Question

a block is placed on piston which is moving vertically with a simple moyionmos period 1second.At what amplitude of the motion will the block and piston just get separated?if the piston has an amplitude of 5cm upto what frequensy will the block remain continuosly in contact with piston?

Answer 1

Answer on Question #59257-Physics-Mechanics-Relativity

A block is placed on piston which is moving vertically with a simple harmonic motion period 1 second. At what amplitude of the motion will the block and piston just get separated? If the piston has amplitude of 5 cm up to what frequency will the block remain continuously in contact with piston?

Solution

The maximal acceleration is needed to be equal and opposite the acceleration due to the gravity:

$$a_{max} = \omega^{2} A = g.$$ $$T = \frac{2\pi}{\omega} \rightarrow \omega = \frac{2\pi}{T}$$ $$A = \frac{g}{\omega^{2}} = \frac{g}{\left(\frac{2\pi}{T}\right)^{2}} = \frac{9.81 \, \text{m/s}^{2}}{\left(\frac{2\pi}{1 \, \text{s}}\right)^{2}} = 0.248 \, \text{m}.$$

The frequency will be:

$$f = \frac{\omega}{2\pi} = \frac{1}{2\pi} \sqrt{\frac{g}{A}} = \frac{1}{2\pi} \sqrt{\frac{9.81 \, \text{m/s}^{2}}{0.05 \, \text{m}}} = 2.23 \, \text{Hz}.$$

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