The prongs of a tuning fork each vibrate with an amplitude...

The prongs of a tuning fork each vibrate with an amplitude of $-0.50 \mathrm{mm}$ at the tuning fork's frequency of $440 \mathrm{Hz}$ a. What is the maximum speed of the tip of one prong? b. A $10 \mu \mathrm{g}$ flea was sitting on the tip of the prong when the tuning fork was sounded. Surface tension allows a flea's feet to hold onto a smooth surface with a force of up to $1.0 \mathrm{mN}$. Will the flea be able to hold onto the vibrating prong, or will it be thrown off?

The prongs of a tuning fork each vibrate with an amplitude of
$-0.50 \mathrm{mm}$ at the tuning fork's frequency of $440 \mathrm{Hz}$
a. What is the maximum speed of the tip of one prong?
b. A $10 \mu \mathrm{g}$ flea was sitting on the tip of the prong when the tuning fork was sounded. Surface tension allows a flea's feet to hold onto a smooth surface with a force of up to $1.0 \mathrm{mN}$. Will the flea be able to hold onto the vibrating prong, or will it be thrown off?

Key Concepts

Simple Harmonic Motion (SHM)

SHM describes the oscillatory motion of objects where the restoring force is directly proportional to the displacement and acts in the opposite direction. It provides the framework for analyzing periodic vibrations, including the relationship between amplitude, frequency, angular frequency, and the resulting velocities and accelerations of vibrating bodies.

Angular Frequency and Maximum Speed

Angular frequency (?) is a measure of how rapidly an object oscillates in SHM, calculated as 2? times the frequency. The maximum speed of an oscillating object is given by v_max = ?A, where A is the amplitude. This relationship is fundamental in determining how fast the tip of a vibrating object, such as a prong, moves at its fastest point.

Inertial Forces in Oscillatory Motion

In SHM, the maximum acceleration of the oscillating object is found using a_max = ?^2A. Multiplying this acceleration by the object's mass yields the inertial force acting on it. This concept is important when assessing whether additional objects on the vibrating system, such as a flea, can remain attached given the inertial forces induced by the oscillation.

Surface Tension and Adhesion

Surface tension and adhesion refer to the forces that allow small organisms or objects to stick to surfaces. In contexts where external forces act on a small body, such as a flea on a vibrating surface, comparing the maximum inertial force with the adhesion force (provided by surface tension in this case) is critical in determining whether the organism can hold on or be dislodged.

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