# How much work would it take to push a  6 kg  weight up a  12 m  plane that is at an incline of  pi / 4 ?

Apr 2, 2016

51 Joules

#### Explanation:

Here,
Hypotenuse (h) = 12m
Angle of inclination ($\theta$)= π/4
Perpendicular (p) = ?

We have, $S \in \theta = \frac{p}{h}$
or,  Sin (π/4) = p/12
or, $p = \frac{12}{\sqrt{2}}$
Hence, p = 8.5 m, which is the distance travelled.

Since work(W) is given by
W = F * S,
Where F = Force ( here weight) = 6 kg wt = 6 N
(Note kg wt, unlike kg, is same as Newton and is a unit of weight, not mass).
S is the distance traveled given by the perpendicular 8.5m
Therefore,
$W = 6 \cdot 8.5 = 51 \text{Joules}$