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103. Problem 16.27P (HRW) A block is on a piston that is moving vertically with simple harmonic motion. Period of SHM is 1.0 s. We have to find (a) the amplitude of motion that will separate the block and the piston. (b) If the piston has amplitude of 5.0 cm, we have to estimate the maximum frequency for which the block and piston will be in contact continuously. |
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Solution: Click For PDF Version (a) Piston and block will separate when the downward acceleration of the piston exceeds g. SHM period of the piston is 1.0 s. Angular frequency of SHM,
Amplitude of acceleration, x, and the maximum acceleration,
Amplitude of SHM for maximum acceleration to be g will therefore be
(b) We find next the maximum frequency for which the block and the piston will be in contact continuously. We use the relation for SHM between the maximum acceleration and amplitude for a given frequency,
The piston and the block will be in contact continuously for
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,
will therefore be
,
during the SHM are related as
.
.
For
, and
is