Question

A large box of mass M is pulled across a horizontal, frictionless surface by a horizontal rope with tension T. A small box of mass m sits on top of the large box. The coefficients of static and kinetic friction between the two boxes are μs and μk, respectively.Find an expression for the maximum tension T max for which the small box rides on top of the large box without slipping.

Answer 1

Answer:

Explanation:

Given

Mass of big box is M and small box is m

Tension T will cause the boxes to accelerate

$T=(M+m)a$

where a=acceleration of the boxes

Now smaller box will slip over large box if the acceleration force will exceed the static friction

i.e. for limiting value

$\mu _smg=ma$

$a=\mu _s\cdot g$

thus maximum tension

$T=\mu _s(M+m)g$