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.

Hint:

In problems related to the elongation of strings due to tension, the relationship between tension and elongation is often linear, and the constant of proportionality (spring constant) can be used to find the original length.

Answer 1

Correct Answer: 1

\[ T = K(\ell - \ell_0) \] \[ \Rightarrow 5 = K(1.4 - \ell_0) \] \[ \Rightarrow 7 = K(1.56 - \ell_0) \] \[ \Rightarrow \frac{5}{1.4 - \ell_0} = \frac{7}{1.56 - \ell_0} \] \[ \therefore \ell_0 = 1 \, \text{m} \]