A large block P executes horizontal simple harmonic motion as It slides across a

Question

A large block P executes horizontal simple harmonic motion as It slides across a frictionless surface with a frequency f- 1.60 Hz. Block B rests on it, and the coefficlent of static friction between the two is us-0.650. What maximum amplitude of oscillation can the system have if block B Is not to slip? Consider the maximum force of friction that acts to prevent slipping, and the acceleration that corresponds to that maximum force. What amplitude of oscillation leads, during the oscillatory motion, to acceieration no large acceleration corresponding to the maximum force of friction? cm r than the Need Help? Readt

Explanation / Answer

FN = m g costheta

FN = mg [for theta = 0]

Ff = mu m g

F = ma , F = Ff

a = mu g

F = k A [from hookes law]

k = F / A

m = F / a = F / mu g

frequency = (1 / 2 pi) sqrt (k/m) = (1 / 2 pi )* sqrt ( (F/A) / (F / mu g)) = (1 / 2 pi) * sqrt (mu g / A)

maximum amplitude = mus g / (2 pi f)2

= (0.650 * 9.8) / (2 pi * 1.60)2

maximum amplitude = 0.0630 m = 6.30 cm

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