To calculate the maximum kinetic energy of the insect, we need to determine the maximum velocity of the prong at the amplitude of vibration.
The maximum velocity of the prong can be calculated using the equation for simple harmonic motion:
v_max = 2πfA
where: v_max is the maximum velocity, f is the frequency of vibration (in Hz), and A is the amplitude of vibration (in meters).
Converting the given amplitude from millimeters to meters: A = 0.500 mm = 0.500 × 10^(-3) m = 0.0005 m
Substituting the values into the equation: v_max = 2π × 350 Hz × 0.0005 m = 3.5π m/s
Now we can calculate the maximum kinetic energy of the insect. Since the mass of the insect is given as 0.025 g, we first need to convert it to kilograms: mass = 0.025 g = 0.025 × 10^(-3) kg = 2.5 × 10^(-5) kg
The kinetic energy can be calculated using the formula: K.E. = (1/2)mv^2
Substituting the values into the equation: K.E. = (1/2) × 2.5 × 10^(-5) kg × (3.5π m/s)^2
Calculating the kinetic energy: K.E. ≈ 1.22 × 10^(-4) J
Therefore, the maximum kinetic energy of the insect is approximately 1.22 × 10^(-4) Joules.