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Chapter 15: Q.35 (page 416)

Vision is blurred if the head is vibrated at 29 Hz because the vibrations are resonant with the natural frequency of the eyeball in its socket. If the mass of the eyeball is 7.5 g, a typical value, what is the effective spring constant of the musculature that holds the eyeball in the socket?

Short Answer

Expert verified

The effective sprint constant is 248.757 N/m

Step by step solution

01

Introduction

The frequency of oscillation of a spring-mass system is given by

f=12πkm

where

ff=29HzHz is the frequency of oscillation

m=7.5g=0.0075kgis the mass of the eyeball

k is the spring constant

Solving equation for k

k=2×π×292×0.0075k=(2×3.14×29)2×0.0075 k=248.757N/m

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Most popular questions from this chapter

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On your first trip to Planet Xyou happen to take along a 200gmass, a 40cm-long spring, a meter stick, and a stopwatch. You’re curious about the free-fall acceleration on Planet X, where ordinary tasks seem easier than on earth, but you can’t find this information in your Visitor’s Guide. One night you suspend the spring from the ceiling in your room and hang the mass from it. You find that the mass stretches the spring by 31.2cm. You then pull the mass down 10.0cmand release it. With the stopwatch you find that 10oscillations take 14.5s. Based on this information, what is g?

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