## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

$T_{max} = (M+m)~g~\mu_s$
While the small box rides on the large box without slipping, the force of static friction provides the force to move the small box. We can find the maximum acceleration that the force of static friction can provide for the small box as; $F_f = ma$ $mg~\mu_s = ma$ $a = g~\mu_s$ We can use a force equation to find $T_{max}$ when the acceleration of the system is $g~\mu_s$; $\sum F = (M+m)~a$ $T_{max} = (M+m)~g~\mu_s$