A man of mass `75 kg` is pushing a heavy box on a flat floor. The coefficient of kinetic and static friction between the floor and the box is `0.20`, and the coefficient of static friction between the man's shoes and the floor is `0.80`. If the man pushes horizontally, what is the maximum values (in `kg`) of the box he can move?

Options

A. `300 kg`
B. `60 kg`
C. `900 kg`
D. none of these

Answer

A

Explanation

From FBD of the box, the box will move if
`Fgef_B`
`implies Fge0.2mg`………i
If the man is moving the box, then there is no sliping of te soes of the man on the floor. So friction on the man `f_m` will be static.

From FBD of the man `f_m=F`
but `f_mlemu_(s) 75g`
`impliesFlemus 75g` ............iii
From eqn i and ii we get
`0.2mgleFlemu_s 75g`
`implies 0.2mggemu_s 75g`
`impliesmle0.8/0.2xx75impliesmle300kg`