Question

1. A force of 2 N will stretch a rubber band 0.02 m. How far will a 4 N force stretch the band (assume Hooke's Law applies)? How much work does it take to stretch the band this far?

Answer 1

From hooke's law,

F = k*x

here, F = force,

k = spring constant

x = change in length

then, F1/F2 = x1/x2

given, F1 = 2 N, F2 = 4 N

x1 = 0.02 m

then, x2 = x1*F2/F1 = 0.02*4/2

x2 = 0.04 m

Now, work done to stretch the spring is given by,

$\\ W = \int F*dx = \int (k*x)*dx \\ \\ W = 0.5*k*x^2$

here, k = spring constant = F2/x2 = 4/0.04 = 100 N/m

x = stretch in rubber band = 0.04 m

then, W = 0.5*100*0.04^2

W = 0.08 J

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