13. Gravitational fields
A section of Physics, 9702
Listing 10 of 105 questions
By reference to the definition of gravitational potential, explain why gravitational potential is a negative quantity. Two stars A and B have their surfaces separated by a distance of 1.4 × 1012 m, as illustrated in . star A star B 1.4 = 1012 m P x Point P lies on the line joining the centres of the two stars. The distance x of point P from the surface of star A may be varied. The variation with distance x of the gravitational potential φ at point P is shown in . –2 –4 –6 –8 –10 –12 –14 –16 0.2 0.4 0.6 0.8 1.0 1.2 1.4 x / 1012 m / 108 J kg–1 q A rock of mass 180 kg moves along the line joining the centres of the two stars, from star A towards star B. Use data from to calculate the change in kinetic energy of the rock when it moves from the point where x = 0.1 × 1012 m to the point where x = 1.2 × 1012 m. State whether this change is an increase or a decrease. change = J At a point where x = 0.1 × 1012 m, the speed of the rock is v. Determine the minimum speed v such that the rock reaches the point where x = 1.2 × 1012 m. minimum speed = m s−1
9702_s16_qp_43
THEORY
2016
Paper 4, Variant 3
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Define gravitational potential at a point. Starting from the equation for the gravitational potential due to a point mass, show that the gravitational potential energy EP of a point mass m at a distance r from another point mass M is given by EP = – GMm r where G is the gravitational constant. shows the path of a comet of mass 2.20 × 1014 kg as it passes around a star of mass 1.99 × 1030 kg. X Y 34.1 km s–1 comet mass 2.20 × 1014 kg star mass 1.99 × 1030 kg path of comet (not to scale) At point X, the comet is 8.44 × 1011 m from the centre of the star and is moving at a speed of 34.1 km s–1. At point Y, the comet passes its point of closest approach to the star. At this point, the comet is a distance of 6.38 × 1010 m from the centre of the star. Both the comet and the star can be considered as point masses at their centres. Calculate the magnitude of the change in the gravitational potential energy ΔEP of the comet as it moves from position X to position Y. ΔEP = J State, with a reason, whether the change in gravitational potential energy in is an increase or a decrease. Use your answer in to determine the speed, in km s–1, of the comet at point Y. speed = km s–1 A second comet passes point X with the same speed as the comet in and travelling in the same direction. This comet is gradually losing mass. The mass of this comet when it passes point X is the same as the mass of the comet in . Suggest, with a reason, how the path of the second comet compares with the path shown in .
9702_s22_qp_42
THEORY
2022
Paper 4, Variant 2
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Define gravitational potential at a point. The Moon may be considered to be an isolated uniform sphere of mass 7.3 × 1022 kg and radius 1.7 × 106 m. Calculate the gravitational potential at the surface of the Moon. Give a unit with your answer. gravitational potential = unit An isolated uniform spherical planet has gravitational potential φ at its surface. A particle of mass m is projected vertically upwards from the surface. The particle is given just enough kinetic energy to travel to an infinite distance away from the planet, escaping from the gravitational pull of the planet, without any additional work being done on it. Determine an expression, in terms of m and φ, for the gravitational potential energy EP of the particle at the surface of the planet. EP = Show that the speed v at which the particle is projected upwards from the surface of the planet is given by v = –2φ. A particle is moving upwards at the surface of the Moon. Use your answer in and the expression in to determine the minimum speed of this particle that will result in it escaping from the gravitational pull of the Moon. speed = m s–1 Hydrogen may be assumed to be an ideal gas. The mass of a hydrogen molecule is 3.34 × 10–27 kg. Calculate the root-mean-square (r.m.s.) speed of a hydrogen molecule in hydrogen gas that is at a temperature of 400 K. r.m.s. speed = m s–1 The surface of the Moon reaches temperatures of approximately 400 K when in direct sunlight. Use your answers in and to suggest a reason why the Moon does not have an atmosphere consisting of hydrogen.
9702_w23_qp_42
THEORY
2023
Paper 4, Variant 2
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Questions Discovered
105