Final answer:
The frequency at which the maximum force on a 75 g block equals its weight is approximately 1.58 Hz.
Step-by-step explanation:
To determine the frequency at which the maximum force on a 75 g block is equal to its weight, we can use the formula for the maximum force in simple harmonic motion, which is given by F_max = m * w² * A, where m is the mass, w is the angular frequency, and A is the amplitude of the oscillation.
Since the maximum force is equal to the weight of the block, we have F_max = m * g, where g is the acceleration due to gravity. Setting these two equations equal to each other, we can solve for the frequency:
F_max = m * w² * A = m * g
w² = g / A
w = sqrt(g / A)
Finally, we can convert the angular frequency to the frequency in Hz, by using the formula f = w / (2 * pi), where f is the frequency.
Plugging in the values, we get:
f = sqrt(g / A) / (2 * pi)
Substituting g = 9.8 m/s² and A = 0.18 m, we can calculate the frequency:
f = sqrt(9.8 / 0.18) / (2 * pi) ≈ 1.58 Hz