Practise deriving and applying g = GM/r² for an isolated mass, comparing field strength at different radii and explaining the near-surface constant-g approximation.
Use Newton's law of gravitation to show that the gravitational field strength g at a distance r away from a point mass M is given by
g=F / m
C1
F=GMm/r2
and so
g=[GMm/r2]/m=GM/r2
A1
The Earth has a mass of 5.98×1024 kg and a radius of 6.37×106 m.
The Moon has a mass of 7.35×1022 kg and a radius of 1.74×106 m.
The Earth and the Moon can both be considered as point masses at their centres. Their centres are a distance of 3.84×108 m apart.
Show that the gravitational field strength at the surface of the Moon due to the mass of the Moon is 1.62 N kg−1.
g=(6.67×10−11×7.35×1022)/(1.74×106)2=1.62 N kg−1
A1
Describe qualitatively the variation, if any, with distance x of the speed of the particle as it
moves from x=12 cm to x=25 cm
passes through x=26 cm
moves from x=27 cm to x=31 cm
reaches x=32 cm
2. The particle has charge 3.2×10−19C and mass 6.6×10−27 kg.
Calculate the maximum speed of the particle.
speed = ms−1
By reference to the pattern of the lines of gravitational force near to the surface of the Earth, explain why the acceleration of free fall near to the Earth's surface is approximately constant.
Any three from:
- the lines are radial
- near the surface the lines are (approximately) parallel
- parallel lines so constant field strength
- constant field strength hence constant acceleration of free fall
B3
The Moon may be considered to be a uniform sphere that is isolated in space. It has radius 1.74×103 km and mass 7.35×1022 kg.
Calculate the gravitational field strength at the Moon's surface.
g=GM/R2g=(6.67×10−11×7.35×1022)/(1.74×103×103)2
C1
g=1.62 N kg−1
A1