Question

How much work does it take to raise a `6 kg` weight `72 m`?

Answer 1

`4320` Joules

Explanation:

The formula to know how much work is done is:-

Work `=` Force `×` Displacement `× cos theta color(blue)(rarr 1)`

Here in the mentioned problem, the object weighing `6kg` is raised to a height of `72 m`

Here, `6kg` is actually the mass of the object and `72kg` is the displacement.

`:. Mass = 6 kg`

and

`Displacement =72 m color(blue)(rarr 2)`

We will take acceleration due to gravity`(g)` to be `10 ms^-2`

The formula for Force is:-

Force`= Mass × g`

`:.`By plugging in values of `Mass` and `g`, we get

Force = `6×10`

Force =`60` Newtons `color(blue)( rarr 3)`

In this problem, we see that the force is also applied in the upward direction and the displacement is also in upward direction.
This implies, that the angle between force and displacement is `0^｡`
`:. theta = 0^｡ color(blue)(rarr 4)`

Plugging in the values of displacement, force and `theta` from `color(blue)(2,3,4)` respectively in `color(blue)(1)`.

Work`= 60×72× cos 0`

Work`= 4320×1`

Work`= 4320`

`:.` Work `= 4320` Joules

Answer 2

`4233.6 \ "J"`

Explanation:

We use the work equation, which states that,

`W=F*d`

• `F` is the force in newtons

• `d` is the distance in meters

Here, the force is the weight of the box.

Weight is defined by the equation,

`W=mg`

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

• `g` is the gravitational acceleration, which is around `9.8 \ "m/s"^2`.

So here, the weight is,

`6 \ "kg"*9.8 \ "m/s"^2=58.8 \ "N"`

Therefore, the work is,

`W=58.8 \ "N"*72 \ "m"`

`=4233.6 \ "J"`