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Results: central forces

assignment Homework

Central Force

Which of the following forces can be central forces? which cannot?

  1. The force on a test mass \(m\) in a gravitational field \(\vec{g~}\), i.e. \(m\vec g\)
  2. The force on a test charge \(q\) in an electric field \(\vec E\), i.e. \(q\vec E\)
  3. The force on a test charge \(q\) moving at velocity \(\vec{v~}\) in a magnetic field \(\vec B\), i.e. \(q\vec v \times \vec B\)

assignment Homework

Spiral Orbit
A mass \(\mu\), under the influence of a central-force field, moves in a logarithmic spiral orbit given by \(r = ke^{\alpha \phi}\), where \(k\) and \(\alpha\) are constants. Determine the force law of this central-force field.

computer Mathematica Activity

30 min.

Effective Potentials
Students use a pre-written Mathematica notebook or a Geogebra applet to explore how the shape of the effective potential function changes as the various parameters (angular momentum, force constant, reduced mass) are varied.

assignment Homework

Find Force Law

Find the force law for a central-force field that allows a particle to move in a spiral orbit given by \(r=k\phi^2\), where \(k\) is a constant.

groups Whole Class Activity

10 min.

Air Hockey
Students observe the motion of a puck tethered to the center of the airtable. Then they plot the potential energy for the puck on their small whiteboards. A class discussion follows based on what students have written on their whiteboards.
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