A spiral spring has a length of 14cm when a force of 4N is hung on it. A force of 6N extends the spring by 4cm. Calculate the unstretched length of the spri...
Question 1 Report
A spiral spring has a length of 14cm when a force of 4N is hung on it. A force of 6N extends the spring by 4cm. Calculate the unstretched length of the spring
Answer Details
Given: a load of 4 N makes the spring 14 cm long; a load of 6 N produces an extension of 4 cm. Let the unstretched (natural) length be \(L_0\) and the force constant be k.
By Hooke's law, extension is proportional to load, so the force constant is found from the second statement:
\[ k = \frac{F}{e} = \frac{6\ \text{N}}{4\ \text{cm}} = 1.5\ \text{N cm}^{-1} \]
Extension produced by the 4 N load:
\[ e_1 = \frac{F}{k} = \frac{4}{1.5} = 2.67\ \text{cm} \]
The length under the 4 N load is 14 cm, and this equals natural length plus extension:
\[ L_0 = 14 - e_1 = 14 - 2.67 = 11.33\ \text{cm} \]
The unstretched length of the spring is approximately 11.3 cm.
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