The force, F newtons (N) between two particles is inversely proportional to the square of the distance, d m, between them. When

Question

2 years ago

11

The force, F newtons (N) between two particles is inversely proportional to the square of the distance, d m, between them. When

the particles are 2m apart,
the force between them is 10 N. Find
1- the force between the particles when they are 5m apart,
2- the distance between the particles when the force between them is 25 N.

Mathematics

1 answer:

allsm [11] · Answer 1 · 2023-07-14T05:15:02+03:00

The force is 1.6N and the distance between them is 1.3 meters

<h3>The force between them</h3>

An inverse variation from force to the square of distance is represented s:

k = Fd^2

Where k represents the variation constant

When F = 10, d = 2.

So, we have:

k = 10 * 2^2

k = 40

Substitute k = 40 in k = Fd^2

Fd^2 = 40

When d = 5, we have:

F * 5^2 = 40

This gives

25F = 40

Divide by 25

F = 1.6

Hence, the force is 1.6N

<h3>The distance between them</h3>

In (a), we have:

Fd^2 = 40

When F = 25, we have:

25 * d^2 = 40

This gives

25d^2 = 40

Divide by 25

d^2 = 1.6

Take the square root of both sides

d = 1.3

Hence, the distance between them is 1.3 meters