Question #322865

An example in the xy -plane. A force F=x^2yi+xy^2j acts on a body as it



moves between (0, 0) and (1, 1). Determine the work done when the path is along the line y=x.



Select one:



A. 1




B. 14




C. 13




D. 12


1
Expert's answer
2022-04-06T11:44:50-0400

(0,0)(1,1)Fdl=[y=xdl=(dx,dx)F=(x3,x3)Fdl=x3dx+x3dx=2x3dx]=012x3dx=2144=0.5Nocorrectvariant\int_{\left( 0,0 \right)}^{\left( 1,1 \right)}{Fdl}=\left[ \begin{array}{c} y=x\\ dl=\left( dx,dx \right)\\ F=\left( x^3,x^3 \right)\\ Fdl=x^3dx+x^3dx=2x^3dx\\\end{array} \right] =\int_0^1{2x^3dx}=2\cdot \frac{1^4}{4}=0.5\\No\,\,correct\,\,variant


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