The gravitational potential energy U(r) of a point mass m at a distance r from the centre of a planet of mass M is given by U(r) = −GMm/r, where G is Newton’s Gravitational Constant. (a) What is the total energy of an asteroid of mass 3500 kg if it is moving directly towards the centre of the Earth at a speed of 12 kms−1 at a distance of 10 Earth radii from the centre of the Earth? (b) What is the kinetic energy of the asteroid when it hits the surface of the Earth? (c) What is the speed of the asteroid when it hits the surface of the Earth? Note: in parts (b) & (c) you may neglect any friction with Earth’s atmosphere; you may take the mass of the Earth to be 5.97 × 1024 kg and the radius of the Earth to be 6.37 × 106 m.
The gravitational potential energy U(r) of a point mass m at a distance r from the
centre of a planet of mass M is given by
U(r) = −GMm/r,
where G is Newton’s Gravitational Constant.
(a) What is the total energy of an asteroid of mass 3500 kg if it is moving directly
towards the centre of the Earth at a speed of 12 kms−1 at a distance of 10
Earth radii from the centre of the Earth?
(b) What is the kinetic energy of the asteroid when it hits the surface of the Earth?
(c) What is the speed of the asteroid when it hits the surface of the Earth?
Note: in parts (b) & (c) you may neglect any friction with Earth’s atmosphere; you
may take the mass of the Earth to be 5.97 × 1024 kg and the radius of the Earth to
be 6.37 × 106 m.
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