Question

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A force has the dependence \(F_{x}(x)=-k x^{4}\) on the displacement \(x\) where the constant \(k=20.3 \mathrm{~N} / \mathrm{m}^{4}\). How much work does it take to change the displacement, working against the force, from \(0.730 \mathrm{~m}\) to \(1.35 \mathrm{~m}^{2}\)

Answer 1

THINK:

To determine the work done, integrate the force as function of with respective to the variable,

The limits for are:

RESEARCH:

The work done by a variable force, with change in the displacement from is given by

…… (1)

CALCULATE:

Given,

Force has the dependence on the displacement as

Here the constant

Change in the displacement from

The work done by the force is,

…… (2)

By substituting all the known values in the equation (2), we get

ROUND:

The required work done the force is,