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Newton's law of gravitation questions
One equation covers the apple and the Moon. Every pair of masses attracts, with a force set by their product and by the inverse square of their separation. Divide out the test mass and the same law gives the field strength anywhere.
19 original questions · 53 marks · the newton's law of gravitation notes · Gravitational fields
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State Newton's law of gravitation for two point masses.
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The force is attractive and proportional to the product of the masses (1); and inversely proportional to the square of their separation, F = GMm/r2 (1).Two point masses, each of mass 5.0 kg, are 2.0 m apart. Calculate the gravitational force between them.
G = 6.67 × 10−11 N m2 kg−2Mark scheme
F = GMm/r2 = (6.67 × 10−11 × 5.0 × 5.0)/2.02 (1)
F = 4.17 × 10−10 N (1)Define gravitational field strength and write down the equation relating it to the force on a mass.
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Gravitational force per unit mass on a small test mass at the point (1); g = F/m (1).The Earth pulls a student of mass 60 kg with a gravitational force of 590 N. State the magnitude of the gravitational force the student exerts on the Earth, and explain why the Earth's resulting motion is negligible.
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590 N: by Newton's third law the two forces are equal in magnitude (and opposite in direction) (1). The Earth's mass is enormous, so its acceleration a = F/M is far too small to notice (1).The gravitational field strength at the Earth's surface is 9.8 N kg−1. Without using values of G or the Earth's mass, determine the field strength at a point 3 Earth radii from the Earth's centre.
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g follows an inverse-square law, so trebling the distance from the centre divides g by 32 = 9 (1)
g = 9.8/9 = 1.1 N kg−1 (1)State what is meant by a point mass, and explain why Newton's law of gravitation can be applied to spherical planets.
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A mass whose size is negligible compared with the separation involved, so that it can be treated as being at a single point (1). A (uniform) sphere behaves, from outside, as if all its mass were concentrated at its centre, so the law applies with r measured from the centre (1).A planet of mass 6.0 × 1024 kg and its moon of mass 7.3 × 1022 kg are separated by a distance of 3.8 × 108 m. Calculate the gravitational force between them.
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F = GMm/r2 = (6.67 × 10−11 × 6.0 × 1024 × 7.3 × 1022)/(3.8 × 108)2 (1)
F = 2.02 × 1020 N (1)A planet has a mass of 6.0 × 1024 kg and a radius of 6.4 × 106 m. Calculate the gravitational field strength at its surface.
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g = GM/r2 = (6.67 × 10−11 × 6.0 × 1024)/(6.4 × 106)2 (1)
g = 9.77 N kg−1 (1)For the same planet, calculate the gravitational field strength at a distance of 1.28 × 107 m from its centre. Comment on how your value compares with the surface value.
A satellite of mass 500 kg orbits the planet at a distance of 7.0 × 106 m from its centre. Calculate the gravitational field strength at this distance and hence the gravitational force on the satellite.
Two snooker balls, each of mass 74 g, rest with their centres 6.0 cm apart. Calculate the gravitational force each ball exerts on the other, and suggest why this force has no noticeable effect.
G = 6.67 × 10−11 N m2 kg−2A planet of mass 6.4 × 1023 kg orbits a star of mass 2.0 × 1030 kg at a distance of 2.3 × 1011 m. Calculate the gravitational force of the star on the planet, and the acceleration of the planet.
G = 6.67 × 10−11 N m2 kg−2The gravitational field strength at a point above a planet of mass 6.4 × 1023 kg is 1.0 N kg−1. Determine the distance of this point from the planet's centre.
G = 6.67 × 10−11 N m2 kg−2Mars has a mass of 6.4 × 1023 kg and a radius of 3.4 × 106 m. Show that the gravitational field strength at the surface of Mars is approximately 3.7 N kg−1.
The gravitational field strength at the surface of a planet of radius 6.4 × 106 m is 9.81 N kg−1. Determine the mass of the planet.
Explain why the gravitational field strength of a planet decreases with distance from its centre, and state the mathematical form of this decrease.
A magazine article describes two newly discovered planets orbiting another star:
planet K: mass 3.0 × 1025 kg, radius 1.6 × 107 m
planet L: mass 8.9 × 1024 kg, radius 7.7 × 106 m
The article claims that both planets have a surface gravitational field strength greater than the Earth's value of 9.8 N kg−1. Deduce whether the claim is correct.
G = 6.67 × 10−11 N m2 kg−2Estimate the gravitational force of attraction between two people sitting 1.0 m apart, and estimate how many orders of magnitude smaller this is than your weight.
G = 6.67 × 10−11 N m2 kg−2A crewed space laboratory orbits 4.2 × 105 m above the surface of a planet of mass 6.0 × 1024 kg and radius 6.4 × 106 m. Show that the gravitational field strength at this altitude is about 8.6 N kg−1, and explain why the crew float inside the laboratory even though g there is far from zero.
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