Chapter 8 - Dynamics II: Motion in a Plane - Exercises and Problems - Page 199: 12

The coin will not slide off.

Work Step by Step

We can find the maximum possible force of static friction. $F_f = mg~\mu_s$ $F_f = (0.0050~kg)(9.80~m/s^2)(0.80)$ $F_f = 0.0392~N$ We can find the speed of the coin as it rotates at a rate of 60 rpm. $v = (60~rpm)(2\pi~r)(\frac{1~min}{60~s})$ $v = (60~rpm)(2\pi)(0.15~m)(\frac{1~min}{60~s})$ $v = 0.942~m/s$ We can find the centripetal force required to keep the coin moving around in a circle. $F_c = \frac{mv^2}{r}$ $F_c = \frac{(0.0050~kg)(0.942~m/s)^2}{0.15~m}$ $F_c = 0.0296~N$ Since the maximum force of static friction on the coin is greater than the required force to keep the coin moving around in a circle, the coin will not slide off.

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