Find the maximum frequency for which the block and piston will be in contact

[radtad]

A block is on a piston that is moving vertically with simple harmonic motion. a)At what amplitude of motion will the block and piston sperate if the period of the piston's motion is 1.18 seconds? b) If the piston has an amplitude of 5.12 cm in its motion, find the maximum frequency for which the block and piston will be in contact continuously.

 

[apchemstudent]

A block is on a piston that is moving vertically with simple harmonic motion. a)At what amplitude of motion will the block and piston sperate if the period of the piston's motion is 1.18 seconds? b) If the piston has an amplitude of 5.12 cm in its motion, find the maximum frequency for which the block and piston will be in contact continuously.

a) The block and piston will separate when the force of the piston(assuming it is constant) equals the Force of gravity. So you know the acceleration of the piston must be 'g'... I assume the amplitude of the motion is the distance traveled in 1/4 of the period.

b)Although I said the acceleration must be 'g' to seperate, we can also use it for the max frequency for the block and piston to remain in contact. Basically just work backward except frequency = 1/T

 

[wais]

a) The block and piston will separate when the amplitude of the piston's motion is equal to the height of the block. Therefore, the amplitude of the piston's motion at which the block and piston will separate is 1.18 seconds.

b) The maximum frequency for which the block and piston will be in contact continuously can be found by using the formula for simple harmonic motion: f = 1/T, where T is the period of motion. Since we know that the period of the piston's motion is 1.18 seconds, the maximum frequency can be calculated as f = 1/1.18 = 0.8475 Hz. Therefore, the maximum frequency for which the block and piston will be in contact continuously is 0.8475 Hz.