Two identical blocks placed one on top of the other are at rest ona frictionless

Question

Two identical blocks placed one on top of the other are at rest ona frictionless horizontal air track. The lower block is attached toa spring of spring constant k=600.0N/m. When displaced slightlyfrom its equilibrium position, the system oscillates with afrequency of 1.80 Hz. When the amplitude of oscillation exceeds5.00 cm, the upper block starts to slide relative to the lower one.
a) What are the masses of the two blocks? b)What is the coefficient of static friction between the twoblocks?
a) What are the masses of the two blocks? b)What is the coefficient of static friction between the twoblocks?

Explanation / Answer

let each mass be m. a) when amplitude is below 5 cm, the 2 blocks oscillatetogether. f = (1/2)(k/2m) = 1.8 k/2m = (1.8*2)^2 m = k/[2(1.8*2)^2] = 600/[2(1.8*2)^2] = 2.35kg b) when the upper one begins to slide, spring force F = kx justexceeds friction f. f = 600(.05) = 30 newtons = N = mg = 30/(2.35*9.8) = 1.3

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