(help pls)A wooden rod is placed on top of the piston, performs a vertical simple harmonic motion. find 1) and 2)?
1) Let the period of the simple harmonic motion be 1.0s. What amplitude of the motion can the wooden rod and piston be separated?
2) When the motion's amplitude is 5.0cm, what is the maximum frequency needed for the block and the piston to keep the motion while still being attached to each other?
1) Let the period of the simple harmonic motion be 1.0s. What amplitude of the motion can the wooden rod and piston be separated?
2) When the motion's amplitude is 5.0cm, what is the maximum frequency needed for the block and the piston to keep the motion while still being attached to each other?
1 Answer
1) For amplitudes of
2) The rod and piston will remain in contact for angular frequencies up to
Explanation:
1)
For SHM in the vertical direction, with co-ordinate
-
#ddot y = - omega^2 y# -
#y = Y sin omega t#
The tendency of the rod, absent the piston, would be to freefall with acceleration
Max downward acceleration of piston occurs at
#ddot y = - omega^2 Y#
The piston and rod will separate if:
#abs( - omega^2 Y) gt abs(- g) qquad implies Y gt g/omega^2 qquad square#
Here:
# Y gt g/( 4 pi^2) [approx bb( 0.25" m")]# , with#g approx 9.81 \ m s^(-2)#
So for amplitudes of
2)
Re-writing
#omega gt sqrt(g/Y)#
With same approximate value for
# sqrt(9.81/0.05) approx 14 \ rad \ s^(-1)#
Bearing in mind the rounding and approximate values, the rod and piston will remain in contact for angular frequencies up to
[To convert to oscillation frequency