Question

What is the mass of a person in free fall with a weight (force) of 800 N?

Answer 1

`81.6` `"kg"`

Explanation:

I'll assume here the air resistance can be neglected (it usually can be unless otherwise stated).

The magnitude of the weight of an object is given by the equation

`w = mg`

where

• `m` is the mass of the object, in `"kg"`

• `g` is he acceleration due to gravity near earth's surface, `9.8` `"m/s"^2`

We know the person's weight is `color(red)(800` `color(red)("N"`, so let's solve this equation for the mass:

`m = w/g = (color(red)(800)color(white)(l)color(red)("N"))/(9.8color(white)(l)"m/s"^2) = color(blue)(81.6` `color(blue)("kg"`

Answer 2

`81.6` `"kg"`

Explanation:

`W = m g`

`Rightarrow 800` `"N" = m cdot 9.81` `"m s"^(- 2)`

`Rightarrow 800` `"kg" cdot "m s"^(- 2) = m cdot 9.81` `"m s"^(- 2)`

`Rightarrow frac(800 " kg" cdot "m s"^(- 2))(9.81 " m s"^(- 2)) = frac(m cdot 9.81 " m s"^(- 2))(9.81 " m s"^(- 2))`

`therefore m = 81.6` `"kg"`