Answered: How high can the mass be dropped…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

A body with a mass of m=20 kg is at rest in the vertical circular cylinder in the picture at a height h from the rigid base plate. The piece slides frictionlessly in the cylinder and hits the bottom plate under the influence of gravity g=9.81 m/s^2. The collision is completely inelastic and the bottom plate is completely rigid. The cross-sectional area of the cylinder is A=1500 mm^2, the elastic coefficient of the material is E=70 GPa and the length of the pipe is L=1.0 m. Present the responses of the system to displacement, velocity and acceleration.

How high can the mass be dropped without an initial velocity so that the amplitude of the oscillation does not increase more than 1 mm?

E
h
X
Kuvan pystysuorassa ympyräsylinterissä korkeudella h jäykästä
pohjalevystä on levossa kappale, jonka massa on m = 20 kg. Kappale
liukuu kitkattomasti sylinterissä ja osuu pohjalevyyn painovoiman
vaikutuksesta g = 9.81 m/s². Törmäys on täysin kimmoton ja
pohjalevy on täysin jäykkä. Sylinteriputken poikkipinta-ala on
A = 1500 mm2, materiaalin kimmokerroin on E = 70 GPa ja putken
pituus on L = 1.0 m.
Esitä systemin vasteet siirtymälle, nopeudelle ja kiihtyvyydelle.
Kuinka korkealta massa voidaan tiputtaa ilman alkunopeutta, jotta
värähtelyn amplitudi ei kasva suuremmaksi kuin 1mm.

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