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Q. 53

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 157

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Short Answer

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

See the step by step solution

Step by Step Solution

Step 1. The small box acceleration

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

Step 2. Acceleration needed for the small box to start slipping 

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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