# How much work does it take to push an object with a mass of 1 kg  up a 6 m  ramp, if the ramp has an incline of (5pi)/12 and a kinetic friction coefficient of  4 ?

Feb 3, 2016

$W = 117 , 83592$ "Joule"

#### Explanation:

$s t e p : 1$
$\text{let's convert radian to degree}$

$\theta = 180 \cdot \frac{5 \cancel{\pi}}{12 \cancel{\pi}} = {75}^{o}$
$\sin 75 = 0 , 966$
$\cos 75 = 0 , 259$
$G = m \cdot g = 1 \cdot 9 , 81 = 9 , 81 N$

$s t e p : 2$
$\textcolor{g r e e n}{{F}_{1}} = G \cdot \sin \theta = 9 , 81 \cdot 0 , 966 = 9 , 47616 N$
$\textcolor{red}{{F}_{2}} = G \cdot \cos \theta = 9 , 81 \cdot 0 , 259 = 2 , 54079 N$
$\textcolor{red}{N = - {F}_{2}} = - 2 , 54079 N$
$\textcolor{red}{N} \text{is the reacting force to" color(red)(F_2)"by acting surface}$
$\textcolor{p u r p \le}{{F}_{f}} = k \cdot \textcolor{red}{N} \text{(friction force)}$
$\textcolor{p u r p \le}{{F}_{f}} = 4 \cdot 2 , 54079 = 10 , 16316 N$
$\text{now let's sum these forces}$
$\sum F = \textcolor{g r e e n}{{F}_{1}} + \textcolor{p u r p \le}{{f}_{f}}$
$\sum F = 9 , 47616 + 10 , 16316$
$\sum F = 19 , 63932 N$

$s t e p : 3$

$\sum F \text{ is the minimum force that will transport object from}$
$\text{the point A to the point B}$
$W = \sum F \cdot \Delta x$
$W = 19 , 63932 \cdot 6$
$W = 117 , 83592$ "Joule"