Edexcel A-Level Physics A2 5.6.158 Gravitational Potential in a Radial Field Questions
Review gravitational potential in Edexcel A-Level Physics through radial-field calculations, satellite energy changes and escape-velocity arguments.
Syllabus
Pearson Edexcel International Advanced Subsidiary/Advanced Level
Course
Physics XPH11/YPH11
Level
A2
Exam points
calculate gravitational potential or potential energy changes using V = −GM/r and mass data
explain why mgh is not valid when g changes significantly across a radial field
derive or apply escape velocity results from gravitational potential energy and kinetic energy
Edexcel A-Level Physics A2 5.6.158 Gravitational Potential in a Radial Field Questions question 1
[Maximum number: 4]
Weather satellites may be in an equatorial orbit or a polar orbit, as shown.
Question (a)
(a)
A weather satellite in a polar orbit circles the Earth at a height of 8.50 × 10^5 m above the surface of the Earth.
[ 4 ]
Question (i)
(i)
Show that the gravitational potential at this height is about −5.5 × 10^7 J kg^-1. mass of Earth = 5.98 × 10^24 kg radius of Earth = 6360 km
[ 2 ]
Use V_grav = −GM/r, with r = 6.36 × 10^6 + 8.50 × 10^5 m. V_grav = −(6.67 × 10^-11)(5.98 × 10^24)/(7.21 × 10^6) = −5.53 × 10^7 J kg^-1.
Question (ii)
(ii)
Hence calculate the increase in gravitational potential energy when the satellite is placed in orbit. satellite mass = 4990 kg gravitational potential at the Earth’s surface = −6.27 × 10^7 J kg^-1
Increase in gravitational potential energy =
[ 2 ]
Use ΔE_grav = ΔV_grav × m. ΔE = [−5.53 − (−6.27)] × 10^7 × 4990 = 3.69 × 10^10 J, about 3.7 × 10^10 J.