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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Accepted Answer

Correct answer: 1. (1) 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: T=K(l-l_0) where l is the length of the string under tension and l_0 is the original length. When the tension is 5 N, the equation becomes: 5=K(1.4-l_0) When the tension increases to 7 N, the equation is: 7=K(1.56-l_0) By setting up a ratio from the two equations, we have: 51.4-l_0= 71.56-l_0 Solving this proportion gives us the original length l_0 : l_0=1 m Thus, the original length of the string is 1 meter.

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

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