Gravitational Potential Energy and Work
For point masses U=-GMm/r with zero at infinity, gravitational work is -Delta U, and in an isolated conservative motion K+U remains constant.
Why this shows up in the exam
Raising bodies to finite altitude · Radial fall and impact speed · Work to separate gravitating systems
Learn the idea
Gravity is conservative, so work and speed changes follow from endpoint potential energies. A path may curve, but gravitational work depends only on the starting and ending configurations.
🧠 Memory hook: Use exact endpoint energy when height is not tiny.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- U = -GMm/r — two-body potential energy
- W_gravity = -Delta U — work done by gravity
- K_i + U_i = K_f + U_f — mechanical-energy conservation
How to approach it
- 1Choose the system and potential zero
- 2Write energy at both endpoints
- 3Cancel common terms before evaluating
Common slip-ups that cost marks
- •Using mgh at planetary heights
- •Forgetting that bound-state U is negative
- •Adding work by gravity with the wrong sign
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A satellite moves in a circular orbit where GM = 4 x 10^14 m^3/s^2 and orbital radius is 2 x 10^6 m. Find its orbital speed.
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