How much work would it take to push a  1 kg  weight up a  3 m  plane that is at an incline of  (5pi) / 12 ?

Jul 29, 2017

Answer:

$W = 28.4$ $\text{J}$

Explanation:

I'll assume the incline plane is frictionless, as no information is given.

We're asked to find the total work done on a $1$-$\text{kg}$ object as it is pushed up an incline $3$ $\text{m}$ long and at an angle of $\frac{5 \pi}{12}$.

The force is given by

$F = m g \sin \theta = \left(1 \textcolor{w h i t e}{l} {\text{kg")(9.81color(white)(l)"m/s}}^{2}\right) \sin \left(\frac{5 \pi}{12}\right)$

$= 9.48$ $\text{N}$

Now, we use the equation

$W = F s$ (one-dimensional)

to find the necessary work ($s = 3$ $\text{m}$):

W = (9.48color(white)(l)"N")(3color(white)(l)"m") = color(red)(ul(28.4color(white)(l)"J"