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A "stiff" spring has a force law given by F = – kx 3 . The work required to stretch the spring from the relaxed state x = 0 to the stretched length x = l is W0. In terms of W 0 , how much work is required to extend the spring from the stretched length 1 to the length 2l?

A "stiff" spring has a force law given by F = – kx3. The work required to stretch the spring from the relaxed state x = 0 to the stretched length x = l is W0. In terms of W0, how much work is required to extend the spring from the stretched length 1 to the length 2l?

Grade:upto college level

2 Answers

Navjyot Kalra
askIITians Faculty 654 Points
8 years ago
232-281_1.PNG
Hasan Naqvi
97 Points
8 years ago
F = – kx3
W = ∫F.dx
W= – ∫kx3.dx
= – kx4/4
Wo = -kl4/4
W in stretching from 0 to 2l= -16kl4/4 = 16 Wo
Work in stretching from l to 2l = 15Wo

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