A tray is moved horizontally back and forth in simple harmonicmotion at a freque

Question

A tray is moved horizontally back and forth in simple harmonicmotion at a frequency of f = 2.18 Hz. On this tray is an empty cup. Obtain thecoefficient of static friction between the tray and the cup, giventhat the cup begins slipping when the amplitude of the motion is4.55 x 10-2m.
s =
Thank you for your help!! A tray is moved horizontally back and forth in simple harmonicmotion at a frequency of f = 2.18 Hz. On this tray is an empty cup. Obtain thecoefficient of static friction between the tray and the cup, giventhat the cup begins slipping when the amplitude of the motion is4.55 x 10-2m.
s =
Thank you for your help!!

Explanation / Answer

.    Frequency (f) = 2.18 Hz .    Amplitude (A) = 4.55 * 10-2  m . From conservation of force : .    m a =   s mg .    ==> a =    s  g   .    ==>     s = a /g     -------------------(1) . We know that : acceleration is : a = A 2   = A ( 2 f)2   . Hence equation (1) changes to : .        s =   A ( 2f )2   / g    .       = ( 4.55 * 10-2  m * 4 2  * f2 )/ g .       = ( 4.55 * 10-2  m * 4 2  *(2.18)2 ) / 9.8 .       = ---------- . Solve it. . Hope this helps u!

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