# How much work does it take to push an object with a mass of 6 kg up a 1 m ramp, if the ramp has an incline of (5pi)/12  and a kinetic friction coefficient of 7 ?

Jul 8, 2017

The work is $= 163.3 J$

#### Explanation:

The coefficient of kinetic friction is

${\mu}_{k} = {F}_{r} / m g \cos \theta$

${F}_{r} = {\mu}_{k} m g \cos \theta$

The mass is m=6kg

The coefficient of kinetic friction is ${\mu}_{k} = 7$

The angle is $\theta = \frac{5}{12} \pi$

The distance is $d = 1 m$

Resolving in the direction parallel to the plane ↗^+#

The force is

$F = m g \sin \theta + \mu m g \cos \theta$

The work is

$W = F d$

$= \left(m g \sin \theta + \mu m g \cos \theta\right) \cdot d$

$= m g \left(\sin \theta + {\mu}_{k} \cos \theta\right) \cdot d$

$= 6 g \left(\sin \left(\frac{5}{12} \pi\right) + 7 \cos \left(\frac{5}{12} \pi\right)\right) \cdot 1$

$= 163.3 J$