assignment Homework

Find Force Law: Logarithmic Spiral Orbit
Central Forces 2023 (3 years)

In science fiction movies, characters often talk about a spaceship “spiralling in” right before it hits the planet. But all orbits in a \(1/r^2\) force are conic sections, not spirals. This spiralling in happens because the spaceship hits atmosphere and the drag from the atmosphere changes the shape of the orbit. But, in an alternate universe, we might have other force laws.

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

group Small Group Activity

120 min.

Projectile with Linear Drag
Theoretical Mechanics (4 years)

Projectile Motion Drag Forces Newton's 2nd Law Separable Differential Equations

Students consider projectile motion of an object that experiences drag force that in linear with the velocity. Students consider the horizontal motion and the vertical motion separately. Students solve Newton's 2nd law as a differential equation.

assignment Homework

Find Force Law: Spiral Orbit
Central Forces 2023 (3 years)

In science fiction movies, characters often talk about a spaceship “spiralling in” right before it hits the planet. But all orbits in a \(1/r^2\) force are conic sections, not spirals. This spiralling in happens because the spaceship hits atmosphere and the drag from the atmosphere changes the shape of the orbit. But, in an alternate universe, we might have other force laws.

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.