Question

The length of a wire is a metre when the tension is 4N, Length is b metre when the tension is 5N, What is the length when the tension is 9N?

Answer 1

The length of a wire is a metre when the tension is 4N, Length is b metre when the tension is 5N, What is the length when the tension is 9N?

Solution

Using Hooks law:

$$4 = k * (a - l) ;$$ $$5 = k * (b - l) ;$$ $$9 = k * (c - l) ;$$

Where $l$ – initial length, $c$ – length when the tension is 9N, $k$ – elastic coefficient.

From (1) and (2) we will find initial length and elastic coefficient:

$$K = \frac{4}{(a - l)} ;$$ $$5 = \frac{4}{(a - l)} * (b - l);$$ $$5 * (a - l) = 4 * (b - l);$$ $$5 * a - 4 * b = l ;$$

Let's substitute (5) into (4):

$$K = \frac{4}{(a - 5 * a + 4 * b)} = \frac{1}{(b - a)} ;$$

Let's substitute (6) and (5) into (3):

$$9 = \frac{1}{(b - a)} * (c - 5 * a + 4 * b);$$ $$9 * b - 9 * a = c - 5 * a + 4 * b;$$ $$5 * b - 4 * a = c;$$

Answer: the length when the tension is 9N is $(5 * b - 4 * a)m$.