A small bolt with a mass of 33.0 g sits on top of a piston. The piston is undergoing simple harmonic motion in the vertical direction with a frequency of 3.05 Hz. What is the maximum amplitude with which the piston can oscillate without the bolt losing contact with the piston's surface? Use g = 9.81 m/s^2 for the acceleration due to gravity.

Question

Braiden Brewer

Physics

16 August, 00:55

A small bolt with a mass of 33.0 g sits on top of a piston. The piston is undergoing simple harmonic motion in the vertical direction with a frequency of 3.05 Hz. What is the maximum amplitude with which the piston can oscillate without the bolt losing contact with the piston's surface? Use g = 9.81 m/s^2 for the acceleration due to gravity.

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Answers (1)

Know the Answer?

Orlando Valentine · Answer 1

A=0.0267 m

Explanation:

Given that

m = 33 g = 0.033 kg

Frequency, f = 3.05 Hz

We know that

ω = 2 π f

ω = 2 x 3.05 π

ω = 6.1 π s⁻¹

ω² m = K

K=Spring constant

(19.16) ² x 0.033 = K

K = 12.11 N/m

The maximum amplitude A

K A = m g

12.11 x A = 0.033 x 9.81

A=0.0267 m