13. Gravitational fields
A section of Physics, 9702
Listing 10 of 105 questions
An isolated spherical planet has a diameter of 6.8 × 106 m. Its mass of 6.4 × 1023 kg may be assumed to be a point mass at the centre of the planet. Show that the gravitational field strength at the surface of the planet is 3.7 N kg−1. A stone of mass 2.4 kg is raised from the surface of the planet through a vertical height of 1800 m. Use the value of field strength given in to determine the change in gravitational potential energy of the stone. Explain your working. change in energy = J A rock, initially at rest at infinity, moves towards the planet. At point P, its height above the surface of the planet is 3.5 D, where D is the diameter of the planet, as shown in . path of rock P 3.5 D planet D
9702_w14_qp_41
THEORY
2014
Paper 4, Variant 1
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An isolated spherical planet has a diameter of 6.8 × 106 m. Its mass of 6.4 × 1023 kg may be assumed to be a point mass at the centre of the planet. Show that the gravitational field strength at the surface of the planet is 3.7 N kg−1. A stone of mass 2.4 kg is raised from the surface of the planet through a vertical height of 1800 m. Use the value of field strength given in to determine the change in gravitational potential energy of the stone. Explain your working. change in energy = J A rock, initially at rest at infinity, moves towards the planet. At point P, its height above the surface of the planet is 3.5 D, where D is the diameter of the planet, as shown in . path of rock P 3.5 D planet D
9702_w14_qp_42
THEORY
2014
Paper 4, Variant 2
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State what is meant by gravitational potential at a point. Suggest why, for small changes in height near the Earth’s surface, gravitational potential is approximately constant. The Moon may be considered to be a uniform sphere with a diameter of 3.5 × 103 km and a mass of 7.4 × 1022 kg. A meteor strikes the Moon and, during the collision, a rock is sent off from the surface of the Moon with an initial speed v. Assuming that the Moon is isolated in space, determine the minimum speed of the rock such that it does not return to the Moon’s surface. Explain your working. minimum speed = m s–1
9702_w18_qp_41
THEORY
2018
Paper 4, Variant 1
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State what is meant by gravitational potential at a point. Suggest why, for small changes in height near the Earth’s surface, gravitational potential is approximately constant. The Moon may be considered to be a uniform sphere with a diameter of 3.5 × 103 km and a mass of 7.4 × 1022 kg. A meteor strikes the Moon and, during the collision, a rock is sent off from the surface of the Moon with an initial speed v. Assuming that the Moon is isolated in space, determine the minimum speed of the rock such that it does not return to the Moon’s surface. Explain your working. minimum speed = m s–1
9702_w18_qp_43
THEORY
2018
Paper 4, Variant 3
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Define gravitational potential at a point. A rocket is launched from the surface of a planet and moves along a radial path, as shown in . R R 4R A B rocket path planet mass M The planet may be considered to be an isolated sphere of radius R with all of its mass M concentrated at its centre. Point A is a distance R from the surface of the planet. Point B is a distance 4R from the surface. Show that the difference in gravitational potential Δφ between points A and B is given by the expression Δφ GM R = where G is the gravitational constant. The rocket motor is switched off at point A. During the journey from A to B, the rocket has a constant mass of 4.7 × 104 kg and its kinetic energy changes from 1.70 TJ to 0.88 TJ. For the planet, the product GM is 4.0 × 1014 N m2 kg–1. It may be assumed that resistive forces to the motion of the rocket are negligible. Use the expression in to determine the distance from A to B. distance = m
9702_m17_qp_42
THEORY
2017
Paper 4, Variant 2
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Define gravitational potential at a point. The gravitational potential φ at distance r from point mass M is given by the expression φ = – GM r where G is the gravitational constant. Explain the significance of the negative sign in this expression. A spherical planet may be assumed to be an isolated point mass with its mass concentrated at its centre. A small mass m is moving near to, and normal to, the surface of the planet. The mass moves away from the planet through a short distance h. State and explain why the change in gravitational potential energy ΔEP of the mass is given by the expression ΔEP = mgh where g is the acceleration of free fall. The planet in has mass M and diameter 6.8 × 103 km. The product GM for this planet is 4.3 × 1013 N m2 kg–1. A rock, initially at rest a long distance from the planet, accelerates towards the planet. Assuming that the planet has negligible atmosphere, calculate the speed of the rock as it hits the surface of the planet. speed = m s–1
9702_s12_qp_41
THEORY
2012
Paper 4, Variant 1
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Define gravitational potential at a point. The gravitational potential φ at distance r from point mass M is given by the expression φ = – GM r where G is the gravitational constant. Explain the significance of the negative sign in this expression. A spherical planet may be assumed to be an isolated point mass with its mass concentrated at its centre. A small mass m is moving near to, and normal to, the surface of the planet. The mass moves away from the planet through a short distance h. State and explain why the change in gravitational potential energy ΔEP of the mass is given by the expression ΔEP = mgh where g is the acceleration of free fall. The planet in has mass M and diameter 6.8 × 103 km. The product GM for this planet is 4.3 × 1013 N m2 kg–1. A rock, initially at rest a long distance from the planet, accelerates towards the planet. Assuming that the planet has negligible atmosphere, calculate the speed of the rock as it hits the surface of the planet. speed = m s–1
9702_s12_qp_43
THEORY
2012
Paper 4, Variant 3
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Define gravitational potential at a point. A stone of mass m has gravitational potential energy EP at a point X in a gravitational field. The magnitude of the gravitational potential at X is φ. State the relation between m, EP and φ. An isolated spherical planet of radius R may be assumed to have all its mass concentrated at its centre. The gravitational potential at the surface of the planet is − 6.30 × 107 J kg−1. A stone of mass 1.30 kg is travelling towards the planet such that its distance from the centre of the planet changes from 6R to 5R. Calculate the change in gravitational potential energy of the stone. change in energy = J
9702_s14_qp_41
THEORY
2014
Paper 4, Variant 1
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Define gravitational potential at a point. A stone of mass m has gravitational potential energy EP at a point X in a gravitational field. The magnitude of the gravitational potential at X is φ. State the relation between m, EP and φ. An isolated spherical planet of radius R may be assumed to have all its mass concentrated at its centre. The gravitational potential at the surface of the planet is − 6.30 × 107 J kg−1. A stone of mass 1.30 kg is travelling towards the planet such that its distance from the centre of the planet changes from 6R to 5R. Calculate the change in gravitational potential energy of the stone. change in energy = J
9702_s14_qp_43
THEORY
2014
Paper 4, Variant 3
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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_41
THEORY
2016
Paper 4, Variant 1
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Questions Discovered
105