Work through the list without notes. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions.
Understanding
- I can explain why potential energy belongs to a system of two or more objects, not to one object. (Guide: “Potential energy belongs to a system”)
- I can say what makes a force conservative and show with numbers that friction has no potential energy. (Guide: “Potential energy belongs to a system”; Practice Q7)
- I can explain why the choice of zero potential energy changes values of U but never changes ΔU. (Guide: “Defining U with an integral”)
- I can explain why mgΔy is an approximation and when it fails. (Guide: Worked example 2)
Calculation
- I can derive U(x) from a conservative force with ΔU = −∫F dx, including for a nonideal spring. (Guide: Worked example 3; Practice Q4)
- I can derive U_s = ½k(Δx)² and U_g = −Gm₁m₂/r by integration, stating the zero I used. (Guide: “Elastic potential energy” and “Gravitational potential energy”)
- I can find F_x = −dU/dx at a point and give its direction. (Guide: Worked example 1; Practice Q1)
- I can add pair energies to find the potential energy of three or more objects. (Guide: “Systems with three or more objects”; Practice Q3)
Reasoning and representations
- I can locate equilibrium positions from dU/dx = 0 and classify them with the second derivative or by nudging. (Guide: Worked example 1; Practice Q2, Q5)
- I can sketch U(r) and F(r) on aligned axes and mark the minimum, zero crossings and long-range behaviour. (Guide: Figure 1; Practice Q5)
- I can estimate a force and an equilibrium position from a table of U(x) values. (Practice Q6)
All ticked? Move on to Topic 3.4, Conservation of Energy, or return to the course roadmap.