A runner of mass wishes to accelerate as rapidly as possible on two different surfaces:

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics

Problem

A runner of mass

65\,\text{kg}

wishes to accelerate as rapidly as possible on two different surfaces: (A) a dry asphalt track with coefficient of static friction

\mu_{sA} = 0.70

and (B) a smooth icy surface with coefficient of static friction

\mu_{sB} = 0.05

. Answer the following questions. (i) Show that the maximum possible horizontal acceleration

a_{\max}

of the runner on any surface is

a_{\max} = \mu_s g

, where

\mu_s

is the coefficient of static friction for that surface. (ii) Calculate the ratio of the maximum accelerations on the two surfaces,

a_{\max A} : a_{\max B}

. (iii) If the runner wants to reach a speed of

9\,\text{m\,s}^{-1}

from rest using the maximum possible constant acceleration in each case, determine the minimum time required on surface A and on surface B.