Rubber tends to be nonlinear as an elastic material. Suppose a particular rubber band exerts a restoring force given by Fx(x) = −Ax − Bx^2,
where the empirical constants are A = 10 N/m andB = 3.1 N/m2 so that
Fx is in newtons when x is in meters. Calculate the change in elastic potential energy of the rubber band when an external force stretches it from x = 0
to x = 0.18 m.
= J
If the force is
F(x) = −Ax − Bx^2
the work is
∫F(x) dx = -Ax^2 - B/3 x^3