# 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  8 ?

Work done to displace the object of $1 k g$ mass upward on a plane of length $l = 6 m$ inclined at an angle of $\setminus \theta = \frac{5 \setminus \pi}{12}$
$= \setminus \textrm{o p p o \sin g f \mathmr{and} c e} \setminus \times \setminus \textrm{\mathrm{di} s p l a c e m e n t a g a \in s t t h e \mathrm{di} r e c t i o n o f f \mathmr{and} c e}$
$= \left(m g \setminus \sin \setminus \theta + \setminus \mu m g \setminus \cos \setminus \theta\right) \setminus \times l$
$= \left(1 \setminus \cdot 9.81 \setminus \sin \setminus \frac{5 \setminus \pi}{12} + 0.8 \setminus \cdot 1 \setminus \cdot 9.81 \setminus \cos \setminus \frac{5 \setminus \pi}{12}\right) \setminus \times 6$
$= 58.86 \left(\setminus \frac{\setminus \sqrt{3} + 1}{2 \setminus \sqrt{2}} + 0.8 \setminus \cdot \setminus \frac{\setminus \sqrt{3} - 1}{2 \setminus \sqrt{2}}\right)$
$= 58.86 \left(\setminus \frac{1.8 \setminus \sqrt{3} + 0.2}{2 \setminus \sqrt{2}}\right)$
$= 69.04166533116205 \setminus J$