bead parabola accelerometer

Atwood's machine ] bag of marbles ] balance moon stone ] ball up/down ] [ bead parabola accelerometer ] boat anchor lake ] boat time ] bobbin on incline ] bosun's chair ] bouncing ball ] bowling ball rolling ] bug on band ] bursting shell ] falling chain ] Feynman's restaurant problem ] five pills ] flying cable ] forced pendulum ] gold mountain ] half pills ] hallway pole ] impelled rod ] inelastic relativistic collision ] infinite pulleys ] mass on an incline ] maximum angle of deflection ] packs of shirts ] particle in bowl ] particle in cone ] particle on sphere ] particle points parabola ] pile of bricks ] pion muon neutrino ] piston ramp spring ] plank weight trough ] rocket vs. jet ] roll without slipping ] rough inclined plane ] shooting marbles ] speedometer test ] three balls ] three logs ] turntable cart ] two rolling balls exercise ] wheel and block ] whirling pendulum ] worlds fair ornament ]

service

This problem was contributed by Gert Hamacher.

An accelerometer is made of a piece of wire in the shape of a parabola  y = kx2  with a bead on it that can slide without friction, as shown in the drawing. The bead is initially attached to the wire at the lowest point of the parabola. The wire is accelerated with a constant acceleration parallel to the x-axis, and then the bead is released. Find the relationship between the acceleration a of the wire and the beadís maximum horizontal displacement x relative to the wire.

Answer


Solutions (listed by author)

 

Sukumar Chandra, (html, 3k)

Michael A. Gottlieb, (pdf, 86k)

 

Copyright © 2000-2013 Michael A. Gottlieb. All rights reserved.