For a rope obeying Hooke's law, show that the elastic potential energy stored in the rope is given by
\[ E = \frac{1}{2} k x^2 \]
where \( k \) is the elastic spring constant and \( x \) is the extension.
Answer (2)
The average force can be calculated as F/2, where
F = kx
Therefore, substituting this in to the equation for energy:
Energy = Force * Distance Energy = F/2 * x Energy = kx/2 * x Energy = 1/2 kx^2
The elastic potential energy stored in a rope obeying Hooke's law is expressed by the formula E = 2 1 k x 2 . This equation arises from calculating the work done to stretch the rope, where k represents the spring constant and x represents the extension. It reflects the linear relationship between force and extension as described by Hooke's law.
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