# A block weighing 4 kg is on a plane with an incline of (pi)/2 and friction coefficient of 4/5. How much force, if any, is necessary to keep the block from sliding down?

Mar 15, 2016

$F \ge 49 , 05 \text{ } N$

#### Explanation:

color(brown)(F_f)=color(red)(F)*mu" "mu=4/5" "color(brown)
$\textcolor{b r o w n}{{F}_{f}} = \textcolor{red}{F} \cdot \frac{4}{5}$
$\textcolor{b r o w n}{{F}_{f}} \ge \textcolor{g r e e n}{G}$
$\text{Object is not slides;}$
$\text{if the friction force is equal or greater than weight of object}$
$\frac{4}{5} \cdot {F}_{f} \ge m g$
$\frac{4}{5} \cdot F \ge 4 \cdot 9 , 81$
$\frac{4}{5} \cdot F \ge 39 , 24$
$F \ge \frac{5 \cdot 39 , 24}{4}$
$F \ge 49 , 05 \text{ } N$