Gravitation
- State the inverse square law of gravitation.
- Calculate the gravitational force between two cars parked 0.50 m apart. The mass of each car is 1000 kg.
- Calculate the gravitational force between the Earth and the Sun.
- (a) By considering the force on a mass, at the surface of the Earth, state the expression for the gravitational field strength, g, in terms of the mass and radius of the Earth.
(b) (i) The gravitational field strength is 9.8 N kg-1 at the surface of the Earth. Calculate a value for the mass of the Earth.
(ii) Calculate the gravitational field strength at the top of Ben Nevis, 1344 m above the surface of the Earth.
(iii) Calculate the gravitational field strength at 200 km above the surface of the Earth.
- (a) What is meant by the gravitational potential at a point?
(b) State the expression for the gravitational potential at a point.
(c) Calculate the gravitational potential:
(i) at the surface of the Earth
(ii) 800 km above the surface of the Earth.
- ‘A gravitational field is a conservative field.’ Explain what is meant by this statement.
- Calculate the energy required to place a satellite of mass 200 000 kg into an orbit at a height of 350 km above the surface of the Earth.
- Which of the following are vector quantities: gravitational field strength, gravitational potential, escape velocity, universal constant of gravitation, gravitational potential energy, period of an orbit?
- A mass of 8.0 kg is moved from a point in a gravitational field where the potential is –15 J kg-1 to a point where the potential is –10 J kg-1.
(a) What is the potential difference between the two points?
(b) Calculate the change in potential energy of the mass.
(c) How much work would have to be done against gravity to move the mass between these two points?
- (a) Explain what is meant by the term ‘escape velocity’.
(b) Derive an expression for the escape velocity in terms of the mass and radius of a planet.
(c) (i) Calculate the escape velocity from both the Earth and from the Moon.
(ii) Using your answers to (i) comment on the atmosphere of the Earth and the Moon.
- Calculate the gravitational potential energy and the kinetic energy of a 2000 kg satellite in geostationary orbit above the Earth.
- (a) A central force required to keep a satellite in orbit. Derive the expression for the orbital period in terms of the orbital radius.
(b) A satellite is placed in a parking orbit above the equator of the Earth.
(i) State the period of the orbit.
(ii) Calculate the height of the satellite above the equator.
(iii) Determine the linear speed of the satellite.
(iv) Find the central acceleration of the satellite.
- A white dwarf star has a radius of 8000 km and a mass of 1.2 solar masses.
(a) Calculate the density of the star in kgm-3.
(b) Find the gravitational potential at a point on the surface.
(c) Calculate the acceleration due to gravity at a point on the surface.
(d) Estimate the potential energy required to raise your centre of gravity from a sitting position to a standing position on this star.
(e) A 2 kg mass is dropped from a height of 100 m on this star. How long does it take to reach the surface of the star?
- (a) How are photons affected by a massive object such as the Sun?
(b) Explain, using a sketch, why light from a distant star passing close to the Sun may suggest that the star is at a different position from its ‘true’ position.
(c) Explain what is meant by the term ‘black hole’.
