Solution 5.6c

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First the maximum friction must be calculated.

To do this we need the normal reaction force \displaystyle R.

Resolving in the normal direction

\displaystyle \begin{align} & R-mg\cos {{20}^{\circ }}=0 \\ & R=72\times 9\textrm{.}8\times 0\textrm{.}94=663\ \text{N} \\ \end{align}

Then the maximim friction \displaystyle F is

\displaystyle \mu R=0\textrm{.}2\times 663=132\ \text{N}

The gravitational force which we denote as \displaystyle G \text 1, down the slope is

\displaystyle G1=mg\sin {{20}^{\circ }}=72\times 9\textrm{.}8\times 0\textrm{.}342=241\ \text{N}

The forces are in equilibrium down the slope. If we denote the air resistance force as \displaystyle F \text 1, we get,

\displaystyle G1-F1-F=0

giving

\displaystyle F1=G1 -F=241-132=109\ \text{N}