Originally Posted by **oz93666** Everything you need is there benit .. they ask for the maximum mass of the box. |

Okay, thanks. I was a bit puzzled because it just seems like it's going to state what it is and then doesn't, but maybe the question is phrased as one of those "the answer is this... now prove it" ones and the OP wanted to keep the statement hidden.

Your answer is fine, but here's the formulae anyway in case the OP is interested.

Assuming that the pushing force that the person exerts on the box is the same as the frictional force from the person's shoes (Newton's third law), the maximum force the person can apply is:

$\displaystyle F_{person} = \mu_{person} m_{person} g$

The box will move when this force exceeds the friction force of the box on the floor.

$\displaystyle F_{box} = \mu_{box} m_{box} g$

The maximum mass of the box is therefore the mass that makes the box's friction force equal to the person's pushing force, i.e.

$\displaystyle F_{person} = F_{box}$

Substitute and rearrange for $\displaystyle m_{box}$:

$\displaystyle m_{box} = m_{person} \cdot \frac{\mu_{person}}{\mu_{box}} = 75 \times \frac{0.8}{0.2} = 300 kg$