Question

The force to pull a nonlinear spring is function of the stretched distance x (the displacement of the spring from its unstretched length) measured in meters. If F-292x3 + 30x2 (N) Find the work needed to compress the spring a distance of 0.55m.

Answer 1

Answer: work = 8.34 Nm

Hi! The work W done by a force F to move an object from a to b is defined as (in the one dimensional case):

`W = \int\limits^a_b {F}\, dx`

In this case

`F = 292x^3 + 30x^2`

`W = \int\limits^(0.55)_0 ({292x^3 + 30*x^2}) \, dx`

`W = (292)/(4) x^4 + (30)/(3) x^3 \Big|_(0)^(0.55) = 8.34`