An elastic material of length 3m is to be stretched to reduce an extension three times its original length. Calculate the force required to produce the exte...
An elastic material of length 3m is to be stretched to reduce an extension three times its original length. Calculate the force required to produce the extension
Principle (Hooke's law). Within the elastic limit the applied force is directly proportional to the extension produced:
\[ F = K e \]
where \(K\) is the force constant of the elastic material and \(e\) is the extension.
Given data
Original length, \(L = 3\text{ m}\)
Force constant, \(K = 988.3\text{ N/m}\)
Extension is three times the original length: \(e = 3 \times L = 3 \times 3 = 9\text{ m}\)
Calculation
\[ F = K e = 988.3 \times 9 \]\[ F = 8894.7\text{ N} \]
The force required to produce the extension is \(8894.7\text{ N}\).