Man pulling a cube on a rough surface

1. Feb 4, 2015

Karol

1. The problem statement, all variables and given/known data
A man of mass 70[kg] pules a box at an angle 100. the static coefficient of friction between his legs and the floor is 0.6 and the kinetic coefficient between the box and the floor is 0.3
What's the maximum's box's mass

2. Relevant equations
Friction: f=μN

3. The attempt at a solution
The horizontal force the man can apply:
$$70\cdot 9.81\cdot 0.6=412.02=F\cdot \cos 10^0\rightarrow F=418.38$$
The vertical component of F raises the box: $F\cdot \sin 10^0=418.02\cdot\sin 10^0=72.65$
the force needed to pull the box:
$$(mg-F\cdot \sin 10^0)0.3=412.02\rightarrow (mg-72.65)0.3=412.02\rightarrow m=147.4[kg]$$
It should be 164.85

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2. Feb 4, 2015

BvU

The vertical component of F does more than just that !

3. Feb 4, 2015

Karol

The vertical component also presses down on the man:
$$\left\{ \begin{array}{l} (mg-F\cdot \sin10^0)0.3=(70\cdot g+F\cdot \sin10^0)0.6 \\ F\cdot \cos10^0=(mg-F\cdot \sin10^0)0.3 \end{array} \right.$$
$$\rightarrow F=467.88,\ m=164.87\ \surd$$