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Question Number 184726 by yaslm last updated on 10/Jan/23

Answered by mr W last updated on 11/Jan/23

k(√(20))=6000  ⇒k=((6000)/( (√(20))))=((3000)/( (√5)))≈1342  R=∫_0 ^(20) k(√x)dx=((2k)/3)(20)^(3/2) =((2×20×6000)/3)=80 000 N  X^− =(1/R)∫_0 ^(20) kx(√x)dx=(1/R)×((2k)/5)(20)^(5/2) =((3×20)/5)=12 m

$${k}\sqrt{\mathrm{20}}=\mathrm{6000} \\ $$$$\Rightarrow{k}=\frac{\mathrm{6000}}{\:\sqrt{\mathrm{20}}}=\frac{\mathrm{3000}}{\:\sqrt{\mathrm{5}}}\approx\mathrm{1342} \\ $$$${R}=\int_{\mathrm{0}} ^{\mathrm{20}} {k}\sqrt{{x}}{dx}=\frac{\mathrm{2}{k}}{\mathrm{3}}\left(\mathrm{20}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} =\frac{\mathrm{2}×\mathrm{20}×\mathrm{6000}}{\mathrm{3}}=\mathrm{80}\:\mathrm{000}\:{N} \\ $$$$\overset{−} {{X}}=\frac{\mathrm{1}}{{R}}\int_{\mathrm{0}} ^{\mathrm{20}} {kx}\sqrt{{x}}{dx}=\frac{\mathrm{1}}{{R}}×\frac{\mathrm{2}{k}}{\mathrm{5}}\left(\mathrm{20}\right)^{\frac{\mathrm{5}}{\mathrm{2}}} =\frac{\mathrm{3}×\mathrm{20}}{\mathrm{5}}=\mathrm{12}\:{m} \\ $$

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