Youre an engineer for a company that makes bungeejump cords

You\'re an engineer for a company that makes bungee-jump cords, and you\'re asked to develop a formula for the work involved in stretching cords to double their length. Your cords have force- distance relations described by F = - (kx + bx^2 + cx^3 + dx^4), where k, b, c, and d are constants, (a) Given a cord with un- stretched length L_0, what\'s your formula? (b) Evaluate the work done in doubling the stretch of a 10-m cord with k = 420 N/m, b = -86 N/m^2. c = 12 N/m^3 and d = -0.50 N/m^4.

Solution

a) For unstretched length L₀ , the stretching x can be considered as zero. Therefore the formula becomes,

   F = - {(k * 0) + (b * 0) + (c * 0) + (d * 0)}

Therefore F = 0

b) The actual length, L = 10m

    The length doubled while stretching. Therefore x = 10m

F = - {(420 * 10) + (-86 * 100) + (12 * 1000) + (-0.50 * 10000)}

F = - ( 4200 - 8600 + 12000 - 5000)

F = - 2600 N

The work done, W = F . S

since the stretching and restoring force are in opposite direction, W = FS cos 180

W = - FS = 2600 * 10 = 26000 J = 26 kJ