Case study·Hard exam skill (4/5)·No calculator
Difficulty guide
The label describes the problem, not your ability.
1/5 - Foundational
Warm-up setup; checks one basic idea.
2/5 - Routine exam skill
Normal syllabus skill; usually one main rule or interpretation.
3/5 - Standard multi-step
Exam-style problem with multiple steps or a common trap.
4/5 - Hard exam skill
High-end exam problem; combines methods carefully.
5/5 - Challenge
Stretch problem beyond normal exam pressure.
Question
A satellite of mass is taken from rest at Earth's surface and placed into a circular orbit of radius about Earth. Earth's mass is and radius is . Ignore air resistance and Earth's rotation.
Total: 5 marks
(a) Write the satellite's initial mechanical energy at rest on the surface. (1 mark)
(b) Write its potential energy in the orbit. (1 mark)
(c) Write its kinetic energy in the circular orbit. (1 mark)
(d) Find the total mechanical energy in the orbit. (1 mark)
(e) Find the minimum work required to place it in that orbit. (1 mark)
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