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

Answer:

$D = 0.42m$

Step-by-step 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;

$F\alpha \frac{1}{D^2}$

Convert proportion to equation

$F = \frac{k}{D^2}$

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

Make k the subject of formula

$F * D^2 = \frac{k}{D^2} * D^2$

$FD^2 = k$

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 $F = \frac{k}{D^2}$

Substitute $k = 0.13312$ and F = 0.74;

$0.74 = \frac{0.13312}{D^2}$

Multiply both sides by D²

$0.74 * D^2 = \frac{0.13312}{D^2} *D^2$

$0.74 * D^2 = 0.13312$

Divide both sides by 0.74

$\frac{0.74 * D^2}{0.74} = \frac{0.13312}{0.74}$

$D^2 = \frac{0.13312}{0.74}$

$D^2 = 0.17989189189$

Take square roots of both sides

$D = \sqrt{0.17989189189}$

$D = 0.42413664294$

$D = 0.42m$ (Approximated)