AcademyPotential Energy and Conservation
Academy
Reading Energy Diagrams
Level 1 - Physics topic page in Potential Energy and Conservation.
Principle
An energy diagram compares total mechanical energy with potential energy to show where motion is possible.
Notation
\(E\)
total mechanical energy
\(\mathrm{J}\)
\(U(x)\)
potential energy curve
\(\mathrm{J}\)
\(K\)
kinetic energy
\(\mathrm{J}\)
\(x_t\)
turning point
\(\mathrm{m}\)
Rules
Kinetic energy from diagram
\[K=E-U(x)\]
Allowed region
\[E\ge U(x)\]
Turning point
\[E=U(x)\]
Speed
\[v=\sqrt{\frac{2(E-U)}{m}}\]
Method
Compare levels
\[K=E-U(x)\]
Find allowed x
\[E\ge U(x)\]
Find turning points
\[E=U(x)\]
Examples
Question
At a point where
\[E=20\,\text{J}\]
and \[U=12\,\text{J}\]
find \(K\).Answer
\[K=E-U=20-12=8\,\text{J}\]
Checks
- Motion is allowed only where \(E\ge U\).
- Turning points occur where \(K=0\).
- Potential minima are stable equilibria.
- The vertical gap \(E-U\) is kinetic energy.