Assignment – Universal Gravitation and Gravitational Fields
1. A 6.1kg bowling ball and a 7.2kg ball experience a gravitational force between them of 2.0*10-9N. What is their distance of separation?
2. If you climb to the top of Mt. Everest, you will be about 8850m above sea level. What is the acceleration due to gravity at this location?
3. After landing on Mars, an astronaut dropping a rock measures its rate of acceleration as 3.73m/s2. Given that its radius is 3.39*106m, find the mass of Mars.
4. The International Space Station is in Low Earth Orbit, which is any altitude below a level of 2200km. If the gravitational field strength on ISS is 7.28N/kg, find:
- The altitude of the space station
- Its orbital speed
5. Find the orbital period for Mercury, whose average orbital radius is 5.79*1010m.
6. Imagine bringing your fingertips together. Each finger contains a finite mass, and the distance between them is zero when they touch. From the Law of Universal Gravitation, one might conclude that the attractive force between the fingers is infinite as their distance of separation is infinitely small, and, therefore, that your fingers must remain stuck together forever. What is wrong with this argument?
7. At what altitude above Earth’s surface is the acceleration due to gravity equal to g/2?
8. Two satellites orbit the Earth, with satellite 1 at a greater altitude than satellite 2. Which satellite has the greater orbital speed? Explain.
9. At a certain distance from the centre of Earth, a 4.6kg object has a weight of 2.2N. If the object is released and allowed to fall, what is its initial rate of acceleration?
10. Planet Alpha has a radius 1.41 times that of Earth and a mass 2.28 times that of earth. If the force of gravity on your mass is 800.N on Earth, what will it be on Alpha?
11. The force of attraction between two masses was 87.0N when they were 14.1m apart. The distance between them was changed and the force became 56.8N. How far apart were they then?