During an earthquake, a floor oscillates horizontally in approximately simple ha

Question

During an earthquake, a floor oscillates horizontally in approximately simple harmonic motion. Assume it oscillates at a single frequency with a period of 0.68 s.

(a) After the earthquake, you are in charge of examining the video of the floor motion and discover that a box on the floor started to slip when the amplitude reached 5 cm. From your data, determine the coefficient of static friction between the box and the floor.


(b) If the coefficient of friction between the box and floor were 0.34, what would be the maximum amplitude of vibration before the box would slip?
cm

Explanation / Answer

T =0.68 s,

(a) A = 5 cm

for simple harmoic motion amax = -w^2*A

from newton second law F= ma

Fs= mg*u = ma

a = u*g

u* g = w^2*A

u*9.8 =(2*3.14/0.68)^2*0.05

u =0.435

(b) u =0.34

u* g = w^2*A

0.34*9.8 =(2*3.14/0.68)^2*A

A = 3.91 cm

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