AP Physics C: Mechanics / Unit 3: Work, Energy, and Power
3.3 Potential Energy
Notes
- Gravitational: $U_g=mgh$ near Earth.
- Spring: $\displaystyle U_s=\frac{1}{2}kx^2$.
- Potential energy belongs to a system (object + Earth, or spring + mass).
Practice
A 2 kg book lifted 3 m gains (g = 10):
$mgh$.
A spring ($k=100$ N/m) compressed 0.2 m stores:
$\displaystyle \frac{1}{2}(100)(0.04)$.
Potential energy depends on:
Stored by arrangement.
If $U(x)=x^2-4x$, the force is $\displaystyle F=-\frac{dU}{dx}=$
Force is the negative slope of $U$.
Equilibrium for $U(x)=x^2-4x$ is at:
$F=0$ where $\displaystyle \frac{dU}{dx}=0$.
Ready for more? Take the Unit 3 test.