# How much work does it take to raise a 31 kg  weight 32 m ?

Mar 27, 2018

Consider the change is potential energy incurred as a result of raising the body of mass.

Recall,

$\text{PE} = m g H$

$W = F \cdot d \cdot \cos \theta$ where $\cos \theta = 1$ in this case,

due to the assumption of "horizontal" acceleration.

We can then say, $W = \Delta \text{PE}$, and assume we move the body of mass from a height of $0 m$

Hence,

$W = m g H - 0$
$\implies W = 31 \text{kg" * (9.8"m")/"s" * 32"m" approx 9.7*10^3"J}$

of work must be done on this body of mass to raise to the height you describe.

Mar 27, 2018

I get $9721.6 \setminus \text{J}$.

#### Explanation:

Well, work is defined through the equation,

$W = F \cdot d$

• $F$ is the force in newtons

• $d$ is the distance moved in meters

The force here is the weight of the box, which is given by,

$W = m g$

• $m$ is the mass of the object in kilograms

• $g$ is the gravitational acceleration in ${\text{m/s}}^{2}$, on Earth it's around $9.8 \setminus {\text{m/s}}^{2}$.

And so, the weight here is $31 \setminus \text{kg"*9.8 \ "m/s"^2=303.8 \ "N}$.

Therefore, the work done is:

$W = 303.8 \setminus \text{N"*32 \ "m}$

$= 9721.6 \setminus \text{J}$