# How much work would it take to push a  2 kg  weight up a  6 m  plane that is at an incline of  pi / 3 ?

Feb 3, 2016

The amount of work done on the object is equal to the net change in the potential energy of the object.

$W = \Delta U = m g \Delta h$

Where $m$ is the mass of the object, $g$ is the acceleration due to gravity, and $\Delta h$ is the final height of the object. Notice that only the change in height matters, not the entire distance that the object travels. Since the plane is at an angle we can find the vertical component of the objects displacement using the $\sin$ function.

$\Delta h = \left(6 \text{m}\right) \sin \left(\frac{\pi}{3}\right)$

$= 2 \sqrt{3} \text{m}$

Now we can use the work formula above to get;

$W = \left(2 \text{ kg")(9.8 " ms"^-2)(2sqrt3 " m}\right)$

$= 67.9 \text{ J}$