Piston Question that I do not understand

[LandOfStandar]

[SOLVED] Piston Question that I do not understand

Homework Statement

A block rides on a piston that is moving vertically with simple harmonic motion.
(a) If the SHM has a period 1.0s, at what amplitude of motion will the block and piston separate?
(b) If the piston has an amplitude of 5.0cm, what is the maximum frequency for which the block and piston will be in contact continuously?

The attempt at a solution

I don't understand the question. What is a piston, what causes the block to separate, how do I start the question?

 

[LandOfStandar]

I searched it more and got an answer

 

[Moetasim]

As a scientist, it is important to first understand the terminology and concepts being used in a question before attempting to solve it. A piston is a component of an engine or pump that moves back and forth in a cylinder, creating pressure and motion. In this scenario, the piston is moving vertically with simple harmonic motion, meaning it is moving up and down in a regular pattern.

To start the question, you can first try to visualize the scenario described. Imagine a block sitting on top of a piston that is moving up and down. Now, think about what might cause the block and piston to separate. This could be due to the amplitude of the piston's motion, or the frequency at which it is moving.

To solve part (a), you can use the equation for simple harmonic motion: x = A*sin(ωt), where x is the displacement, A is the amplitude, ω is the angular frequency (2πf), and t is time. The question states that the period of the SHM is 1.0s, which means the time for one complete cycle is 1.0s. From this, you can calculate the angular frequency (ω = 2π/1.0s = 2π rad/s). Now, you can set up the equation for the block and piston separating, which is when the displacement of the block (x) is equal to the amplitude of the piston (A). So, you can solve for A by plugging in the known values: A = x/sin(ωt).

For part (b), you can use the equation for frequency: f = 1/T, where f is frequency and T is period. The question states that the piston has an amplitude of 5.0cm, which means the maximum displacement of the block is 5.0cm. Now, you can set up the equation for the block and piston being in contact continuously, which is when the displacement of the block (x) is less than or equal to the amplitude of the piston (A). So, you can solve for the maximum frequency by plugging in the known values: f = 1/T = 1/2π * A/x.

I hope this explanation helps you understand the question better. It is important to always clarify any confusion or doubts before attempting to solve a problem.