# How much work would it take to push a  2 kg  weight up a  8 m  plane that is at an incline of  (5pi) / 12 ?

Apr 17, 2016

$W = 40.56 N m$

#### Explanation:

In this model you have to assume there is no air resistance or friction, and the acceleration of gravity is a constant $9.8 \frac{m}{s} ^ 2$ straight down.

The weight force of the object is given by

${F}_{\text{straight down}} = m g = 2 k g \cdot 9.8 \frac{m}{s} ^ 2 = 19.6 N$.

However, the Earth gets in the way of going straight down, so the closest the object can get to straight down is to go down the plane. Using trigonometry, we can find the force down the plane as

${F}_{\text{down plane}} = 19.6 N \cdot \cos \left(\frac{5 \pi}{12}\right)$
$= 19.6 \cos 75 = 5.07 N$

In order to move the mass up the plane, you need a force greater than or equal to the force down the plane, so

${F}_{\text{up plane}} = 5.07 N$.

Work is calculated by the equation

$W = F d$,

where $F$ is the forcee you've already found and $d$ is the distance of $8 m$ up the plane, so

$W = 5.07 N \cdot 8 m = 40.56 N m$