Law of Gravitation
1. With what force does the Moon act on 1 m3 of seawater (ρ = 1013 kg.m-3) on the surface of the Earth?
Solution:
Analysis:
m(H2O)=1013 kg, mM =7.4×1022kg, r = 3.84×108m, κ = 6.67×10-11N.m2.kg-2
The Moon attracts 1 m³ of seawater with a force of about 0.034 N.
2.With what force is the Moon attracted to the Earth if mZ= 6×1024kg, mM = 7.4×1022kg. The distance between the Earth and the Moon is 3.84×108m.
Solution:
The Moon is attracted to the Earth with a force of 2.05×1020N.
3.Two identical spheres are touching and exert a gravitational force Fg = 4.16×10-4 N on each other. What are their radii R if each has a mass of 4 tons?
Solution:
Analysis:
The spheres have radii R1 = R2 = 0.8 m.
4. Determine the mass of the Moon and the mass of the Earth from the following data:
- Moon: RM = 1.72×106m, gM = 1.67 m.s-2
- Earth: RZ = 6.378×106m, gZ = 10 m.s-2
Solution:
The mass of the Moon is 7.4×1022 kg, and the Earth’s mass is 6×1024 kg.
5.On the surface of the Earth, the gravitational acceleration is g = 10 m.s-2. At what distance from the surface of the Earth will the acceleration be half?
Solution:
Analysis:
The gravitational acceleration is half at a distance of about 2566 km above the Earth.
6. A spacecraft is moving at an altitude of 300 km above the Earth. Determine:
- a) the gravitational acceleration on this spacecraft
- b) the orbital speed of the spacecraft
- c) the orbital period of the spacecraft around the Earth
Solution:
Analysis:
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