Halliday, Resnick & Walker — Force and Motion–II: Problem 96_BIO

Icy curb ramps. Slipping and falling while walking on an icy surface is a very common occurrence in winter weather. The danger comes when a person steps forward because then the full weight is over only the rear foot while that foot pushes backward. The static coefficient of friction of a common shoe (flat shoe or pump) on ice is \(\mu_s = 0.050\). Let the person’s mass be \(m = 70 \text{ kg}\). (a) On a level surface, what magnitude \(F\) of the horizontal backward push puts the person on the verge of slipping? (b) Most urban communities require curb ramps (Fig. 6.50) so that wheelchairs can travel between sidewalk and street. The common allowed slope is for a rise of 1 distance unit to a (horizontal) length of 12 distance units, which gives a slope of 8.33%. If the person attempted to stand on such a ramp that is covered with ice, what would be the magnitude of the component of the gravitational force on the person down the ramp? (c) What would be the maximum magnitude of the static frictional force up the ramp? (d) Can the person stand like that without slipping (or walk up the ramp)? (e) What is the maximum angle \(\theta_{\text{verge}}\) of a ramp such that the person is on the verge of slipping? (f) Some brands of winter footwear allow a person to walk up a ramp that is at the maximum allowed angle of 7.0° without slipping. If the backward force magnitude that puts the person on the verge of slipping is 34 N, what is the coefficient of static friction between the footwear and the ice?