Question

In a certain engine a piston executes vertical SHM with amplitude 2 cm. A washer rests on the top of the piston. If the frequency of the piston is slowly increased, at what frequency will the washer no longer stay in contact with the piston?

Answer 1

The frequency at which the washer will lose contact with the piston is when the maximum acceleration of the SHM is greater than gravity; this frequency can be calculated using the formula for maximum acceleration in SHM.

Step-by-step explanation:

The student is asking about the conditions under which a washer resting on a piston undergoing vertical simple harmonic motion (SHM) will lose contact with the piston if the frequency of the piston's motion is increased. When the piston is at its highest point of the SHM, the acceleration is at its maximum and directed downwards.

For the piston and washer to lose contact, this acceleration must be greater than the acceleration due to gravity (g).

We know that for a system in SHM, the maximum acceleration (a) is given by a = (2πf)2A, where f is the frequency and A is the amplitude of the motion. Setting this equal to g and solving for f, we find the critical frequency where the washer will lose contact: f = √(g / (4π2A)).

Substituting the given amplitude of 2 cm (or 0.02 m) and using the approximate value of g = 9.81 m/s2, we get the frequency value where the washer loses contact with the piston.