1) A small ball is attached to one end of a spring that has an unstrained length

Question

1) A small ball is attached to one end of a spring that has an unstrained length of 0.204 m. The spring is held by the other end, and the ball is whirled around in a horizontal circle at a speed of 2.97 m/s. The spring remains nearly parallel to the ground during the motion and is observed to stretch by 0.009 m. By how much would the spring stretch if it were attached to the ceiling and the ball allowed to hang straight down, motionless? 2) When responding to sound, the human eardrum vibrates about its equilibrium position. Suppose an eardrum is vibrating with an amplitude of 6.20 10-7 m and a maximum speed of 3.10 10-3 m/s. (a) What is the frequency (in Hz) of the eardrum's vibration? (b) What is the maximum acceleration of the eardrum?

Explanation / Answer

when the mass is inrotation in horizontal plane we write

kx=mv^2/R...because this is a centripetal force

then k/m=v^2/Rx

here v=2.97 m/s
R=20cm+.9cm=20.9cm=0.209m
x=.9cm=.009m

then we know the value of k/m

If the mass is attached to the spring we will write

kx=mg

then
k/m=g/x we know k/m then

x= g(m/k)

here x is the spring strech when the mass is attached to the spring, g=9.8

find x??

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