Question Number 184726 by yaslm last updated on 10/Jan/23
Answered by mr W last updated on 11/Jan/23
$${k}\sqrt{\mathrm{20}}=\mathrm{6000} \\ $$$$\Rightarrow{k}=\frac{\mathrm{6000}}{\:\sqrt{\mathrm{20}}}=\frac{\mathrm{3000}}{\:\sqrt{\mathrm{5}}}\approx\mathrm{1342} \\ $$$${R}=\int_{\mathrm{0}} ^{\mathrm{20}} {k}\sqrt{{x}}{dx}=\frac{\mathrm{2}{k}}{\mathrm{3}}\left(\mathrm{20}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} =\frac{\mathrm{2}×\mathrm{20}×\mathrm{6000}}{\mathrm{3}}=\mathrm{80}\:\mathrm{000}\:{N} \\ $$$$\overset{−} {{X}}=\frac{\mathrm{1}}{{R}}\int_{\mathrm{0}} ^{\mathrm{20}} {kx}\sqrt{{x}}{dx}=\frac{\mathrm{1}}{{R}}×\frac{\mathrm{2}{k}}{\mathrm{5}}\left(\mathrm{20}\right)^{\frac{\mathrm{5}}{\mathrm{2}}} =\frac{\mathrm{3}×\mathrm{20}}{\mathrm{5}}=\mathrm{12}\:{m} \\ $$