Question 217: Properties of Matter

Question

The length of a light string is 1.4 m when the tension on it is 5 N . If the tension increases to 7 N , the length of the string is 1.56 m . The original length of the string is__________m.

Accepted Answer

To find the original length of the string, we use the relationship between tension, elasticity constant ($ K $), and the change in length of the string.
Given the equation for tension:
$    \mathrm{T} = \mathrm{K}(\ell - \ell_0)    $
where $\ell$ is the length of the string under tension and $\ell_0$ is the original length.
When the tension is 5 N, the equation becomes:
$    5 = \mathrm{K}(1.4 - \ell_0)    $
When the tension increases to 7 N, the equation is:
$    7 = \mathrm{K}(1.56 - \ell_0)    $
By setting up a ratio from the two equations, we have:
$    \frac{5}{1.4 - \ell_0} = \frac{7}{1.56 - \ell_0}    $
Solving this proportion gives us the original length $ \ell_0 $:
$    \ell_0 = 1 \, \mathrm{m}    $
Thus, the original length of the string is 1 meter.

Properties of Matter

The length of a light string is 1.4 m when the tension on it is 5 N . If the tension increases to 7 N , the length of the string is 1.56 m . The original length of the string is__________m.

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