You see the boy next door trying to push a crate down the sidewalk. He can barely keep it moving, and his feet occasionally slip. You start to wonder how heavy the crate is. You call to ask the boy his mass, and he replies " 51.0kg ." From your recent physics class you estimate that the static and kinetic coefficients of friction are 0.900 and 0.4 for the boy's shoes, and 0.5 and 0.2 for the crate. Estimate the mass of the crate?

Mc = 230kg

Explanation:

Please see the attachment below.

The boy is attempting to move the crate and himself by applause force. In order to do this successfully, he would have to apply a force on the ground which then exerts a reverse force that pushes the boy forward.

F = μsb ×Mb ×g

Assuming static friction force is at maximum, μsb = 0.9

This force must also equal the kinetics friction that must be balanced must to keep the crate moving. This force

F = μkc ×Mc ×g

So

F = μsb×Mb×g = μkc×Mc×g

Mc = μsb×Mb/μkc

= 0.9×51.0/0.2 = 229.5 ≈ 230kg

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