Gravitational Potential Problems (Cambridge International AS and A Level Physics Coursebook p274, 275, 277)
- Calculate the gravitational force of attraction between
- Two objects separated by a distance of 1.0cm and each having a mass of 100g.
- Two asteroids separated by a distance of 4.0 x 109 m and each having a mass of 5.0 x 1010
- A satellite of mass of 1.4 x 104 kg orbiting the Earth at a distance of 6800 km from the Earth’s center. (The mass of the Earth is 6.0 x 1024)
- Estimate the gravitational force of attraction between two people sitting side by side on a park bench. How does this force compare with the gravitational force exerted on each of them by the Earth, i.e. their weight?
You will need the data in the table below to answer these questions.
|Body||Mass / kg||Radius / km||Distance from Earth /km|
|Earth||6.0 x 1024||6400||–|
|Moon||7.4 x 1022||1740||3.8 x 105|
|Sun||2.0 x 1030||700 000||1.5 x 108|
- Mount Everest is approximately 9.0 km high. Calculate how much less a mountaineer of mass 100 kg would weigh at its summit, compared to his weight at sea level. Would this difference be measureable with a bathroom scale?
- a)Calculate the gravitational field strength:
- i) Close to the surface of the moon
- ii) Close to the surface of the sun
b) Suggest how your answers above help to explain why the Moon has only a thin atmosphere , while the sun has a dense atmosphere.
- Calculate the Earth’s gravitational field strength at the position of the moon.
- Calculate the force that the Earth exerts on the Moon. Hence determine the moon’s acceleration towards Earth.
- Jupiter’s mass is 320 times that of the Earth and its radius is 11.2 times the Earth’s. The Earth’s gravitational field strength is 9.81 N.kg-1. Calculate the gravitational field strength close to the surface of Jupiter.
- The moon and the sun both contribute to the tides on the Earth’s oceans. Which has a bigger pull on each kilogram of seawater, the sun or the moon?
- Astrologers believe that the planets exert an influence on us, particularly from the moment of birth. (They don’t necessarily believe that this is an effect of gravity!)
a) Calculate the gravitational force on a 4.0 kg baby caused by Mars when the planet is at its closest to the Earth at a distance of 100 000 000km. Mars has a mass of 6.4 x 1023
b)Calculate the gravitational force on the same baby due to its 50 kg mother at a distance of 0.40 m.
- There is a point on the line joining the centers of the Earth and the Moon where their combined gravitational field strength is zero. Is the point closer to the Earth or the moon? Calculate how far it is from the center of the Earth.
- Gravitational constant G = 6.67 x 10-11 m2.kg-2
a)Determine the gravitational potential at the surface of the Earth.
b) Determine the gravitational potential at the surface of the moon.
c) Which is the shallower potential well, the Earth or the moon? Draw a diagram similar to figure 18.8 (on the right) to compare the potential wells of the Earth and the moon.
d) Use your diagram to explain why a large rocket is needed to lift a spacecraft from the surface of the Earth but a much smaller rocket can be used to launce from the moon’s surface.