Question

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

Answer 1

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

Recall,

`"PE" = mgH`

`W=F*d*costheta` where `costheta = 1` in this case,

due to the assumption of "horizontal" acceleration.

We can then say, `W = Delta"PE"`, and assume we move the body of mass from a height of `0m`

Hence,

`W = mgH - 0`
`=> W = 31"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.

Answer 2

I get `9721.6 \ "J"`.

Explanation:

Well, work is defined through the equation,

`W=F*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=mg`

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

• `g` is the gravitational acceleration in `"m/s"^2`, on Earth it's around `9.8 \ "m/s"^2`.

And so, the weight here is `31 \ "kg"*9.8 \ "m/s"^2=303.8 \ "N"`.

Therefore, the work done is:

`W=303.8 \ "N"*32 \ "m"`

`=9721.6 \ "J"`