A large box of mass is pulled across a horizontal, frictionless surface by a horizontal rope with tension . 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 and , respectively. Find an expression for the maximum tension for which the small box rides on top of the large box without slipping.
The expression is
First we isolate the F.B.D of each mass,
we start with the smaller one who is on top of the bigger box
The small box need to accelerate to to induce a force to make it slip
Now let take the F.B.D of the large box, the large box is moving in a frictionless surface
We will use the acceleration needed for the small box to start slipping, because the reference frame of the small box is the large box
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