What is potential energy near a surface?

When the field is treated as uniform, lifting a mass m through a height h changes its gravitational potential energy by

WAPhysicsSyllabus dot point

How do gravitational field strength and gravitational potential energy describe a field?

Define gravitational field strength and analyse changes in gravitational potential energy in a field

A focused answer to the WACE Year 12 Physics Unit 3 content point on gravitational fields and energy. Field strength as force per unit mass, field-line representation, near-surface and changing potential energy, and the work done moving a mass in a field.

Generated by Claude Opus 4.77 min answerUpdated 2026-05-29

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking

WACE wants you to describe gravity as a field, calculate field strength, and analyse the energy changes when a mass moves within it. The field model lets you predict the force on any mass placed at a point without re-deriving it each time.

Field strength

The gravitational field strength at a point is the force per unit mass placed there:

g=\frac{F}{m}=\frac{GM}{r^2}\quad(\text{N kg}^{-1}).

Numerically this equals the free-fall acceleration in m s-2, which is why $g$ near Earth's surface is $9.8$ in both units. Field strength is a vector pointing toward the source mass.

Representing the field

Field lines show the direction a small test mass would be pushed and, by their spacing, the strength. Around a single planet the lines are radial and inward, spreading out with distance so the field weakens as $1/r^2$ . Close to a small patch of surface the lines are nearly parallel and evenly spaced, which is why we treat the field as uniform for everyday problems.

Potential energy near a surface

When the field is treated as uniform, lifting a mass $m$ through a height $\Delta h$ changes its gravitational potential energy by

\Delta E_p=mg\,\Delta h.

Raising a mass increases $E_p$ ; letting it fall converts that energy to kinetic energy. This near-surface model is what WACE expects for projectile and ramp problems, where $g$ barely changes over the heights involved.

Work done and energy conservation

The work done by you against gravity to raise a mass equals the increase in potential energy, and the work done by gravity on a falling mass equals the loss in potential energy. Combined with the kinetic energy $E_k=\tfrac{1}{2}mv^2$ , energy conservation gives launch and landing speeds directly. For a mass falling from rest through height $h$ , $mgh=\tfrac{1}{2}mv^2$ , so $v=\sqrt{2gh}$ , independent of mass.

Energy of a launched and falling mass

A 2.0 kg mass thrown upward at 15 m s-1

Take $g=9.8\ \text{m s}^{-2}$ . First find the maximum height using energy conservation, where all kinetic energy converts to potential energy:

\tfrac{1}{2}mv^2=mg\,\Delta h\;\Rightarrow\;\Delta h=\frac{v^2}{2g}=\frac{(15)^2}{2(9.8)}=11.5\ \text{m}.

Gravitational potential energy gained at the top, relative to launch:

\Delta E_p=mg\,\Delta h=2.0\times 9.8\times 11.5=225\ \text{J}.

This equals the initial kinetic energy $\tfrac{1}{2}(2.0)(15)^2=225\ \text{J}$ , confirming energy is conserved as the mass slows and rises.

Field strength versus potential energy

Keep the two ideas distinct: field strength is force per unit mass (a property of the field at a point), while potential energy depends on the mass placed there and its position. A region can have a strong field yet a chosen mass have little potential energy if it has barely moved.

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