Gravitational potential energy and potential (HL)
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Question
Define gravitational potential V_g.
Answer
The **work done per unit mass** to bring a small test mass from infinity to a point: $V_g = -\frac{GM}{r}$. Unit: **J kg⁻¹**.
Question
Formula for gravitational potential?
Answer
$V_g = -\dfrac{GM}{r}$ — negative, zero at infinity.
Question
Formula for gravitational potential energy (full field)?
Answer
$E_p = mV_g = -\dfrac{GMm}{r}$.
Question
Why are V_g and E_p negative?
Answer
The **zero is set at infinity**; a mass **loses** PE moving inward, so everywhere closer is below zero.
Question
Where is gravitational potential zero?
Answer
At **infinity** — infinitely far from every mass.
Question
How does V_g depend on r?
Answer
$V_g \propto 1/r$ (one over r), while field strength $g \propto 1/r^2$.
Question
What is an equipotential surface?
Answer
A surface joining all points at the **same V_g**; around a point mass these are **concentric spheres**.
Question
Angle between equipotentials and field lines?
Answer
Always **90° (perpendicular)**.
Question
Work done moving along an equipotential?
Answer
**Zero**, because ΔV_g = 0.
Question
Work to move a mass between two potentials?
Answer
$W = m\,\Delta V_g = m(V_{final} - V_{initial})$.
Question
Why can't SL's E_p = mgh be used in deep space?
Answer
Because **g changes with distance** ($g = GM/r^2$); mgh only works where g is roughly constant.
Question
Is gravitational potential a scalar or vector?
Answer
A **scalar** — add the values from several masses with **no direction**.
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