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 0.67 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

Explanation / Answer

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

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