9702 · 13.4
Gravitational potential flashcards
Revision flashcards for Cambridge 9702 Gravitational potential (syllabus 13.4). Flip, recall, then mark a real past-paper question.
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Define gravitational potential.
The work done per unit mass by an external agent to move a unit mass from infinity to a specific point within a gravitational field.
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Why is gravitational potential always negative at finite distances?
Because energy is released (work is done *by* the field) as a mass moves from infinity towards a gravitating body, meaning the work done *by an external agent* is negative.
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State the formula for gravitational potential (\phi) at a distance 'r' from a point mass 'M'.
\phi = -\frac{GM}{r}
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How is gravitational potential energy (E\_p) related to gravitational potential (\phi)?
E\_p = m\phi, where 'm' is the mass experiencing the potential.
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What is the energy required to move an object completely out of a gravitational field?
It is equal to the negative of its initial gravitational potential energy (or the absolute value of its initial gravitational potential energy).
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What are the standard units for gravitational potential?
Joules per kilogram (J kg^-1).
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What is the conventional value for gravitational potential at an infinite distance?
Zero (\phi = 0).
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Can gravitational potential ever be a positive value?
No. Since gravitational forces are always attractive, energy is always released as masses approach each other, leading to negative potential.
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How is 'G' used in the gravitational potential formula?
'G' is the universal gravitational constant, valued at 6.67 \times 10^{-11} N m^2 kg^{-2}, crucial for calculating gravitational interactions.
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How are uniform spherical masses treated for external potential calculations?
Their entire mass 'M' can be considered concentrated as a point mass at their geometric centre.
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What is an equipotential surface?
A surface in space where the gravitational potential is the same at all points. No work is done when moving a mass along an equipotential surface.
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How are gravitational field strength (g) and gravitational potential (\phi) related?
Gravitational field strength is the negative gradient of the gravitational potential. Mathematically, g = -Δφ/Δr. It represents the steepness of the potential gradient.
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What is the work done to move a mass between two points in a gravitational field?
The work done is equal to the change in the mass's gravitational potential energy, W = ΔE_p = mΔφ = m(φ_final - φ_initial).
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Why does moving to a higher orbit require energy, even though the final GPE is 'less negative'?
Moving to a higher orbit increases the GPE (it becomes less negative, i.e., closer to zero). This increase in potential energy must be supplied by doing positive work on the object, for example, by firing its rocket engines.
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What is the distinction between GPE = mgh and E_p = -GMm/r?
GPE = mgh is an approximation for the change in potential energy in a uniform gravitational field near a planet's surface. E_p = -GMm/r is the general formula for potential energy in a radial field, valid at any distance 'r' from the centre of mass M.