In: Physics
During an earthquake, a floor oscillates horizontally in approximately simple harmonic motion. Assume it oscillates at a single frequency with a period of 0.67 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 11 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 0.39, what would be the maximum amplitude of vibration before the box would slip?
_______________cm
timeperiod T = 0.67 s , frequency f = 1/T = 1/0.67 = 1.492 Hz,
angular frequency W = 2*pi*f
= 2*3.14*1.4925
= 9.373
maximum static frictional force = mues *mg , F = k*x, x= A cos (wt)
k*A Cos wt = mues*mg w= sqrt(k/m) => k = w^2*m
w^2*m*A = mues *mg
mues= w^2*A/g = 9.373^2*11*10^-2 / 9.8 = 0.9861
b) mues= w^2*A/g
A = mues*g / w^2
= 0.39*9.8 / 9.373 ^2
= 0.0435 m
= 4.3 cm