8. A di m e, m ass = 25 gra m s, is placed 4.00 cm from the center of a rotating

Question

8. A dime, mass = 25 grams, is placed 4.00 cm from the center of a rotating circular platform which has a radius = 16 cm. The platform is rotating at a frequency of 1.4 rev/sec.   The coefficient of static

friction between the dime and the platform is 0.6and the coefficient of kinetic friction is 0.2

(a) Will the dime stay in a circle of radius 4.00 cm?    (b) if the frequency is increased to 2.8

rev/sec, will the dime remain "stationary" on the platform? (c) When will it slide off the platform?

Part (c) is difficult, consider the force on the dime as the centrifugal (outward force) and kinetic friction as the inward force, and note that the centrifugal force varies with the radius of the dime.

Explanation / Answer

a) speed of dime =2*pi*4*1.4 cm/sec =35.19 cm/sec

mv^2 /r =25*35.9*35.9/4 =8055 gram*cm/sec^2

frictional force =0.6 *25*98.1=1470

mv^2 /r is way larger then static frictional force so therefore dime doesn't stay in that circle of radius 4cm

b)speed of dime =2*pi*4*2.8 cm/sec =70.37cm/sec

mv^2 /r =25*70.37*70.37/4 =30949

kinetic friction = 0.2*25*98.1

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