# How much work does it take to push an object with a mass of 2 kg up a 1 m ramp, if the ramp has an incline of (5pi)/12  and a kinetic friction coefficient of 7 ?

Dec 29, 2017

The work is $= 54.4 J$

#### Explanation:

Resolving in the direction parallel to the plane ↗

$\text{Force to push up the object "= "component of the weight parallel to the plane"+ "force of kinetic friction}$

$F = {\mu}_{k} \cdot m g \cos \theta + m g \sin \theta$

The work done is

$W = F \times d$

The mass of the object is $m = 2 k g$

The distance $d = 1 m$

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

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

The acceleration due to gravity is $g = 9.8 m {s}^{-} 2$

Therefore,

The work done is

$W = \left(7 \cdot 2 \cdot 9.8 \cdot \cos \left(\frac{2}{12} \pi\right) + 2 \cdot 9.8 \sin \left(\frac{5}{12} \pi\right)\right) \cdot 1$

$= 54.4 J$