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
\[E=U(x)\]
-4-20240246810xenergyU(x)E
The particle can move where the total-energy line is above the potential curve.

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.