# A box with an initial speed of 4 m/s is moving up a ramp. The ramp has a kinetic friction coefficient of 5/6  and an incline of pi /3 . How far along the ramp will the box go?

Nov 10, 2016

$s = {v}^{2} / \left(2 g \left(\sin \alpha + k \cos \alpha\right)\right)$

$s = 0.64 m$

#### Explanation:

${E}_{k} = {E}_{p} + {W}_{T}$
$m {v}^{2} / 2 = m g h + {F}_{t} s$
${F}_{t} = {F}_{n} = m g \cdot \cos \alpha$
$\frac{h}{s} = \sin \alpha$
$m {v}^{2} / 2 = m g s \cdot \sin \alpha + k m g s \cos \alpha$
$s = {v}^{2} / \left(2 g \left(\sin \alpha + k \cos \alpha\right)\right)$
$k = \frac{5}{6}$
$\alpha = \frac{\pi}{3}$
$g = 9.81 \frac{m}{s} ^ 2$
$s = 0.64 m$