41. To meet a U.S. Postal Service requirement, employeesâ€™ footwear must have a coefficient of static friction of 0.5 or more on a specified tile surface. A typical athletic shoe has a coefficient of static friction of 0.800. In an emergency, what is the minimum time interval in which a person starting from rest can move 3.00 m on the tile surface if she is wearing (a) footwear meeting the Postal Service minimum and (b) a typical athletic shoe?
`F = ma, f_s = \mu_sn, d=1/2at^2`
(a) 1.11 s (b) 0.875 s
`a_(max) = F_(max)/m` `F_(max) = f_s =\mu_smg` `a_(max) = (\mu_smg)/m = \mu_sg` `d = 1/2at^2` `t = sqrt((2d)/a_(max))` (a) `t = \sqrt(6/(0.5\times9.8)) = 1.11 s` (b) `t = \sqrt(6/(0.800\times9.8)) = 0.875 s`