Gravitational potential (A-level only) Flashcards – AQA A-level Physics (7408)

What is gravitational potential at a point in terms of potential energy?

Gravitational potential energy per unit mass at that point.

How is gravitational potential at a point defined in terms of work done by an external agent?

The work done per unit mass to bring a small mass from infinity to the point without changing its kinetic energy.

Where is gravitational potential conventionally taken to be zero?

At infinity.

Is gravitational potential a scalar or a vector?

A scalar.

What is the unit of gravitational potential?

$\mathrm{J\,kg^{-1}}$

What is gravitational potential difference between two points?

The change in gravitational potential energy per unit mass: $\Delta V=V_{\mathrm{final}}-V_{\mathrm{initial}}$

For a mass $m$, what is the change in gravitational potential energy across a potential difference $\Delta V$?

$\Delta W=m\Delta V$ This is also the work done by an external agent if kinetic energy does not change.

What work does the gravitational field do when a mass $m$ moves across a potential difference $\Delta V$?

$-m\Delta V$

What is a gravitational equipotential surface?

A surface where gravitational potential is the same at every point.

Why does the gravitational field do no net work on a mass moving between points on the same equipotential surface?

The mass has no change in gravitational potential energy.

How is the gravitational field oriented relative to an equipotential surface?

It is perpendicular to the surface, with no component along it.

What is the gravitational potential at distance $r$ outside a spherical mass $M$, taking potential as zero at infinity?

$V=-\frac{GM}{r}$, where $G$ is the gravitational constant and $r$ is measured from the centre.

What does the negative gravitational potential outside a spherical mass imply about moving a mass to infinity?

The potential is below its value at infinity, so energy must be supplied to move the mass to infinity without changing its kinetic energy.

What are the magnitude and direction of the gravitational field strength at distance $r$ outside a spherical mass $M$?

$g=\frac{GM}{r^2}$, directed towards the mass.

How do graphs of gravitational potential and field-strength magnitude change with distance outside a spherical mass?

Potential rises towards zero from below as $-1/r$; field-strength magnitude decreases towards zero as $1/r^2$. Neither reaches zero at a finite distance.

How is the radial gravitational field component related to the gradient of potential, for a local gradient and for a constant gradient?

Local: $g_r=-\frac{\mathrm{d}V}{\mathrm{d}r}$

Constant gradient: $g_r=-\frac{\Delta V}{\Delta r}$

What does the minus sign in the gravitational field–potential gradient relation indicate?

The field points towards decreasing potential.

How is the potential change between two radial positions related to the signed area under a graph of $g_r$ against $r$?

It is the negative signed area: $\Delta V=-\int g_r\,\mathrm{d}r$

For an outward displacement, what does the area under a graph of the positive magnitude of an inward gravitational field against distance give?

The increase in gravitational potential.