Physics HL · Chapter 3: Work, Energy and Power
3.3 Potential Energy Models
Develop gravitational and elastic potential energy as system-level bookkeeping tools.
Estimated time: 24 minutes
Gravitational Potential Energy Near Earth
For height changes small compared with Earth’s radius, gravitational potential energy change is modeled by mgΔh. This representation is practical because it captures gravity’s path-independent contribution using only endpoints.
Reference level is arbitrary: only differences in potential energy are physically relevant.
Potential energy belongs to a system configuration, not to an isolated object by itself. In classroom problems, explicitly naming "object + Earth" helps avoid confusion about where energy is stored and why sign choices remain coherent across steps.
Elastic Potential Energy in Springs
If a spring obeys Hooke’s law, the force required to stretch it grows linearly with extension. The work needed to reach extension x is the area under the force-extension line, giving a quadratic storage law.
Between two extensions x_1 and x_2, use ΔE_elastic = (1/2)k(x_2^2 - x_1^2).
Because energy rises with x^2, doubling extension quadruples elastic energy. That non-linear scaling explains why small additional stretches near the end of extension can require significantly more work.
Choosing a Reference Level for Gravitational Potential
The zero level of gravitational potential energy can be chosen on any convenient horizontal reference, not only ground level. The physics is unchanged because only potential-energy differences appear in measurable predictions. This is why textbook examples give identical final speeds even when height is measured from different baselines.
A strong exam habit is to pick the reference that minimizes arithmetic and keeps signs clear. For pendulum and ramp problems, choosing zero at the lowest point often simplifies terms. For projectile problems from tables, choosing the floor as zero often keeps final-state expressions compact.