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3.2.4Work, Energy, and Power

Gravitational Potential Energy Near a Surface — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 9 parts Lesson 7 of 14 1 quiz

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Lesson summary

3.2.4 Gravitational Potential Energy Near a Surface — AP PHYSICS 1 notes: Calculate changes in gravitational potential energy near a planet's surface with ΔUg = mgΔy and use them with kinetic energy.ΔUg = mgΔy — the change for the object–planet system when the object's height cha…

  • Uniform field
  • Reference level
  • Lifting and lowering
  • Scalar and path-independent
  • Lifting at constant speed
  • Work by gravity

Part 1 of 7The equation

ΔUg
ΔUg mgΔy
  • the change for the object–planet system when the object's height changes by Δy.
  • ΔUg in J, m in kg, g the field strength in N/kg (9.8 m/s2 on Earth), Δy the vertical change in m.
Uniform field
  • Uniform field g is approximately constant near a planet's surface.
Reference level
  • Reference level at height y above a chosen zero, Ug = mgy; zero points are relative.
Lifting and lowering
  • Lifting and lowering lifting stores energy in the system, lowering releases it.
Scalar and path-independent
  • Scalar and path-independent only the vertical change matters because gravity is conservative.

Part 2 of 7Link to work

Link to work
Lifting at constant speed
  • Lifting at constant speed applied work mgΔy equals ΔUg.
Work by gravity
  • −mgΔy.
Incline
  • Incline gravity's work is −(mg sinθ)d, and d sinθ = Δy, giving the same −mgΔy.

Part 3 of 7Conservation of mechanical energy

1Condition
  • Condition gravity is the only force doing work.
    • (no friction or drag, normal forces perpendicular to motion)
2Equation
  • Ki + Ui = Kf + Uf, or ½mvi2 + mgyi = ½mvf2 + mgyf.
3Mass cancels
  • Mass cancels speed at a given height is independent of mass.
4Release from rest through height h
  • Release from rest through height h v = √(2gh), as in free fall.
5Track shape
  • Track shape only the vertical drop matters for a roller coaster or pendulum.
6With friction
  • Ki + Ui + Wf = Kf + Uf with Wf negative.

Part 4 of 7Graphs and bar charts

Bar charts
  • K and U at different positions with constant total height when energy is conserved.
Ball thrown upward
  • U against height is a straight line through the origin with gradient mg.
K against height
  • K against height a straight line falling to zero at the top; K and U mirror each other and sum to a constant.
K against time
  • K against time parabolic.

Part 5 of 7Limits

Limits
Small height changes only
  • Small height changes only the formula needs height change small compared with the planet's radius.
Large distances
  • Large distances use U = −GMm/r instead.
System
  • System the energy belongs to the object–Earth system.

Part 6 of 7Energy methods versus kinematics

Energy methods versus kinematics
Use energy
  • Use energy when heights and speeds are given but not times, or the path is curved or unknown.
Use kinematics
  • Use kinematics when time is asked for or acceleration is constant and known.
Pendulum released at angle θ
  • Pendulum released at angle θ drop is L(1 − cosθ), so v = √(2gL(1 − cosθ)).
Projectile launched at v from height y0
  • Projectile launched at v from height y0 impact speed is √(v2 + 2gy0) whatever the launch angle.
Resistive forces
  • Resistive forces include friction or drag as a negative work term.

Part 7 of 7More from the specification

1Potential energy and reference frames
  • Potential energy and reference frames gravitational potential energy depends on relative vertical separation, remaining consistent across uniform inertial reference frames.
2Observer
  • Person or instrument measuring from within a frame.
3Driver
  • The external system supplying the periodic force.
4Scalar quantity
  • A quantity with magnitude only, such as potential
5Reference frame
  • Coordinate system used by an observer.
6Spring constant
  • Stiffness k in N/m.
7Elastic
  • Returns to original shape when force is removed.
8Velocity
  • Rate of change of displacement.
9Satellite
  • A body that orbits a larger one; the Moon is the Earth's natural satellite.
10Stationary
  • Not moving.

Key terms

TermMeaning
Gravitational potential energyEnergy stored by position in a gravitational field, mgΔy near a surface.
Reference levelHeight chosen as zero potential energy.
Conservation of mechanical energyK + U constant when only conservative forces do work.
Vertical dropChange in height used in energy calculations.
SystemObjects considered together, such as ball and Earth.

Avoid these mistakes

1
Using the length along a ramp instead of the vertical height.
2
Thinking speed depends on mass in a frictionless problem.
3
Using an inconsistent zero level.
4
Using mgΔy for very large altitudes.
5
Applying energy conservation when friction does work without including its term.

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