Exercise
https://texercises.raemilab.ch/exercise/acceleration-ramp/
Question
Solution
Short
Video
\(\LaTeX\)
No explanation / solution video to this exercise has yet been created.

Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
The two conducting rails in the drawing are tilted upward so they each make an angle of alO with respect to the ground. The vertical magnetic field has a magnitude of BO. The mO aluminum rod length LO slides without friction down the rails at a constant velocity. includegraphicswidth.textwidth#image_path:accelerated-rod# abcliste abc Determine the direction of the current. abc How much current flows through the rod? abc Calculate the acceleration for a current of IbO. abcliste

Solution:
abcliste abc The two relevant forces are the components F_Gparallel of the gravitational force and F_Bparallel of the magnetic force parallel to the rails. F_Bparallel has to oppose the effect of F_Gparallel i.e. the magnetic force has to have an component in the upward direction. This is only possible if the current flows from right to left. abc The horizontal magnetic force is given by F_B I L B The component F_Bparallel parallel to the rails is F_Bparallel F_B cosalpha I L B cosalpha The component F_Gparallel is F_Gparallel F_Gsinalpha m gsinalpha For a constant velocity the two components have to cancel each other. It follows for the current I fracm gsinalphaL Bcosalhpa IF fracmtimes ncgLtimes Btimestanal I approx resultIP abc The resultant force parallel to the rails is given by sscFres F_Bparallel-F_Gparallel I L B cosalpha - m gsinalpha Using Newton's second law we find for the acceleration a fracsscFresm aF fracIbtimes Ltimes Btimes cosalm - ncgtimessinal a approx resultaP abcliste
Report An Error
You are on texercises.raemilab.ch.
reCaptcha will only work on our main-domain \(\TeX\)ercises.com!
Meta Information
\(\LaTeX\)-Code
Exercise:
The two conducting rails in the drawing are tilted upward so they each make an angle of alO with respect to the ground. The vertical magnetic field has a magnitude of BO. The mO aluminum rod length LO slides without friction down the rails at a constant velocity. includegraphicswidth.textwidth#image_path:accelerated-rod# abcliste abc Determine the direction of the current. abc How much current flows through the rod? abc Calculate the acceleration for a current of IbO. abcliste

Solution:
abcliste abc The two relevant forces are the components F_Gparallel of the gravitational force and F_Bparallel of the magnetic force parallel to the rails. F_Bparallel has to oppose the effect of F_Gparallel i.e. the magnetic force has to have an component in the upward direction. This is only possible if the current flows from right to left. abc The horizontal magnetic force is given by F_B I L B The component F_Bparallel parallel to the rails is F_Bparallel F_B cosalpha I L B cosalpha The component F_Gparallel is F_Gparallel F_Gsinalpha m gsinalpha For a constant velocity the two components have to cancel each other. It follows for the current I fracm gsinalphaL Bcosalhpa IF fracmtimes ncgLtimes Btimestanal I approx resultIP abc The resultant force parallel to the rails is given by sscFres F_Bparallel-F_Gparallel I L B cosalpha - m gsinalpha Using Newton's second law we find for the acceleration a fracsscFresm aF fracIbtimes Ltimes Btimes cosalm - ncgtimessinal a approx resultaP abcliste
Contained in these collections:
  1. 11 | 11

Attributes & Decorations
Branches
Kinematics, Magnetism
Tags
acceleration, electromagnetism, force, lorentzkraft, magnetism, mechanics, mechanik, physics
Content image
Difficulty
(3, default)
Points
3 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator by
Decoration