What is the Velocity of a Cylinder on an Inclined Plane with a Magnetic Field?

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Homework Help Overview

The problem involves a disk rolling down an inclined plane while interacting with a magnetic field. The disk's motion is influenced by both gravitational forces and electromagnetic effects, specifically the induced electric field due to its motion through the magnetic field. The goal is to determine the velocity of the disk's center of mass when it exits the magnetic area.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants explore the conservation of energy and the relationship between kinetic energy and work done by electromagnetic forces. Some question the complexity of modeling the forces acting on the disk, while others suggest approximations to simplify the analysis.

Discussion Status

There is an ongoing exploration of different approaches to the problem, including the use of energy conservation and the effects of induced currents. Participants are actively questioning assumptions about the system, such as the nature of the electric field and the behavior of the disk as it rolls through the magnetic field.

Contextual Notes

Participants note the challenges posed by the varying velocity of the area in the magnetic field and the implications of neglecting certain terms in the equations. There is also mention of the need to consider the time-dependent nature of the system and the potential for approximations to facilitate analysis.

  • #31
Ok so I see now if I do a change of variable ##X=x-R## in my equation I get exactly the same equation as yours, up to constants, since the first and second derivative of X will not yield additional terms.

have to check the constants though, my constants will have to be the same as yours if I take ##R_y, R_x## to be just the internal resistances of the voltage sources ##E_y,E_x##
 

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