Question

The force, F (Newtons), between two objects is inversely proportional to the square of the distance, d (metres), between them. The force is 0.052 Newtons when the distance between the objects is 1.6 metres. Work out d (rounded to 2 DP) when F = 0.74 Newtons.

Answer 1

`D = 0.42m`

Explanation:

Given

Force = 0.052 N when Distance = 1.6 m

Required

Find Force; when distance = 0.74 N

The question says force is inversely proportional to square of distance;

Let F represent Force and D represent Distance;

Mathematically;

`F\alpha (1)/(D^2)`

Convert proportion to equation

`F = (k)/(D^2)`

Where k is the proportionality constant; This means that k is always constant

Make k the subject of formula

`F * D^2 = (k)/(D^2) * D^2`

`FD^2 = k`

When F = 0.052 and D = 1.6; the value of k is as follows

`0.052 * 1.6^2 = k`

`0.13312 = k`

`k = 0.13312`

When F = 0.74;

Recall that k is always constant; so
`k = 0.13312`

To solve for D, we'll make use of
`F = (k)/(D^2)`

Substitute
`k = 0.13312` and F = 0.74;

`0.74 = (0.13312)/(D^2)`

Multiply both sides by D²

`0.74 * D^2 = (0.13312)/(D^2) *D^2`

`0.74 * D^2 = 0.13312`

Divide both sides by 0.74

`(0.74 * D^2)/(0.74) = (0.13312)/(0.74)`

`D^2 = (0.13312)/(0.74)`

`D^2 = 0.17989189189`

Take square roots of both sides

`D = √(0.17989189189)`

`D = 0.42413664294`

`D = 0.42m` (Approximated)