D (M/M-m) 2.41
Explanation:
a) Let's apply Newton's second law to find the summation of force, where each force is given by the law of universal gravitation
F = g m₁m₂ / r²
Σ F = 0
F1- F2 = 0
F1 = F2
We set the reference system in the body of greatest mass (M) the planet
F1 = g m₁ M / x²
F2 = G m1 m / (D-x)²
G m₁ M / x² = G m₁ m / (D-x)²
M (D-x)² = m x²
MD² -2MD x + M x² = m x²
x² (M-m) -2MD x + MD² = 0
We solve the second degree equation
x = [2MD ±√ (4M²D² - 4 (M-m) MD²)] / 2 (M-m)
x = {2MD ± 2D √ (M² + (M-m) M)} / 2 (M-m)
x = D {M ± Ra (2M²-mM)} / (M-m)
x = D (M ± M √ (2-m/M)) / (M-m)
x = D (M / (M-m)) (1 ±√ (2-m/M)
Let's analyze this result, the value of M-m >> 1, so if we take the negative root, the value of x would be negative, it is out of the point between the two bodies, so the correct result must be taken with the positive root
x = D (M / (M-m)) (1 + √2)
x = D (M/M-m) 2.41
b) X = 2/3 D
x = D (M/M-m) 2.41
2/3 D = D (M/(M-m)) 2.41
2/3 (M-m) = M 2.41
2/3 M - 2/3 m = 2.41 M
1.743 M = 0.667 m
M/m = 0.667/1.743
M/m = 0.38
Answer:
Advantages of Hydroelectric Energy
1 Renewable
Hydroelectric energy is renewable. This means that we cannot use up. However, there’s only a limited number of suitable reservoirs where hydroelectric power plants can be built and even less places where such projects are profitable.
2 Green
Generating electricity with hydro energy is not polluting itself. The only pollution occurs during the construction of these massive power plants.
3 Reliable
Hydroelectricity is very reliable energy. There are very little fluctuations in terms of the electric power that is being by the plants, unless a different output is desired. Countries that have large resources of hydropower use hydroelectricity as a base load energy source. As long as there is water in the magazines electricity can be generated.
4 Flexible
As previously mentioned, adjusting water flow and output of electricity is easy. At times where power consumption is low, water flow is reduced and the magazine levels are being conserved for times when the power consumption is high.
5 Safe
Compared to among others fossil fuels and nuclear energy, hydroelectricity is much safer. There is no fuel involved (other than water that is).
Answer:
The first one is Earths Tilt on its axis
It would be safe to stand on the insulated sphere since it is covered by a material that does not allow the passage of current or an insulator. With the insulator, the student can freely touch the sphere but without it, touching the sphere when it is charged is very dangerous as it would electrocute you since the charge from the sphere would freely flow onto your body. Insulators are being used to be able to protect humans from any danger in touching charged objects. Insulators have very high resistance to the flow of current through them. Examples are rubber, glass, cellulose, polystyrene and wood.
